ACCA F9 Workbook Lecture 1 Financial Strategy

ACCA F9 Workbook

Lecture 1 Financial Strategy

ACCA F9 Financial Management Full Course Workbook Solutions!

Shareholder Wealth - Illustration 1

Year Share Price Dividend Paid

2007 3.30 40c

2008 3.56 42c

2009 3.47 44c

2010 3.75 46c

2011 3.99 48c

There are 2 million shares in issue.! ! ! ! ! ! ! ! ! ! ! ! Calculate the increase in shareholder wealth for each year:II. Per shareIII. As a percentageIV. For the business as a whole

Solution

Year Share Price

Share Price Growth

Div Paid

Increase in

S’holder Wealth

As a Percentage

Total Shareholder

Return

2007 3.30 40c

2008 3.56 (3.56 - 3.30) = 26c 42c (26 + 42) = 68c

(68 / 330) = 20.6%

2m x 68c = $1.36m

2009 3.47 (3.47 - 3.56) = -9c 44c (-9 + 44) = 35c

(35 / 356) = 9.8%

2m x 35c = $0.70m

2010 3.75 (3.75 - 3.47) = 28c 46c (28 + 46) = 74c

(74 / 347) = 21.3%

2m x 74c = $1.48m

2011 3.99 (3.99 - 3.75) = 24c 48c (24 + 48) = 72c

(72 / 375) = 19.2%

2m x 72c = $1.44m


EPS - Illustration 2

2010$‘000

2011$‘000

PBIT 2000 2100

Interest 200 300

Tax 300 400

Profit After Tax 1500 1400

Preference Dividend 300 400

Dividend 800 900

Retained Earnings 400 100

Share Capital (50c) 5000 5000

Reserves 3000 3100

Share Price $2.50 $2.80

Calculate the EPS for 2010 and 2011.

Solution

2010 2011

Profit After Tax 1500 1400

Preference Dividend 300 400

Earnings 1200 1000

No. Ordinary Shares (5000 / 0.50) 10,000 10,000

EPS (Earnings / No. Ordinary Shares) 12c 10c


Test Your Knowledge

If you can’t answer all of the questions below without looking at the answer then you need to do some more work on this area!

Multiple Choice Questions

1. The 3 main areas of the business that Finance Managers plan are:

A. Investments, Financing & Profitability.B. Dividend Policy, Financing & Investments.C. Return on Capital, Investments, Profitability.D. Earnings per share, Profitability, Maximising shareholder wealth.

Answer B

2. Examples of 3 external stakeholders are:

A. Shareholders, Customers & Managers.B. Banks, Customers & Employees.C. Suppliers, Government & Customers.D. Unions, Suppliers & Investors.

Answer C

3. The Agency Relationship exists between:

A. Shareholders and Managers.B. Auditors and Managers.C. Shareholders and Stakeholders.D. Stakeholders and Managers.

Answer A

4. The Agency problem exists because...

A. Managers may be interested in maximising their own earnings.B. Shareholders have to rely on management to safeguard the assets of the business.C. Managers may be interested in short term gains over long term stability.D. All of the above.

Answer D


5. In order to maximise the wealth of shareholders, Finance Managers need to increase shareholder wealth. Shareholder wealth increases are made up of:

A. Profit for the year + Dividends Paid.B. Earnings per share + Dividends Per Share.C. Share Price + Dividends Paid.D. Share Price movement + Dividends Paid.

Answer D

6. ABC Co. Paid out a dividend of 35c last year and 42c this year per share. Their share price has increased from $4.33 to $5.24 in that time. What is the percentage shareholder return in the current year.

A. 20.00%B. 21.10%C. 30.72%D. 24.39%

Answer C

Increase in Share Price (4.33 to 5.24) = 91cDividend Paid this year =!42cReturn Per Share! ! ! =!133c

As a % of previous year Share Price (133/433) = 30.72%

7. The following information relates to ABC Co.

Year Share Price Dividend Paid

1 $4.50 82c

2 $4.71 84c

3 $3.85 86c

Which of the following statements is correct?

A. Between Year 1 and Year 2 shareholder wealth decreased.B. Between Year 2 and Year 3 shareholder wealth decreased.C. There was no increase in shareholder wealth between Year 2 and Year 3.D. None of the above.

Answer C


8. In order for dividends to be paid a company must have made profits in the current year.

Is this statement TRUE or FALSE?

Answer FALSE

9. Miller and Modigliani stated in their theory that dividends were ..........................

Answer Irrelevant

10. If a company does not pay dividends then the result will be

A. More tax will be paid.B. Less profit will be made.C. More cash is available for investments.D. More debt will be required.

Answer C

11. The ‘signaling effect’ refers to

A. A signal sent by managers to the auditors to inform them of the dividend.B. A signal sent by Auditors to inform shareholders of the dividend.C. The signal sent to the market by a company announcing their dividend for the year.D. A warning announcement that a firm will make less profit than expected.

Answer C

12. The ‘Bird in the hand’ argument refers to the fact that

A. Investors prefer a dividend now rather than later as there is a risk that the company could not pay a dividend at all.

B. Managers prefer not to pay a dividend as they can re-invest the cash saved into new investments.

C. The government want the company to pay their tax on time.D. The company has an ethical policy to look after any injured birds they might find.

Answer A


13. Which of the following best explains the ‘Clientele Effect’?

A. The clients of the company want as cheap prices as possible.B. The company should choose a dividend policy and stick to it to attract investors who

want that type of policy.C. The company should have a vote every year to ask investors what their dividend policy

should be for the year.D. The company should not pay a dividend.

Answer B

14. A company can reward investors through script dividends without paying out any cash.

Is the above statement TRUE or FALSE

Answer TRUE

15. A ‘script dividend’ is where a company:

A. Pays no dividend at all.B. Pays a dividend every other year.C. Pays a larger than average dividend.D. Pays a dividend in shares rather than cash.

Answer D

16. A ‘share buy back scheme’ refers to a situation where a company buys back it’s own shares from shareholders and then cancels those shares.

Is the above statement TRUE or FALSE?

Answer TRUE

17. A company may decide on a ‘Share-buy-back Scheme’ because

A. It doesn’t have enough cash to pay a dividend.B. It has large cash reserves and wants to reward shareholders.C. The government tells it that it has too many shares.D. It wants to receive cash to pay off some of it’s debt.

Answer B

18. A company may decide not to pay a dividend for which of the following reasons


A. It has retained losses rather than profits.B. It has several new investments it would like to make.C. It has low cash reserves.D. All of the above.

Answer D

19. Investors would like to see a company pay a steadily rising dividend growing at a rate in excess of inflation.

Is the above statement TRUE or FALSE?

Answer TRUE

20. Which of the following is an assumption of Miller and Modigliani’s dividend irrelevancy theory?

A. A company pays a steadily rising dividend that grows every year.B. Dividends and capital gains are taxed at the same rate.C. Investors are irrational.D. All share dealing transactions incur heavy costs.

Answer B


Short Form Questions

1. What are the 3 things that financial managers need to plan?

InvestmentsFinancingDividend Policy

2. What is Corporate Strategy?

Corporate strategy is the overall direction that a firm decides to take and covers such areas as expansion into new markets, penetration of existing markets or diversification into different business areas.

3. Describe the Agency Problem.

The managers of a firm act as the agents of the shareholders as they are the owners of the company.

The managers are interested in maximising their short term interests through pay and benefits, whereas the shareholders are interested in the long term stability and success of their investment.

As such, the goals of management are not the same as those of the shareholders, creating the agency problem.

4. What are the 3 main financial objectives of the financial manager?

Maximisation of shareholder wealth.Maximisation of profit.EPS growth.

5. How do you calculate the increase in shareholder wealth?

Share price growth + dividends paid (Learn this now if you didn’t know!).


6. How do you calculate EPS?

(Profit after tax - Preference dividends) / Number of ordinary shares.

7. Outline 2 potential dividend payment strategies.

Any 2 of:

Pay a constant dividend.Pay a constant proportion of earnings.Pay an inflation linked dividend.Pay whatever is left after making planned investments.

8. Why did Miller & Modigliani say that dividends were irrelevant?

M & M stated that whether the firm paid a dividend or chose to reinvest the money into the business the shareholders would get the same return.

This is because if a dividend is paid the shareholders get their return in the form of revenue. If the money is reinvested in the business this should lead to more profit and thus an increased share price which increases shareholder wealth by the same amount.

9. Outline the Clientele Effect.

A firm should choose a consistent dividend policy so that potential investors can choose their investment based on their preference for a return in the form of revenue or share price growth.

10. What is a script dividend?

A dividend paid in the form of more shares rather than cash.

If you’ve successfully answered all of the above questions then you’re ready to do the exam questions below:


December 2010 Q4 Part (d)June 2010 Q4 Part (c)

Now do it!

!


Lecture 2 Performance Measurement


Performance Analysis Illustration

X1 X2 X3

Non Current Assets 500 700 1000

Current Assets 150 200 300

650 900 1300

Ordinary Shares ($1) 300 300 300

Reserves 100 280 430

Loan Notes 150 200 300

Payables 100 120 270

650 900 1300

Revenue 3000 3500 4200

COS 2000 2400 3200

Gross Profit 1000 1100 1000

Admin Costs 300 350 400

Distribution Costs 200 250 300

PBIT 500 500 300

Interest 100 150 220

Tax 120 90 50

Profit After Tax 280 260 30

Dividends 100 110 30

Retained Earnings 180 150 0

Share Price $3.30 $4.00 $2.20


Using the information on the previous page calculate and comment on the following Ratios:

I. Return on Capital EmployedII. Return on EquityIII. Gross MarginIV. Net MarginV. Operating MarginVI. Revenue GrowthVII. GearingVIII. Interest CoverIX. Dividend CoverX. Dividend YieldXI. P/E Ratio


Solution

ROCE

X1 X2 X3

Equity + LT Liabilities

Shares 300 300 300


LT Loan Notes 150 200 300

Capital Employed 550 780 1030

Non Current Assets + Net Current Assets

Non Current Assets 500 700 1000

Net Current Assets (Current Assets - Current Liabilities)

(150 - 100) = 50 (200 - 120) = 80 (300 - 270) = 30


Total Assets - Current Liabilities

Total Assets 650 900 1300

Current Liabilities 100 120 270


PBIT 500 500 300

Return on Capital Employed

PBIT / Capital Employed

(500 / 550) = 90.91%

(500 / 780) = 64.10%

(300 / 1030) = 29.13%


X1 X2 X3

Return on Capital Employed (ROCE) 90.91% 64.10% 29.13%

In the first year the ROCE was 90.91%. At first glance this would appear to be a good return, however without industry averages or prior period information we are unable to tell if this is the case.In the first year the ROCE was 90.91%. At first glance this would appear to be a good return, however without industry averages or prior period information we are unable to tell if this is the case.In the first year the ROCE was 90.91%. At first glance this would appear to be a good return, however without industry averages or prior period information we are unable to tell if this is the case.In the first year the ROCE was 90.91%. At first glance this would appear to be a good return, however without industry averages or prior period information we are unable to tell if this is the case.

In year X2 the ROCE is 64.10%. This is a fall of 29.5% from the previous year indicating that the business in not able to make the same return on it’s assets that it has previously been able to do.In year X2 the ROCE is 64.10%. This is a fall of 29.5% from the previous year indicating that the business in not able to make the same return on it’s assets that it has previously been able to do.In year X2 the ROCE is 64.10%. This is a fall of 29.5% from the previous year indicating that the business in not able to make the same return on it’s assets that it has previously been able to do.In year X2 the ROCE is 64.10%. This is a fall of 29.5% from the previous year indicating that the business in not able to make the same return on it’s assets that it has previously been able to do.

In the year X3 the ROCE is 29.13%. This is a fall of 54.55% indicating that there may be some serious underlying problems which are affecting the ability of the business to generate the return on capital previously generated.




ROE

X1 X2 X3


Ordinary Shares 300 300 300


Total 400 580 730

Return on Equity (PAT / Ord Shares + Reserves)

(280 / 400) = 70%

(260 / 580) = 44.8%

(300 / 730) = 41%

In the first year the ROE was 70%. At first glance this would appear to be a good return, however without industry averages or prior period information we are unable to tell if this is the case.In the first year the ROE was 70%. At first glance this would appear to be a good return, however without industry averages or prior period information we are unable to tell if this is the case.In the first year the ROE was 70%. At first glance this would appear to be a good return, however without industry averages or prior period information we are unable to tell if this is the case.In the first year the ROE was 70%. At first glance this would appear to be a good return, however without industry averages or prior period information we are unable to tell if this is the case.

In year X2 the ROE is 44.8%. This is a fall of 36% from the previous year indicating that the business in not able to make the same return on the shareholders funds that it has previously been able to do.In year X2 the ROE is 44.8%. This is a fall of 36% from the previous year indicating that the business in not able to make the same return on the shareholders funds that it has previously been able to do.In year X2 the ROE is 44.8%. This is a fall of 36% from the previous year indicating that the business in not able to make the same return on the shareholders funds that it has previously been able to do.In year X2 the ROE is 44.8%. This is a fall of 36% from the previous year indicating that the business in not able to make the same return on the shareholders funds that it has previously been able to do.

In the year X3 the ROE is 41%. This is a fall of 8.4% indicating that the business may be having difficulty generating the returns it was able to do previously.In the year X3 the ROE is 41%. This is a fall of 8.4% indicating that the business may be having difficulty generating the returns it was able to do previously.In the year X3 the ROE is 41%. This is a fall of 8.4% indicating that the business may be having difficulty generating the returns it was able to do previously.In the year X3 the ROE is 41%. This is a fall of 8.4% indicating that the business may be having difficulty generating the returns it was able to do previously.


Margins

X1 X2 X3

Revenue 3000 3500 4200


PAT 280 260 30

PBIT 500 500 300

Gross Margin (Gross Profit / Revenue) (1000 / 3000) = 33.33%

(1100 / 3500) = 31.42%

(1000 / 4200) = 23.89%

Net Margin (PAT / Revenue) (280 / 3000) = 9.3%

(260 / 3500) = 7.4%

(30 / 4200) = 0.7%

Operating Margin (PBIT / Revenue) (500 / 3000) = 16.66%

(500 / 3500) = 14.28%

(300 / 4200) = 7.1%

The Gross Margin is 33.33% in X1 and holds reasonably steady in X2 at 31.42%. However in X3 the Gross Margin falls to 23.89% indicating that the business has either had to cut prices to sell the greater volume it has, or the cost of it’s purchases have gone up.




The Net Margin is 9.3% in X1 but begins to fall in X2 with 7.4% achieved, before falling dramatically to 0.7% in X3. The main reason for this is the fall in Gross Profit as other costs have risen in line with expectations given the increase in sales. However another point to note is that interest costs have risen with the increase in long term loans. The extra interest costs have put pressure on the business.




The Operating Margin dropped slightly in X2 to 14.28% from 16.66% the previous year - a fall of almost 15%. In X3 the Operating Margin fell away to 7.1%, a decrease of over 50%. This is due to the decreasing Gross Margin achieved as well as rises in the other expenses.





Gearing

X1 X2 X3

Debt 150 200 300

Equity Number of Shares

300 300 300

Share Price 3.30 4 2.20

Market Value (300 x 3.30) = 990

(300 x 4) = 1200

(300 x 2.20) = 660

Gearing (Debt / Equity) (150 / 990) = 15%

(200 / 1200) = 16.66%

(300 / 660) = 45.45%

Gearing levels in year X1 are 15%. Without industry averages or prior year data we are unable to assess this level although at first glance it does not seem excessive.Gearing levels in year X1 are 15%. Without industry averages or prior year data we are unable to assess this level although at first glance it does not seem excessive.Gearing levels in year X1 are 15%. Without industry averages or prior year data we are unable to assess this level although at first glance it does not seem excessive.Gearing levels in year X1 are 15%. Without industry averages or prior year data we are unable to assess this level although at first glance it does not seem excessive.Gearing levels in year X1 are 15%. Without industry averages or prior year data we are unable to assess this level although at first glance it does not seem excessive.

In year X2 gearing increases slightly to 16.66%, an increase of 11% from year X1. This is due to debt levels increasing to 200 from 150, although this is offset by the increase in the share price from $3.30 to $4.





In year X3 gearing increases dramatically to 45%, an increase of over 180%. This is due to debt levels rising to 300 from 200 and the share price dropping to $2.20 due to the deteriorating results of the business.






Interest Cover

X1 X2 X3

PBIT 500 500 300


Interest Cover (PBIT / Interest) (500 / 100) = 5 times

(500 / 150) = 3.33 times

(300 / 220) = 1.36 times

Interest coverage in year X1 is 5 times. Without industry averages or prior year data we are unable to assess this level although at first glance it does not seem unreasonable.Interest coverage in year X1 is 5 times. Without industry averages or prior year data we are unable to assess this level although at first glance it does not seem unreasonable.Interest coverage in year X1 is 5 times. Without industry averages or prior year data we are unable to assess this level although at first glance it does not seem unreasonable.Interest coverage in year X1 is 5 times. Without industry averages or prior year data we are unable to assess this level although at first glance it does not seem unreasonable.

In year X2 interest coverage falls to 3.33 times. This has occurred due to the interest charge increasing in the period while PBIT has remained constant.In year X2 interest coverage falls to 3.33 times. This has occurred due to the interest charge increasing in the period while PBIT has remained constant.In year X2 interest coverage falls to 3.33 times. This has occurred due to the interest charge increasing in the period while PBIT has remained constant.In year X2 interest coverage falls to 3.33 times. This has occurred due to the interest charge increasing in the period while PBIT has remained constant.

In year X3 interest coverage has decreased again to 1.36 times. This is caused by the PBIT achieved decreasing to 300 combined with the increase in the interest charge to 220. The increase in interest is caused by the increase in the long term debt of the company as shown by the gearing ratios calculated above.




Dividend Cover

X1 X2 X3

PAT 280 260 30


Dividend Cover (PAT / Dividends) (280 / 100) = 2.8 times

(260 / 110) = 2.36 times

(30 / 30) = 1 time

Dividend coverage in year X1 is 2.8 times. Without industry averages or prior year data we are unable to assess this level although at first glance it does not seem unreasonable.Dividend coverage in year X1 is 2.8 times. Without industry averages or prior year data we are unable to assess this level although at first glance it does not seem unreasonable.Dividend coverage in year X1 is 2.8 times. Without industry averages or prior year data we are unable to assess this level although at first glance it does not seem unreasonable.Dividend coverage in year X1 is 2.8 times. Without industry averages or prior year data we are unable to assess this level although at first glance it does not seem unreasonable.

In year X2 dividend coverage falls to 2.36 times. This would not concern investors as although coverage has gone down slightly, the dividend paid this year is greater than last.In year X2 dividend coverage falls to 2.36 times. This would not concern investors as although coverage has gone down slightly, the dividend paid this year is greater than last.In year X2 dividend coverage falls to 2.36 times. This would not concern investors as although coverage has gone down slightly, the dividend paid this year is greater than last.In year X2 dividend coverage falls to 2.36 times. This would not concern investors as although coverage has gone down slightly, the dividend paid this year is greater than last.

In year X3 dividend coverage has decreased to 1 time. This is caused by the decrease in profit achieved by the company restricting the level of dividend payable. This will be of concern to investors and their concern is reflected in the fall in the share price from $4 in year X2 to $2.20 in year X3.





Dividend Yield

X1 X2 X3

Number of Shares (300 / 1) 300 300 300


Dividends Per Share (100 / 300) = 33c (110 / 300) = 36c (30 / 300) = 10c

Dividend Yield (Dividends Per Share / Share Price)

(33 / 330) = 10% (36 / 400) = 9% (10 / 220) = 4.5%

The Dividend Yield is 10% in year X1. Whilst we do not have comparatives, this seems a reasonable return.The Dividend Yield is 10% in year X1. Whilst we do not have comparatives, this seems a reasonable return.The Dividend Yield is 10% in year X1. Whilst we do not have comparatives, this seems a reasonable return.The Dividend Yield is 10% in year X1. Whilst we do not have comparatives, this seems a reasonable return.

In year X2 the Dividend Yield falls to 9%. This will not be overly concerning to investors as the increase in share price over the year will have more than made up for the slightly lower yield.In year X2 the Dividend Yield falls to 9%. This will not be overly concerning to investors as the increase in share price over the year will have more than made up for the slightly lower yield.In year X2 the Dividend Yield falls to 9%. This will not be overly concerning to investors as the increase in share price over the year will have more than made up for the slightly lower yield.In year X2 the Dividend Yield falls to 9%. This will not be overly concerning to investors as the increase in share price over the year will have more than made up for the slightly lower yield.

In year X3 the Dividend Yield has fallen to 4.5% which is 50% lower than the previous year. This, combined with the fall in share price and reduced profitability will be a major concern to investors.In year X3 the Dividend Yield has fallen to 4.5% which is 50% lower than the previous year. This, combined with the fall in share price and reduced profitability will be a major concern to investors.In year X3 the Dividend Yield has fallen to 4.5% which is 50% lower than the previous year. This, combined with the fall in share price and reduced profitability will be a major concern to investors.In year X3 the Dividend Yield has fallen to 4.5% which is 50% lower than the previous year. This, combined with the fall in share price and reduced profitability will be a major concern to investors.

P/E Ratio

X1 X2 X3

Share Price $3.30 $4 $2.20


No. Ordinary Shares 300 300 300

EPS (280 / 300) = 93c (260 / 300) = 86c (30 / 300) = 10c

P/E Ratio (Share Price / EPS) (330 / 93) = 3.54 (400 / 86) = 4.65 (220 / 10) = 22

The P/E Ratio in year X1 is 3.54. We don not have industry comparatives or prior year information with which to compare this.The P/E Ratio in year X1 is 3.54. We don not have industry comparatives or prior year information with which to compare this.The P/E Ratio in year X1 is 3.54. We don not have industry comparatives or prior year information with which to compare this.The P/E Ratio in year X1 is 3.54. We don not have industry comparatives or prior year information with which to compare this.

In year X2 the P/E Ratio increases to 4.65. This indicates that the market expectations for this share have risen since X1 and that investors are now willing to pay 4.65 times what the business earns in a year to own the share.




In year X4 the P/E ratio has increased dramatically to 22. This is unusual as the earnings have decreased to 12% of the previous year. The share price has fallen to reflect this, but not by as much as would be expected. This may indicate that the market feels that the results in year X3 were perhaps a one-off and that next years results will improve.





Test Your Knowledge


1. In the ROCE calculation what are the 3 ways of calculating Capital Employed?

PBIT / Capital Employed

Equity + Long Term Liabilities.Non Current Assets + Net Current Assets.Total Assets - Current Liabilities.

2. What is the top line of the ROE calculation?

Profit after tax - Preference Dividends.

3. Why do we use PAT - Pref DIvs in the ROE calculation?

This is the distributable profits and thus the amount that the investors in the equity of the firm will be interested in.

4. What should we compare the ratios we calculate with?

The same company in prior years.Industry average.

5. What does gearing tell us?

The amount of financial risk that a firm is exposed to.

6. How do you calculate interest cover?

Profit before interest and tax / Interest


7. How do you calculate EPS?

(Profit after tax - Preference dividends) / Number of ordinary shares

8. What does the P/E Ratio tell us?

The number if times the current earnings that the market is currently willing to pay for the share.

If the P/E ratio is high it indicates that the market expects strong future earnings.

If the P/E ratio is low it indicates that the market expects weak future earnings.

9. How do you calculate dividend cover?

Profit after tax / dividends paid

10. What does dividend yield tell us?

The dividend paid as a proportion of the share price i.e. the amount of dividends that the share has yielded to investors.

If you’ve successfully answered all of the above questions then you’re ready to do the exam question below:

June 2009 Q4 (a)

Now do it!


Lecture 3 Finance Sources


Rights Issue - Illustration 1

XYZ Ltd. intends to raise capital via a rights issue.

The current share price is $8.

They are offering a 1 for 4 issue at a price of $6.

Calculate the Theoretical Ex-rights Price.

Solution

Number of Shares Share Price Total

4 $8 (4 x $8) = 32

1 $6 (1 x $6) = 6

5 38

We now have 5 shares in issue at total value of $38 so the THERP is (38 / 5) = $7.60We now have 5 shares in issue at total value of $38 so the THERP is (38 / 5) = $7.60We now have 5 shares in issue at total value of $38 so the THERP is (38 / 5) = $7.60


Rights Issue - Illustration 2

ABC Ltd. has decided to raise capital via a rights issue.

The share price is currently $5.50 and ABC intends to raise $5m.

There are currently 6.25m shares in issue and ABC is offering a 1 for 5 rights issue.

Calculate the Theoretical Ex-Rights Price.

Solution

Amount of Capital to raiseAmount of Capital to raise $5m

No. of shares issued (6.25m / 5)No. of shares issued (6.25m / 5) 1.25m

Share issue price ($5m / 1.25m)Share issue price ($5m / 1.25m) $4


5 $5.50 (5 x 5.50) = 27.5

1 $4 (1 x 4) = 4

6 31.5

We now have 6 shares in issue at total value of $31.5 so the THERP is (31.5 / 6) = $5.25We now have 6 shares in issue at total value of $31.5 so the THERP is (31.5 / 6) = $5.25We now have 6 shares in issue at total value of $31.5 so the THERP is (31.5 / 6) = $5.25


Test Your Knowledge

If you can’t answer all of the questions below without looking at the answer then you need to do some more work on this area!Multiple Choice Questions

1. Which of the following is NOT something a company will consider when choosing a source of finance?

A. The cost of the finance to the firm.B. The number of employees in the firm.C. Any security that will need to be used.D. Current and future gearing levels.

Answer B

2. What is NOT a function of the stock market?

A. To enable companies to raise capital.B. To enable individuals to sell shares in a company.C. To facilitate transactions between buyers and sellers.D. To increase the cost of equity of listed companies.

Answer D

3. Which of the following are advantages to a company of being listed on the stock exchange?

1. It will lead to a better perception of the firm by potential investors.2. It will be more difficult for the firm to raise capital.3. Listing may well lower the cost of equity of the firm as investors will see it as a safer

investment and thus accept a lower return.4. The company may be required to disclose more information about it’s operations.

A. 1 and 2B. 2 and 3C. 2 and 4D. 1 and 3

Answer D


4. Which of the following are disadvantages to a company of being listed on the stock exchange?

1. It is expensive to become listed.2. There are ongoing costs of listing compliance.3. Control by the current owners will be increased.4. Listing may well lower the cost of equity of the firm as investors will see it as a safer

investment and thus accept a lower return.


Answer A

5. A company has 10m shares in issue at a share price of $7 and undertakes a rights issue of 1 for 5 to raise $12m. What is the Theoretical ex-rights price?

A. $6.17B. $6.83C. $6.00D. $6.44

Answer B


No. of shares issued (10m / 5)No. of shares issued (10m / 5) 2m

Share issue price ($12m / 2m)Share issue price ($12m / 2m) $6


10m $7 $70m

2m $6 $12m

12m $82m

We now have 12m shares in issue at total value of $82m so the THERP is ($82m / 12) = $6.83We now have 12m shares in issue at total value of $82m so the THERP is ($82m / 12) = $6.83We now have 12m shares in issue at total value of $82m so the THERP is ($82m / 12) = $6.83


6. Which of the following best describes an IPO?

A. All of the new Shares being issued to one large institutional investor. B. An offering of new shares to all investors in the market to enable them to purchase

them if they wish.C. Offering shares to current shareholders in the same proportion as they currently own

them.D. An issue to current shareholders of shares instead of dividends.

Answer B

7. Which of the following are disadvantages of an IPO?

i) It can be very expensive.ii) It may need to be underwritten to ensure the shares are taken up.iii)The company will need to to deal with one large institutional investor only.iv)The share price achieved for the issue may not be as high as expected.

A. i) iii) and iv) onlyB. i) ii) and iv) onlyC. All of the aboveD. i) ii) and iii) only

Answer B

8. Which of the following best describes a placing as a means of issuing shares?

A. All of the new Shares being issued to one large institutional investor. B. An offering of new shares to all investors in the market to enable them to purchase

them if they wish.C. Offering shares to current shareholders in the same proportion as they currently own

them.D. An issue to current shareholders of shares instead of dividends.

Answer A

9. Who demands covenants to be placed on debt?

A. ShareholdersB. BanksC. The marketD. The government

Answer B


10. Which of the following is NOT a function of the treasury department in a company?

A. To set and achieve the financial objectives of the firm.B. To manage the liquidity of the firm.C. To prepare the financial statements of the firm.D. To manage any currency risk that the firm may be exposed to.

Answer C



1. What 5 things will a company consider when choosing a source of finance?

The cost of the finance to the firm.The length of time the firm needs the finance for.Any security that will need to be used.Current and future gearing levels.The availability of the finance to the firm.

2. What is the primary function of the stock market?

To enable firms to raise capital and investors to buy equity.

3. What are the advantages to the company of being listed?

It will lead to a better perception of the firm by potential investors.It will be easier for the firm to raise capital.It may well lower the cost of equity of the firm as investors will see it as a safer investment and thus accept a lower return.

4. Are there any disadvantages of being listed?

It is expensive to become listed.There are ongoing costs of listing compliance.Control by the current owners will be diluted.It opens the firm up to a lot of public scrutiny - not all of it fair and balanced.


5. A company has 10m shares in issue at a share price of $7 and undertakes a rights issue of 1 for 5 to raise $12m. What is the Theoretical ex-rights price?


No. of shares issued (10m / 5)No. of shares issued (10m / 5) 2m

Share issue price ($12m / 2m)Share issue price ($12m / 2m) $6


10m $7 $70m

2m $6 $12m

12m $82m

We now have 12m shares in issue at total value of $82m so the THERP is ($82m / 12) = $6.83We now have 12m shares in issue at total value of $82m so the THERP is ($82m / 12) = $6.83We now have 12m shares in issue at total value of $82m so the THERP is ($82m / 12) = $6.83

6. What is an IPO?

An Initial Public Offering of shares to investors as a method of raising capital.

7. What are the disadvantages of an IPO?

It can be very expensive (Legal fees, listing fees, compliance costs, advertising costs, corporate governance requirements, underwriting costs).It may need to be underwritten to ensure the shares are taken up.The share price achieved for the issue may not be as high as expected.

8. What is a placing?

A placing of a new issue of shares with institutional investors such as insurance companies or pension funds.

9. Who demands covenants to be placed on debt?

The bank who offers the finance.


10. What is the function of the treasury department in a company?

To set and achieve the financial objectives of the firm.To manage the liquidity of the firm.To determine the funding requirements of the firm.To manage any currency risk that the firm may be exposed to.


June 2009 Q4 (b) & (c)

Now do it!


Lecture 4 Economic

Environment


Test Your Knowledge


1. Which of the following is not a target of government economic policy?

A. Full employment.B. Price stability.C. High, stable growth.D. Low consumer prices.

Answer D

2. Which of the following are examples of cost-push inflation.

1. Wage increases.2. Rising cost of commodities.3. Sales tax decreases.4. High demand in the economy


Answer A

3. Fiscal policy can be described as tax revenues raised by the government and spent on services and subsidies for the public.

Is this statement

A. TRUEB. FALSE


4. An increase in interest rates is likely to lead to which of the following:

1. Higher cost of borrowing for companies.2. More consumer demand in the economy.3. More sales for many companies.4. Less consumer demand in the economy


Answer D

5. Which of the following might cause policy makers to decide to decrease interest rates?

1. Excessive consumer demand in the economy.2. Reduced consumer demand in the economy.3. Concerns that growth in the economy may be low.4. Expectations that the economy will grow strongly.


Answer B

6. Money markets could be best described as:

A. A market for newly printed notes and coins.B. A market for the trade of foreign currency.C. A market for the trade of commodities such as oil and wheat.D. A market to enable banks to borrow and lend to each other.

Answer D

7. How can financial intermediaries help to make the market more efficient?

A. By buying commodities from sellers and trading them on the commodities exchange.B. By providing insurance on transactions for buyers and sellers.C. By providing finance to enable transactions to take place.D. By selling foreign currency on the currencies exchange.

Answer C



1. What are the 4 targets of economic policy?

Full employment.Price stability.High, stable growth.Balance of payments.

2. Name 2 examples of cost-push inflation.

Wage increases.Rising cost of commodities.Sales tax increases.

3. What is fiscal policy?

Tax revenues raised by government and spent on services and subsidies.

4. How is an increase in interest rates likely to effect the economy?

An increase in interest rates will increase the cost of financing to individuals and companies in the economy. This will decrease demand for goods as consumers will have less money to spend on goods because they are spending more money on the increased cost of financing (mortgages, credit cards etc.).

5. When might policy makers decide to decrease interest rates?

When excessive consumer demand is causing inflation interest rates may be raised to decrease demand.

6. What are the money markets?

Banks borrow and lend to each other in the money markets.


7. How can financial intermediaries help to make the market more efficient?

Financial intermediaries enable the transaction between buyers and sellers by providing finance to the buyers e.g. Banks & finance houses.

8. Name 5 types of securities?

Treasury bills.Long term government bonds.Corporate bonds.Preference shares.Ordinary shares.


Now do it!


Lecture 5 Working Capital


Working Capital Illustration

Balance Sheet

$‘000

ASSETS

Non Current Assets 1000

Inventory 300

Receivables 200

Cash 300

1800

LIABILITIES

Ordinary Shares 800

Reserves 200

Long term Liabilities 700

Payables 100

Overdraft -

1800

Income Statement

$‘000

Revenue 1000

COS 800

Gross Profit 200

Other Costs 100

Net Profit 100

Other Information:

All sales are made on credit.

Required:

Calculate the Cash Operating Cycle for Inter Ltd.


Solution

Item Working Days

Inventory Period 300/800 x 365 137

Collection Period 200/1000 x 365 73

Less:

Payables Period 100/800 x 365 46

164

Working Capital Illustration Part II

Show the journal entries and calculate the Revised Balance sheet if the operating cycle changes to:

Item Days

Inventory Period 200

Collection Period 100

Less:

Payables Period 30

270


Solution

Item New Days Old Days Old Balance

Working New Balance

Movem’t

Inventory 200 137 300 300 x 200/137

438 138

Receivables

100 73 200 200 x 100/73

274 74

Less:

Payables 30 46 100 100 x 30/46

65 -35

270 164

Entries Dr Cr

Dr Inventory 138

Cr Cash 138

Dr Receivables 74

Cr Cash 74

Dr Payables 35

Cr Cash 35


Revised Balance Sheet

$‘000 Movement $‘000

ASSETS

Non Current Assets 1000 1000

Inventory 300 138 438

Receivables 200 74 274

Cash 300 -247 53

1800 1765

LIABILITIES

Ordinary Shares 800 800

Reserves 200 200

Long term Liabilities 700 700

Payables 100 -35 65

Overdraft 0 0

1800 1765


Working Capital Illustration Part III

Show the journal entries and calculate the Revised Balance sheet if the operating cycle changes to:

Item Days

Inventory Period 90

Collection Period 30

Less:

Payables Period 60

60

Solution

Item New Days Old Days Old Balance

Working New Balance

Movem’t

Inventory 90 200 438 438 x 90/200

197 -241

Receivables

30 100 274 274 x 30/100

82 -192

Less:

Payables 60 30 65 65 x 60/30 130 65

60 270


Entries Dr Cr

Dr Cash 241

Cr Inventory 241

Dr Cash 192

Cr Receivables 192

Dr Cash 65

Cr Payables 65

498 498

Revised Balance Sheet

$‘000 Movement $‘000

ASSETS

Non Current Assets 1000 1000

Inventory 438 -241 197

Receivables 274 -192 82

Cash 53 498 551

1765 1830

LIABILITIES

Ordinary Shares 800 800

Reserves 200 200

Long term Liabilities 700 700

Payables 65 65 130

Overdraft 0 0

1765 1830


Test Your Knowledge


1. Which of the following are components of working capital within the financial statements:

1. Non Current Assets.2. Inventory.3. Payables.4. Intangible Assets.


Answer B

2. Which of the following are indicators of overtrading.

i) Reliance on long term finance.ii) Offering lax credit terms.iii) Build up of inventory.iv) Rapidly decreasing sales.v) Deteriorating Current ratio.

A. i) iii) and iv) onlyB. ii) iii) and v) onlyC. All of the aboveD. i) ii) and iii) only

Answer B


3. The following information has been calculated for A Co:

Trade receivables collection period 52 daysRaw material inventory turnover period 42 daysWork in progress inventory turnover period 30 daysTrade payables payment period 66 daysFinished goods inventory turnover period 45 days

What is the length of the working capital cycle?

A 103 days B 131 days C 235 days D 31 days

Answer A

4. If inventory days go up from 100 to 150 the company will need to invest more cash in the business.

Is this statement:

A. TRUEB. FALSE

Answer A

5. Which of the following statements concerning working capital management are correct?

1 The twin objectives of working capital management are profitability and liquidity 2 A conservative approach to working capital investment will increase profitability 3 Working capital management is a key factor in a company’s long-term success

A 1 and 2 only B 1 and 3 only C 2 and 3 only D 1, 2 and 3

Answer B



1 The twin objectives of working capital management are profitability and liquidity 2 A aggressive approach to working capital investment will increase profitability 3 Working capital management is not a key factor in a company’s long-term success


Answer A


1 The twin objectives of working capital management are profitability and liquidity 2 A moderate approach to working capital investment will increase profitability 3 An aggressive approach to working capital investment uses more long term finance than short term.


Answer B


1 A conservative approach to working capital investment employs uses long term finance to finance some fluctuating current assets.2 An aggressive approach to working capital investment will increase profitability 3 Working capital management has no effect on profitability of the company.


Answer A



1. What are the components of working capital?

Current Assets (Inventory, Receivables, Cash)Current Liabilities (Payables)

2. State 6 indicators of overtrading.

Reliance on short term finance.Offering lax credit terms.Build up of inventory.Rapidly expanding sales.Deteriorating Current ratio.Deteriorating Quick Ratio.

3. What is the Quick Ratio and what does it tell us?

(Current Assets - Inventory) / Current Liabilities

4. How do we calculate the cash operating cycle?

Inventory Period + Receivables Period - Payables Period

5. If my inventory days go up from 100 to 150 will I need to invest more or less cash in the business?

More cash as cash is being tied up in inventory.

6. What are permanent current assets?

The level of inventory, receivables and cash that are required to support the day to day running of the business.

7. What are fluctuating current assets?

The levels of inventory, receivables and cash that are required to support seasonal fluctuations in business operations.


8. What is the matching principle?

Matching short term assets with short term finance and long term assets with long term finance.

9. What are the advantages of an aggressive working capital financing policy?

It will lead to more profit as financing short term finance is cheaper.It is more efficient.

10. What are the advantages of a conservative working capital financing policy?

There is less chance of the firm running out of cash i.e. less liquidity risk.The firm is able to meet sales demand changes.By offering more credit the firm may well increase sales.


June 2009 Q3 (a) & (b)

Now do it!


Lecture 6 Managing

Receivables


Receivables - Illustration 1

Credit sales: 1200

3 month credit terms

Overdraft rate = 10%

New Policy

2% discount if paid in less than 10 days

2 month terms for everyone else.

20% will take the discount

Solution

Method = Compare the savings through reducing receivables by offering the discount to the profit lost by doing so.




Working

Receivables BeforeReceivables Before 1200 x 3/12 300

Receivables After 20% who take discount

(1200 x 10/365) x 20%

7

Everyone else (1200 x 2/12) x 80% 160

167

Saving = (Reduction in receivables x Overdraft rate)Saving = (Reduction in receivables x Overdraft rate)

(300 - 167) x 10% 13

Lost Profit = Amount of DiscountLost Profit = Amount of Discount (1200 x 20%) x 2% 4.8

The saving made is greater than the profit lost so the discount should be offeredThe saving made is greater than the profit lost so the discount should be offeredThe saving made is greater than the profit lost so the discount should be offeredThe saving made is greater than the profit lost so the discount should be offered


Receivables - Illustration 2

Receivables are currently $4,600,000. Sales are $37,400,000

A factor has offered to take over the administration of trade receivables on a non-recourse basis for an annual fee of 3% of credit sales. The factor will maintain a trade receivables collection period of 30 days and Gorwa Co will save $100,000 per year in administration costs and $350,000 per year in bad debts. A condition of the factoring agreement is that the factor would advance 80% of the face value of receivables at an annual interest rate of 7%. The current overdraft rate is 5%

Difference on ReceivablesDifference on ReceivablesDifference on Receivables

Current Receivables 4,600,000

Receivables Under Factor 37,400,000 x (30 / 365) 3,073,973

Difference 1,526,027

Benefits & Costs of FactorBenefits & Costs of FactorBenefits & Costs of Factor

Benefits of Using FactorBenefits of Using Factor

Reduced Overdraft Interest 1,526,027 x 0.05 76,301

Admin Cost Savings 100,000

Bad Debt Savings 350,000

Total BenefitsTotal Benefits 526,301

Costs Of Using FactorCosts Of Using Factor

Annual Fee 37,400,000 x 0.03 1,122,000

Extra Interest Cost 3,073,973 x 80% x (7% - 5%) 49,184

Total CostsTotal Costs 1,171,184

Total Benefits Less Total Costs -644,883


Test Your Knowledge



1. How can a company assess the credit worthiness of their customers?

1. Get trade references from other suppliers or from banks.2. Use a credit rating agency. 3. Offer initial high levels of credit.4. Ask for a written promise to pay.


Answer A

2. Which of the following are benefits of a company offering a discount to customers for early payment of invoices?

1. Better liquidity for the firm.2. Less interest as less or no overdraft will be required.3. Risk of more bad debt as customers take longer to pay.4. Loss of customers who don’t take advantage of the discount.


Answer A


3. The management of XYZ Co has annual credit sales of $20 million and accounts receivable of $4 million. Working capital is financed by an overdraft at 12% interest per year. Assume 365 days in a year.

What is the annual finance cost saving if the management reduces the collection period to 60 days?

A $85,479 B $394,521 C $78,904 D $68,384

Answer A

4. Which of the following are disadvantages of debt factoring for a company?

1. It can be expensive.2. It creates a bad impression with customers because the debt is collected by the factor.3. It can increase the liquidity of the company.4. It can lose the goodwill of customers.


Answer D

5. Which of the following statements relate to invoice discounting through a factor?

1. The company retains the risk of bad debt.2. The factor collects the debt.3. The factor advances a percentage of the invoice value to the company.4. Invoice discounting can be used by any company.


Answer B



1. How can a company assess the credit worthiness of their customers?

Get trade references from other suppliers or from banks.Use a credit rating agency.Offer initial low levels of credit.Maintain and review a file on the customer.Maintain an internal credit rating system.

2. Outline 3 ways of maintaining good credit control.

Any 3 of:

Maintain an aged debtors listing.Identify overdue accounts on a timely basis.Send regular statements to customers.Outline a clear policy to customers.

3. What are the benefits of offering a discount to customers?

Better liquidity for the firm.Less interest as less or no overdraft will be required.Less bad debt as customers pay early.New customers as they take advantage of the discount.

4. How do you decide whether to offer a discount or not?

Assess the saving through early payment (Change in receivables x Overdraft interest)Compared to the cost of the discount.

5. What is debt factoring?

A factor (usually a bank) buys the debt of the company for a percentage of the invoice amount. The factor will charge a fee for the service and will charge interest on any amounts outstanding until the money is collected.

6. What are the disadvantages of factoring for a company?

It can be expensive.It creates a bad impression with customers because the debt is collected by the factor.It can lose the goodwill of customers.


7. What is invoice discounting?

A factor forwards the company money secured against the debt ledger of the business but it is still collected by the business.

8. How can a company seek to ensure that foreign receivables are collected?

Agree early payment.Bills of exchange.Letters of credit.References & credit checks.Insurance.Export factor.


Now do it!


Lecture 7 Inventory

Management


EOQ - Illustration 1

Demand of 1200 units per month.

Cost of making an order of $12.

Cost of one unit $10.

Holding cost per year of 10% of the purchase price of the goods.

Calculate the EOQ & check that it is correct.

Solution

Working

Annual Demand 1200 x 12 14,400

Holding Cost $10 x 10% 1

Ordering Cost 12

EOQ √(2 x 12 x 14,400) / 1 588

Test

Ordering Costs (Cost Per order x (Demand / EOQ))

12 x (14,400 / 588) 294

Holding Costs (Cost Per Unit x (EOQ / 2)) 1 x (588 / 2) 294


Buffer Stock - Illustration 2

Company orders when the level of stock reaches 50,000

It takes 4 weeks to receive new stock from the time of ordering.

The company uses 7,500 units on average per week.

Calculate the buffer stock.

Solution

Buffer Stock = Re-order level less usage in lead timeBuffer Stock = Re-order level less usage in lead time

Re-order level 50,000

Lead Time 4 weeks

Usage per week 7,500

50,000 - (4 x 7,500) 20,000


EOQ With Buffer Stock - Illustration 3

Dec 07 Exam Question

The current policy is to order 100,000 units when the inventory level falls to 35,000 units. Forecast demand to meet production requirements during the next year is 625,000 units. The cost of placing and processing an order is €250, while the cost of holding a unit in stores is €0·50 per unit per year. Both costs are expected to be constant during the next year. Orders are received two weeks after being placed with the supplier. You should assume a 50-week year and that demand is constant throughout the year.

Calculate EOQ with buffer stock

Solution

Working

Buffer Stock (Re-order level - (Lead time x amount used per week))

35,000 - (2 weeks x 625,000/50)

10,000

EOQ ignoring buffer stock √ (2 x 250 x 625,000 / 0.5)

25,000

Total cost Calculations

Order Costs (Cost per order x No. Orders) 250 x (625,000/25,000)

6,250

Holding Costs (Holding cost p/unit x Average Stock)

0.5 x (25,000 / 2) 6,250

Holding Cost for Buffer (Holding cost p/unit x Buffer Stock)

0.5 x 10,000 5,000

Total Costs 17,500


EOQ with discounts - Illustration 4

Demand is 1000 units per month.

Purchase cost per unit £11.

Order cost £30

Holding cost 10% p.a. of stock value.

Required

Calculate the minimum total cost with a discount of 1% given on orders of 1500 and over

Solution

EOQ with DiscountsEOQ with DiscountsEOQ with Discounts

1) Calculate EOQ in normal way (and the costs)1) Calculate EOQ in normal way (and the costs)1) Calculate EOQ in normal way (and the costs)

2) Calculate costs at the lower level of each discount above the EOQ2) Calculate costs at the lower level of each discount above the EOQ2) Calculate costs at the lower level of each discount above the EOQ

Working

EOQ √ (2 x 30 x 12,000 / 1.1) 809


Order Costs (Cost per order x No. Orders)

30 x (12,000 / 809) 445


1.1 x (809/2) 445

Cost of Purchases 12,000 x 11 132,000

Total Costs 132,890

If 1500 are ordered to take the discount:


Order Costs (Cost per order x No. Orders)

30 x (12,000 / 1500) 240


(1.1 x 99%) x (1500/2) 817

Cost of Purchases 12,000 x (11 x 99%) 130,608

Total Costs 131,665


Test Your Knowledge


1. Which of the following types of cost we are seeking to minimise by using the Economic Order Quantity?

A. Holding costs and inventory movement costsB. Ordering costs and holding costsC. Ordering costs and insurance costsD. Holding costs and security costs

Answer B

2. If a company uses the Economic Order Quantity as the level at which to order, how will they calculate total ordering costs for the year?

A. Cost per order x (Annual Demand / EOQ)B. Annual Demand x (Cost per order /EOQ)C. (EOQ / Cost per order) x Holding costsD. Annual demand x EOQ

Answer A

3. ABC Co. sells widgets and expects annual demand of 3.4m units. The cost of making an order is $49.71 and the cost of holding one unit for one year is $0.50.

What is the total ordering costs per year:

A. $5,687.34B. $6,413.81C. $6,500.54D. $6,430.32

Answer C


3. ABC Co. sells widgets and expects annual demand of 1.2m units. The cost of making an order is $25.21 and the cost of holding one unit for one year is $0.50.

What is the total holding costs per year:

A. $2,850B. $3,750C. $2,450D. $2,750

Answer D

4. Layla Co. sells 200m wigs in a year with each order taking 15 days to be delivered once made. They make an order every time their stock levels reach 10m wigs.

What is the buffer stock level for Layla Co.

A. 1,780,822B. 6,666,666C. 9,333,333D. 2,345,632

Answer A

5. Which of the following are drawbacks of a company using the Economic Order Quantity method of stock management?

1. Assumes constant ordering costs.2. Assumes constant demand.3. Assumes known annual demand.4. Assumes no buffer stock or lead time.

A 1, 2 and 4 only B 1 and 3 only C All of the aboveD 1, 2 and 3

Answer C


6. Stavros Co’s current inventory policy is to order 60,000 units when the inventory level falls to 55,000 units. Forecast demand to meet production requirements during the next year is 800,000 units. The cost of placing and processing an order is $90, while the cost of holding a unit in stores is $1 per unit per year. Both costs are expected to be constant during the next year. Orders are received three weeks after being placed with the supplier. You should assume a 50-week year and that demand is constant throughout the year.

What is the total cost of ordering at the EOQ level?

A. $12,000B. $6,000C. $7,000D. $19,000

Answer D

Solution

Working

Buffer Stock (Re-order level - (Lead time x amount used per week))

15,000 - (3 weeks x 800,000/50)

7,000

EOQ ignoring buffer stock √ (2 x 90 x 800,000 / 1)

12,000


Order Costs (Cost per order x No. Orders) 90 x (800,000/12,000) 6,000


1 x (12,000 / 2) 6,000

Holding Cost for Buffer (Holding cost p/unit x Buffer Stock)

1 x 7,000 7,000

Total Costs 19,000



1. What are the two types of cost we are seeking to minimise?

Ordering costs.Holding costs.

2. How do we calculate total ordering costs for the year?

Cost per order x Number of orders (Annual Demand / EOQ)

3. How do we calculate total holding costs for the year?

Holding cost per unit x Average stock held (EOQ / 2)

4. How do we calculate the buffer stock?

Re-order level - usage in lead time

5. What are the problems with the EOQ method?

Assumes constant ordering costs.Assumes constant demand.Assumes known annual demand.Assumes no bulk discounts.Assumes no buffer stock or lead time.

6. What are the steps in calculating the total costs when there is a buffer stock?

Calculate the EOQ ignoring the buffer stock.Calculate the buffer stock.Add the holding cost for the buffer.

8. Why might we not use the EOQ when there are bulk discounts available?

The saving on the discount may mean that it is cost beneficial to order at that level.



June 2009 Q3 (d)December 2010 Q3 (a)

Now do it!


Lecture 8 Cash Management


Baumol Cash Model - Illustration 1

A business expects to move 500,000 from it’s interest bearing account into cash over the course of one year.

The interest rate is 7% and the cost of making a transfer is $250.

How much should the business transfer into cash each time it makes a transfer?

Solution

Working

Annual Disbursements $500,000

Interest Rate 7%

Cost of making a transfer $250

Amount to transfer √(2 x 250 x 500,000) / 0.07

$59,761



Using the information in illustration 1 calculate the total cost to the business each year of their cash management policy.

Solution

Working

Holding Cost (Ave Cash Balance x Interest Rate)

($59761 / 2) x 0.07 2091

Trading Cost (Cost of Transfer x No. Transfers)

$250 x (500,000 / 59,761)

2091

Total Cost 4182



Subsonic Speaker Systems (SSS) has annual transactions of $9 million.

The fixed cost of converting securities into cash is $264.50 per conversion.

The annual opportunity cost of funds is 9%.

What is the optimal deposit size?

Solution

Working

Annual Disbursements $9,000,000

Interest Rate 9%

Cost of making a transfer $264.50

Amount to transfer √(2 x 264.5 x 9,000,000) / 0.09)

230,000

Working


(230,000 / 2) x 0.09 10,350


$264.50 x (9,000,000 / 230,000)

10,350

Total Cost 20,700


Miller-Orr Model - Illustration 4

If a company must maintain a minimum cash balance of £8,000, and the variance of its daily cash flows is £4m (ie std deviation £2,000). The cost of buying/ selling securities is £50 & the daily interest rate is 0.025 %.

Calculate the spread, the upper limit & the return point.

Solution

Working

Lower Limit Given in Question 8,000

Spread (3 x ((3/4 x 50 x 4,000,000) / 0.00025))1/3

25,303

Upper Limit (Lower Limit + Spread)

8,000 + 25,303 33,303

Return Point (Lower Limit + (1/3 x Spread)

8,000 + (1/3 x 25,303) 16,434


Test Your Knowledge


1. Which of the following are the reasons for a company to hold cash?

1. Speculation2. Persuasion3. Transaction4. Reaction


Answer B

2. Revaile Co. has annual transactions of $30 million. The fixed cost of converting securities into cash is $500 per conversion. The annual opportunity cost of funds is 6%. What is the optimal deposit size?

A. $21,213B. $42,426C. $707,107D. $42.43

Answer B

Working

Annual Disbursements $30,000,000

Interest Rate 6%

Cost of making a transfer $500

Amount to transfer √(2 x 264.5 x 9,000,000) / 0.09)

707,107


Working


(707,107 / 2) x 0.06 21,213


$500 x (30,000,000 / 707,107)

21,213

Total Cost 42,426

3. Which of the following are problems with the Baumol Model?

1. Assumes constant cash disbursements2. Assumes that there are no cash receipts, just movements3. Assumes a risk free interest rate4. Assumes no safety buffer for cash


Answer D

4. If a company must maintain a minimum cash balance of £20,000, and the variance of its daily cash flows is £6.25m (ie std deviation £2,500). The cost of buying/ selling securities is £80 & the daily interest rate is 0.035 %.

What is the upper-limit using the Miller-Orr model of cash management?

Working

Lower Limit Given in Question 20,000

Spread (3 x ((3/4 x 80 x 6,250,000) / 0.00035))1/3

25,303

Upper Limit (Lower Limit + Spread)

8,000 + 25,303 33,303

Return Point (Lower Limit + (1/3 x Spread)

8,000 + (1/3 x 25,303) 16,434



1. What are the three reasons to hold cash?

SpeculationPrecautionTransaction

2. What does the Baumol Model tell us?

The optimum cash amount to transfer from interest bearing investments into cash each time cash is transferred.

3. Why is there a cost of holding cash?

By holding cash you are not earning interest so the cost is the opportunity cost of the interest you could have earned.

4. How do we calculate the total trading costs in the year?

The cost of moving cash x number of movements (Total cash moved per year / amount moved each time)

5. How do we calculate the total holding costs in the year?

Average cash balance (C / 2) x Interest rate.

6. What are the problems with the Baumol Model?

Assumes constant cash disbursementsAssumes that there are no cash receipts - just movements from interest bearing account to cashAssumes no safety buffer for cash

7. Why does the Miller-Orr model tell us to buy securities with extra cash?

To earn interest on excess cash.


8. How do we calculate the variance of cash flows?

Standard Deviation of cash flows squared.

9. If the interest rate is 8% what figure should be included in the Miller-Orr model for i?

0.00022 (0.08 / 365)

10. How do we calculate the upper limit?

Lower limit + spread.


Pilot Paper Q3 (You now know enough to do this all)

Now do it!


Lecture 9 Investment Appraisal I


ARR - Illustration 1

ABC Ltd are considering expanding their internet cafe business by buying a business which will cost $275,000 to buy and a further $175,000 to refurbish.

They expect the following cash to come in:

Year Net Cash Profits (£)

1 45,000

2 75,000

3 80,000

4 50,000

5 50,000

6 60,000

The equipment will be depreciated to a zero resale value over the same period and, after the sixth year, they can sell the business for $200,000

Calculate the ARR or ROCE of this investment

Solution

Total Profit over 6 years 45,000 + 75,000 + 80,000 + 50,000 + 50,000 + 60,000

360,000

Total Depreciation Equipment of $175,000 fully depreciated

175,000

Total Profits 185,000

Average Profits $185,000 / 6 years 30,833

Average Investment (Capital Investment + Residual Value) / 2

(450,000 + 200,000) / 2 325,000

ROCE (Ave. Profit / Ave Investment)

30,833 / 325,000 9.5%


Relevant Cash Flow Criteria - Illustration 2

A business is considering investing in a new project. They have already spent $20,000 on a feasibility study which suggests that the project will be profitable.

The headquarters of the company has spare floor space which will be allocated to the project with $7,000 of the current monthly rent allocated to the project.

New equipment costing $2.5m will have to be bought and will be depreciated on a straight line basis over 10 years.

A manager who earns $30,000 per year and currently runs a similar project will also manage the new project taking up 25% of his time.

State whether each of the following items are relevant cash flows and explain your answer.

I. The cost of the feasibility study.

II. The rent charged to the project.

III. The new equipment.

IV. The depreciation on the new equipment.

V. The Managers salary.

Item Relevant Cash Flow?

Explain

Feasibility Study No This is a sunk cost as it has already been paid.

Rent No The rent is not relevant as it must be paid whether the project goes ahead or not. It is not incremental.

New Equipment Yes This is a relevant cash flow.

Depreciation No Depreciation is not a cash-flow but an accounting entry.

Managers Salary No The managers salary must be paid whether the project goes ahead or not so is not relevant.


Payback Period - Illustration 3

Initial Investment of $5.8m.

Annual Cash Flows of $400,000.

Calculate the Payback Period.

Solution

Payback Period (Initial Investment / Annual Cash Flows)

$5.8m / $400,000 14.5 years


Payback Period - Illustration 4

Initial Investment of $6.2m.

Cash Flows of:

Year 1: ! $1,200,000

Year 2:! $2,200,000

Year 3:! $2,500,000

Year 4:! $1,700,000

Calculate the Payback Period.

Solution

Year Cash Flows Cumulative Cash Flows

1 1,200,000 1,200,000

2 2,200,000 3,400,000

3 2,500,000 5,900,000

4 1,700,000 7,600,000

Payback period is between 3 and 4 yearsPayback period is between 3 and 4 yearsPayback period is between 3 and 4 years

Additional amount required to return capital (6,200,000 - 5,900,000) = 300,000Additional amount required to return capital (6,200,000 - 5,900,000) = 300,000Additional amount required to return capital (6,200,000 - 5,900,000) = 300,000

Total cash flows in year 4 of 1,700,000 so it will take (300,000 / 1,700,000) x 12 = 2.11 monthsTotal cash flows in year 4 of 1,700,000 so it will take (300,000 / 1,700,000) x 12 = 2.11 monthsTotal cash flows in year 4 of 1,700,000 so it will take (300,000 / 1,700,000) x 12 = 2.11 months


Discounted Cash-flows - Illustration 5

An investor wants a real return of 10%. Inflation is 5%

What is the MONEY/NOMINAL rate required?

Solution

Use Formula: 1+m = (1+r) x (1+inf)

We are looking for m, therefore:

1+m = (1+0.10) x (1+0.05)

1+m = 1.155

m = 0.155 = 15.5%



A company undertakes a project with the following cash-flows:

Year Cash-Flows

1 5,000

2 7,000

3 8,000

4 10,000

5 11,000

6 9,000

The company has a cost of capital of 10%.

Calculate the present value of the cash flows for each of the six years and in total.

Solution

Year Cash-Flows Discount Rate (From Tables)

Present Value

1 5,000 0.909 4,545

2 7,000 0.826 5,782

3 8,000 0.751 6,008

4 10,000 0.683 6,830

5 11,000 0.621 6,831

6 9,000 0.564 5,076

Total 35,072



A company undertakes a project with the following cash-flows:

Year Cash-Flows

1 5,000

2 5,000

3 5,000

4 5,000

5 5,000

6 5,000

The company has a cost of capital of 10%.

Calculate the present value of the total cash flows for the six years

Solution

Year Cash-Flows Discount Rate (From Tables)

Present Value

1 5,000 0.909 4,545

2 5,000 0.826 4,130

3 5,000 0.751 3,755

4 5,000 0.683 3,415

5 5,000 0.621 3,105

6 5,000 0.564 2,820

Total 21,770

Years Cash-flow Discount Rate (Annuity Tables)

Present Value

1 - 6 5,000 4.355 21,775



A company expects to receive $100,000 per year forever.

Their cost of capital is 10%.

Calculate the present value of the perpetuity.

Solution

Annual Cash Flow $100,000

Cost of Capital (10%) 0.10

Perpetuity (Cash-Flow / Cost of Capital) 100,000 / 0.10 = $1m


Test Your Knowledge



1. JoJo Ltd are considering investing in a new project which will cost an initial $375,000 and they expect the following cash to come in:

Year Net Cash Profits (£) 1 25,000 2 55,000 3 70,000 4 80,000 5 40,000 6 30,000

The investment will be depreciated to a scrap value of $175,000 over the period of the project.

What is the Accounting Rate of Return (Return on Capital Employed) of the project?

A. 6%B. 3%C. 18%D. 12%

Answer B

Total Profit over 6 years 25,000 + 55,000 + 70,000 + 80,000 + 40,000 + 30,000

300,000

Total Depreciation (375,000 - 175,000) 200,000

Total Profits 100,000

Average Profits $100,000 / 6 years 16,668

Average Investment (Capital Investment + Residual Value) / 2 (375,000 + 175,000) / 2 550,000

ROCE (Ave. Profit / Ave Investment) 16,668 / 550,000 3%


2. Which of the following are weaknesses of the Accounting Rate of Return (Return on Capital Employed)?

1. The calculation uses accounting profit rather than cash.2. It disregards the timing of the inflows.3. It does not consider the whole life of the project.4. No discount rate is used to allow for inflation and risk.

A 1, 2 and 4 B 1 and 3 only C 2 and 3 only D 1, 2 and 3

Answer A

3. Aldios Co. intends to make an investment of $4.5m in a project lasting 5 years. The project cashflows are forecast to be as follows:

Year Net Cash Profits (£) 1 250,000 2 550,000 3 2,700,000 4 2,800,000 5 400,000

The investment will be depreciated to a scrap value of $1.5m over the period of the project.

What is the Payback period of the investment?

A. 3 Years 4 monthsB. 2 Years 6 monthsC. 4 Years 2 monthsD. 2 Years 4 months

Answer A


Year Cash Flows Cumulative Cash Flows

1 250,000 250,000

2 550,000 800,000

3 2,700,000 3,500,000

4 3,000,000 6,500,000

Payback period is between 3 and 4 yearsPayback period is between 3 and 4 yearsPayback period is between 3 and 4 years

Additional amount required to return capital (4,500,000 - 3,500,000) = 1,000,000Additional amount required to return capital (4,500,000 - 3,500,000) = 1,000,000Additional amount required to return capital (4,500,000 - 3,500,000) = 1,000,000

Total cash flows in year 4 of 2,800,000 so it will take (1,000,000 / 3,000,000) x 12 = 4 monthsTotal cash flows in year 4 of 2,800,000 so it will take (1,000,000 / 3,000,000) x 12 = 4 monthsTotal cash flows in year 4 of 2,800,000 so it will take (1,000,000 / 3,000,000) x 12 = 4 months

4. Jpeg Co. uses a real discount rate of 8%. They are carrying out an investment appraisal using an inflation rate of 5%.

What discount rate should be used to discount the cash flows for the project:

A. 8%B. 5%C. 13%D. 11%

Answer C



1. What are the 6 steps in investment appraisal?

Identify investment opportunities.Screen the proposals to see that they fit with the organisation.Analyse and evaluate the proposals.Approval by the board.Implementation and monitoring.Post completion review or audit.

2. Why carry out a post-completion audit?

To ensure that managers are more careful in future.To evaluate management performance on the project.To evaluate future projects.

3. What is the calculation for the ARR or ROCE?

Average accounting profit / Average investment

4. How do you calculate the average investment?

(Cost + Residual Value) / 2

5. What are the weaknesses of the ARR?

The gain is expressed as a percentage so does not take into account the size of the investment.Uses accounting profit rather than cash so can be manipulated.Disregards the timing of cashflows.No discount rate to allow for inflation and risk.

6. What are the 3 relevant criteria for cash-flows in investment appraisal?

CashIncremental (Caused by the project)Future


7. What are the advantages of using the payback period method?

Simple.Minimises risk as it focuses on getting the capital invested back.Maximises liquidity, again as it focuses on getting the capital invested back.Uses cash rather than accounting profit.Good for conservative managers.

8. Why do we need to discount cash-flows?

To allow for risk and inflation.

9. If the real discount rate is 7% and inflation is running at 3% what is the nominal/money discount rate?

1+m = (1+r) x (1+inf)1+m = (1.07) x (1.03)1+m = 1.10m = 0.10

Money Discount Rate = 10%

10. If I am going to receive $8,000 per year for 6 years and my cost of capital (discount rate) is 8% what is the present value of the total of these cash-flows?

$8,000 x 4.623 (from annuity tables) = $36,984


June 2009 Q2 (a)

Now do it!


Lecture 10 Investment Appraisal II


WDA - Illustration 1

A business buys a piece of equipment for $100.

Capital allowances are available at 25% reducing balance.

The tax rate is 30%

After the 4 year project the equipment can be sold for $25.

Solution

Period Balance 25% WDA 30% Tax Saving

Period

1 100.00 25.00 7.50 2

2 75.00 18.75 5.63 3

3 56.25 14.06 4.22 4

4 42.19

Sale of Item -25.00

17.19 5.16 5

Period 0 1 2 3 4 5

Tax Saving

- - 7.5 5.63 4.22 5.16


Working Capital - Illustration 2

A business requires the following working capital investment into a four year project:

Initial Investment:! ! 30,000

Year 1!! ! ! 35,000

Year 2!! ! ! 45,000

Year 3!! ! ! 32,000

Show the working capital line in the NPV calculation.

Solution

Period 0 1 2 3 4

Total Invested 30,000 35,000 45,000 32,000

Movement to NPV Calculation

-30,000 -5,000 -10,000 13,000 32,000


NPV - Illustration 3

A business is evaluating a project for which the following information is relevant:

I. Sales will be $100,000 in the first year and are expected to increase by 5% per year.

II. Costs will be $50,000 and are expected to increase by 7% per year.

III. Capital investment will be $200,000 and attracts tax allowable depreciation of the full value of the investment over the 5 year length of the project.

IV. The tax rate is 30% and tax is payable in the following year.

V. Working Capital invested will be 20% of projected sales for the following year.

VI. General inflation is expected to be 3% over the course of the project and the business uses a real discount rate of 9%.

Calculate the NPV for the project.

Solution

Working 1 - WDAs

Initial Investment WDAs Tax Saving Periods

200,000 (200,000 / 5) = 40,000

(40,000 x 30%) = 12,000

2 - 6


Working 2 - Inflation

Period 1 2 3 4 5

Sales 100,000 100,000 100,000 100,000 100,000

Inflation - 1.05 1.05 to power of 2

1.05 to power of 3

1.05 to power of 4

Inflated Sales

100,000 105,000 110,250 115,763 121,551

Costs 50,000 50,000 50,000 50,000 50,000

Inflation - 1.07 1.07 to power of 2

1.07 to power of 3

1.07 to power of 4

Inflated Costs

50,000 53,500 57,245 61,252 65,540

Working 3 - Discount Rate

Working

Real Discount Rate In Question 9%

Inflation In Question 3%

Nominal Discount Rate 1 + m = (1 + 0.09) x (1 + 0.03)1 + m = 1.12m = 0.12

12%


Working 4 - Working Capital

Period 0 1 2 3 4 5

Inflated Sales 100,000 105,000 110,250 115,763 121,551

Working Capital Required (20%)

20,000 21,000 22,050 23,153 24,310

Movement -20,000 -1,000 -1,050 -1,103 -1,158 24,310

NPV

Period 0 1 2 3 4 5 6

Inflated Sales (W2)

100,000 105,000 110,250 115,763 121,551

Inflated Costs (W2)

-50,000 -53,500 -57,245 -61,252 -65,540

Profit 50,000 51,500 53,005 54,510 56,011

Tax at 30% -15,000 -15,450 -15,902 -16,353 -16,803

Tax Saving (W1)

12,000 12,000 12,000 12,000 12,000

Capital Investment

-200,000

Working Capital (W4)

-20,000 -1,000 -1,050 -1,103 -1,158 24,310

Total Cash Flows

-220,000 49,000 47,450 48,452 49,451 75,968 -4,803

Discount Rate 12% (W3)

1 0.893 0.797 0.712 0.636 0.567 0.507

Discounted Cash Flows

-220,000 43,757 37,818 34,498 31,451 43,074 -2,435

NPV -31,838


Test Your Knowledge


1. Asfor Co. plans to undertake a project with an initial investment of $5m. The inflation adjusted cash flows expected from the project are as follows:

Year $

1 $1.2m

2 $1.8m

3 $2.1m

4 $2.2m

5 $2.5m

Asfor Co. uses a real discount rate of 6% and general inflation is expected to be 5% per year for the duration of the project.

What is the NPV of the project ignoring tax:

A. $8,178B. $8,108C. $2,010D. $7,010

Answer C

Discount Rate (1.06 x 1.05) = 11%

1 2 3 4 5

Cash 1,200 1,800 2,100 2,200 2,500

DR 11% 0.901 0.812 0.731 0.659 0.593

PV Cash 1,081 1,462 1,535 1,450 1,483

Total PV 7,010

Capital 5,000

NPV 2,010


2. Asfor Co. plans to undertake a project with an initial investment of $16m. The cash flows (profit) before inflation expected from the project are as follows:

Year $

1 $4.2m

2 $4.9m

3 $5.5m

4 $5.8m

5 $6.1m

Asfor Co. uses a real discount rate of 10% and general inflation is expected to be 3% per year for the duration of the project.

The tax rate on profits is 30% payable the following year.

What is the NPV of the project:

A. $417B. $2,048C. -$298D. $2,233

Answer B

Discount Rate (1.10 x 1.03) = 13%

1 2 3 4 5 6

Cash 4,200 4,900 5,500 5,800 6,100

Inflated 4,326 5,198 6,010 6,528 7,072

Tax -1,298 -1,560 -1,803 -1,958 -2,121

Total 4,326 3,901 4,450 4,725 5,113 -2,121

DR 13% 0.885 0.885 0.885 0.885 0.885 0.885

PV Cash 3,829 3,452 3,939 4,182 4,525 -1,878

Total PV Cash

18,048

Capital 16,000

NPV 2,048


3. Asfor Co. plans to undertake a project with an initial investment of $16m and a scrap value of $3m at the end of the project. The cash flows after inflation expected from the project are as follows:

Year $

1 $4.2m

2 $4.9m

3 $5.5m

4 $5.8m

5 $6.1m

Asfor Co. uses a nominal discount rate of 10%. Inflation is expected to be 3% per year.

The tax rate on profits is 30% payable the following year. Tax allowable depreciation is available at 25% reducing balance.


A. $1,477B. $6,945C. $17,477D. $3,340

Answer D


Period

1 16,000 4,000 1,200 2

2 12,000 3,000 900 3

3 9,000 2,250 675 4

4 6,750 1,688 506 5

5 5,063

Sale of Item 3,000

2,063 619 6


0 1 2 3 4 5 6

Cash 4,200 4,900 5,500 5,800 6,100

Tax -1,260 -1,470 -1,650 -1,740 -1,830

Tax Saving on WDAs

1,200 900 675 506 619

Capital -16,000 3,000

Total -16,000 4,200 4,840 4,930 4,825 7,866 -1,211

DR 10% 1.000 0.909 0.893 0.751 0.683 0.621 0.564

PV Cash -16,000 3,818 4,322 3,702 3,295 4,885 -683

NPV 3,340


4. Asfor Co. plans to undertake a project with an initial investment of $10m. The cash flows (profit) after inflation expected from the project are as follows:

Year $

1 $4.2m

2 $4.9m

3 $5.5m

4 $5.8m

5 $6.1m

Asfor Co. uses a nominal discount rate of 10%.

The working capital requirement will initially be $1m rising by 5% each year before being returned at the end of the project.



A. $4,605B. $9.566C. $4,097D. $4,293

Answer D

1 2 3 4 5 6

Cash 4,200 4,900 5,500 5,800 6,100

Tax -1,260 -1,470 -1,650 -1,740 -1,830

W.Capital -1,000 -50 -53 -55 1,158

Total 3,200 3,590 3,978 4,095 5,518 -1,830

DR 10% 0.909 0.893 0.751 0.683 0.621 0.564

PV Cash 2,909 3,206 2,987 2,797 3,427 -1,032

Total PV Cash

14,293

Capital 10,000

NPV 4,293


5. Asfor Co. plans to undertake a project with an initial investment of $6m and scrap value of $1m. The sales price per unit in real terms is $30 with cost per unit of $15.

Year Units

1 200,000

2 300,000

3 350,000

4 400,000

5 320,000


The sales are expected to be subject to inflation of 5% with the costs subject to inflation of 3%.



A. $11,079B. $5,912C. $4,097D. $8,111

Answer A

1 2 3 4 5

Sales Price 30 30 30 30 30

Inflation 1.05 1.052 1.053 1.054 1.055

Inflated 32 33 35 36 38

Cost Price 15 15 15 15 15

Inflation 1.03 1.032 1.033 1.034 1.035

Inflated 15 16 16 17 17

Profit Per Unit 16 17 18 20 21

Units (‘000) 200 300 350 400 320

Total Cash 3,210 5,148 6,418 7,833 6,688


1 2 3 4 5 6

Cash 3,210 5,148 6,418 7,833 6,688

Tax -963 -1,544 -1,925 -2,350 -2,006

Capital -6,000 1,000

Total -2,790 4,185 4,874 5,908 5,338 -2,006

DR 10% 0.909 0.893 0.751 0.683 0.621 0.564

PV Cash -2,536 3,737 3,660 4,035 3,315 -1,132

NPV 11,079


6. Asfor Co. plans to undertake a project with an initial investment of $600,000 and scrap value of $100,000. The sales and costs in real terms are forecast to be

Year Sales$

Costs$

1 200,000 100,000

2 300,000 125,000

3 350,000 155,000

4 400,000 160,000

5 320,000 145,000


The sales are expected to be subject to inflation of 5% with the costs subject to inflation of 3%.


What is the NPV of the project to the nearest ‘000?

A. -$33,000B. -$2,000C. $72,000D. $107,000

Answer D

1 2 3 4 5

Sales 200 300 350 400 320

Inflation 1.05 1.052 1.053 1.054 1.055

Inflated 210 331 405 486 408

Costs 100 125 155 160 145

Inflation 1.03 1.032 1.033 1.034 1.035

Inflated 103 133 169 180 168


1 2 3 4 5 6

Sales 210 331 405 486 408

Costs -103 -133 -169 -180 -168

Profit 107 198 236 306 240

Tax -32 -59 -71 -92 -72

Capital -600 100

Total -493 166 177 235 248 -72

DR 10% 0.909 0.893 0.751 0.683 0.621 0.564

PV Cash -448 148 133 161 154 -41

NPV 107



1. What are we comparing in NPV analysis?

The initial investment in the project is being compared to the forecast cash-flows which are discounted to reflect the risk of the project and inflation.

2. Why do we need a period 0?

The initial investment is made now - in the current time period and as such is not discounted as no inflation will have occurred.

3. Why do we assume that cash-flows occur at the end of each period?

The discount rates given to us in the discount table applys to a whole year i.e. the discount rate for period one applies to cash flows that occur 1 year after the start of the project.

If we did not assume that the cash we earn during year one occurred at the end of that period then we would have to adjust the discount rate for the month in which they occur (by using a fraction of the discount rate).

This would be time consuming and difficult.

4. If I have profits in period 2 of $4,000 and a tax rate of 30% how much tax will I pay and when?

Tax to pay: 4,000 x 0.3 = $1,200

This will be paid in period 3 - one year later.


5. If I receive 25% capital allowances and have a tax rate of 20% what will my tax saving be in each year over a 5 year project if the capital investment is $7,500 with a residual value of $1,500?


Period

1 7500 1875 375 2

2 5625 1406 281 3

3 4219 1055 211 4

4 3164 791 158 5

5 2373

Sale of Item -1500

873 175 6

6. What makes up working capital?

Inventory, Receivables, Payables.

7. How do we account for working capital in NPV analysis?

The initial working capital required is invested in period 0.

We then adjust the working capital for the increase or decrease required in each period.

The closing balance of working capital is returned at the end of the project so that the working capital line in the NPV calculation should add across to zero.

8. If my cash flows in my NPV analysis are inflated should I use the real or the nominal discount rate?

The real rate. If the cash flows are inflated then the discount rate needs to be adjusted for inflation also.



June 2010 Q3 (a) & (b)

Now do it!


Lecture 11 Investment

Appraisal III


IRR - Illustration 1

ABC has evaluated a project and come to the following conclusions.

At a discount rate of 10% the NPV will be $100,000

At a discount rate of 15% the NPV will be -$75,000

What is the IRR?

Solution

! !

! ! 100,000

IRR = !! ! 10 +! 100,000 - (75,000) (15 - 10)


Test Your Knowledge


1. Which of the following best describes the result of calculating the Internal Rate of Return of a prospective project?

A. The forecast return on the project as a percentage of the capital invested.B. The amount of time expected to be taken for the capital invested in the project to be

returned.C. The amount of shareholder wealth expected to be created by the project.D. The discount rate at which the NPV of the project is expected to be zero.

Answer D

2. If a project has cash inflows of $5,000 per year for 5 years and had an initial investment of $17,000 what is the IRR?

A. 14.5%B. 11.5%C. 10.0%D. 15.0%

Answer A

NPV at discount rate of 5%:

Present value of cash flows (5,000 x 4.329) = 21,645Initial investment = 17,000

NPV = 4,645 (21,645 - 17,000)



NPV = -240 (16,760 - 17,000)


Fill into IRR

5 + [(4,645 / (4,645 - -240)) (15 - 5)]

IRR = 14.5%


A. 11.05%B. 10.07%C. 12.07%D. 9.23%

Answer B



NPV = 2,974 (25,974 - 23,000)



NPV = -2,888 (20,112 - 23,000)

Fill into IRR

5 + [(2,974 / (2,974 - -2,888)) (15 - 5)]

IRR = 14.5%


4. Which of the following are advantages of using the Internal Rate of Return (IRR) as an investment appraisal technique?

1. IRR gives an answer in the form of an understandable percentage.2. IRR uses accounting profit to assess the project.3. IRR covers the payback period of the project.4. IRR focuses on the maximisation of shareholder wealth.

A 1 and 2 only B 1 and 3 only C 2 and 3 only D 1 and 4 only

Answer D

5. Which of the following are disadvantages of using the Internal Rate of Return (IRR) as an investment appraisal technique?

1. It gives an absolute figure rather than a percentage as the result.2. All of the figures are based on forecasts.3. It is possible to get multiple IRRs depending on the timing of the cashflows.4. IRR assumes that all returns are re-invested in the project which is not necessarily the

case.

A 1, 2 and 4 B 2, 3 and 4 C 2 and 3 only D 1 and 3 only

Answer B



1. What are we trying to find with the Internal Rate of Return?

We are trying to find the discount rate at which the NPV of the project would equal zero i.e. if we discounted the cash flows at that discount rate the project would have neither a positive or negative NPV but an NPV of 0.

2. What is the formula for the IRR?

L + [(NPV L / (NPV L - NPV H)) (H - L)]




NPV = 4,645 (21,645 - 17,000)



NPV = -240 (16,760 - 17,000)

Fill into IRR

5 + [(4,645 / (4,645 - -240)) (15 - 5)]

IRR = 14.5%

4. What are the advantages of the IRR?

IRR gives an answer in the form of an understandable percentage.IRR uses cash flows and not accounting profit.IRR covers the whole life of the project.IRR (like NPV) focuses on the maximisation of shareholder wealth.


5. What are the disadvantages of the IRR?

The calculation is assumed to be complicated.It gives a percentage rather than an absolute figure as the result.All of the figures are based on forecasts.It is possible to get multiple IRRs depending on the timing of the cashflows.IRR assumes that all returns are re-invested in the project which is not necessarily the case.


June 2009 Q2 (b) & (c)December 2010 Q1 (a) & (b)December 2007 Q2 (a) & (b)Pilot Paper Q4

Now do it!


Lecture 12 Further Appraisal


Expected Values - Illustration 1

A business is considering 2 different projects. The likely profit made from each project is outlined below:

Project AProject A Project BProject B

Projected Profit Percentage Likely-hood


$10,000 10% $10,000 15%

$15,000 30% $15,000 25%

$20,000 40% $20,000 30%

$23,000 20% $23,000 30%

Calculate the expected value for each of the projects.

Solution

Project AProject AProject AProject A Project BProject BProject BProject B

Projected

Profit

Percentage

Likely-hood

Working EV Projected

Profit

Percentage

Likely-hood

Working EV

$10,000 0.1 (10,000 x 0.1)

$1,000 $10,000 0.15 (10,000 x 0.15)

$1,500

$15,000 0.3 (15,000 x 0.3)

$4,500 $15,000 0.25 (15,000 x 0.25

$3,750

$20,000 0.4 (20,000 x 0.4)

$8,000 $20,000 0.3 (20,000 x 0.3)

$6,000

$23,000 0.2 (23,000 x 0.2)

$4,600 $23,000 0.3 (23,000 x 0.3)

$6,900

1 EV $18,100 1 EV $18,150


Sensitivity Margin - Illustration 2

A business is considering a project which will cost them an initial 20,000

The sales expected for the 2 year duration are 20,000pa.

The variable costs are 2,000pa

Cost of capital 10%

Calculate the sensitivity margin of:

I. The initial investment.

II. The variable costs of the projects.

III. The sales of the project.

Solution

Working 1 - NPV of Project

Period 0 1 2

Capital Investment -20,000

Cash-Flows 20,000 20,000

Variable Cost -2,000 -2,000

Total Cash Flows -20,000 18,000 18,000

Discount Rate 10% 1 0.909 0.826

PV Cash Flows -20,000 16,362 14,868

NPV 11,230


Working 2 - PV of each item

Period 0 1 2

Variable Costs -2,000 -2,000

Discount Rate 10% 0.909 0.826

Total -1,818 -1,652

Present Value of Variable Costs (1,818 + 1,652) = $3,470Present Value of Variable Costs (1,818 + 1,652) = $3,470Present Value of Variable Costs (1,818 + 1,652) = $3,470Present Value of Variable Costs (1,818 + 1,652) = $3,470

Sales 20,000 20,000

Discount Rate 10% 0.909 0.826

Total 18,180 16,520

Present Value of Sales (18,180 + 16,520) = $34,700Present Value of Sales (18,180 + 16,520) = $34,700Present Value of Sales (18,180 + 16,520) = $34,700Present Value of Sales (18,180 + 16,520) = $34,700

Present Value of Initial Investment = $20,000Present Value of Initial Investment = $20,000Present Value of Initial Investment = $20,000Present Value of Initial Investment = $20,000

Sensitivity Margins

Item Working Sensitivity Margin

Explanation

Initial Investment

NPV / PV Initial Investment (11,230 / 20,000)

56% The NPV is 56% of the initial investment.

Variable Costs

NPV / PV Variable Costs (11,230 / 3470)

323% The Variable costs would need to rise by 323% to create a negative NPV

Sales NPV / PV Sales (11,230 / 34,700)

32% Sales would need to drop by 32% before the NPV would be negative.


Lease V Buy - Illustration 3

Machine cost $10,000

The Machine has a useful economic life of 5 years with no scrap value

Capital allowances available at 25% reducing balance

Finance choices

1) 5 year loan 14.28% pre tax cost

2) 5 year Finance Lease @ $2,200 pa in advance

If the machine is purchased then maintenance costs of $100 per year will be incurred.

The tax rate is 30%.

The leasing company will maintain the machine if it is leased.

Should the company lease or buy the machine.

Solution

Buy

Working 1 - Capital Allowances


Period

1 10000.00 2500.00 750.00 2

2 7500.00 1875.00 562.50 3

3 5625.00 1406.25 421.88 4

4 4218.75 1054.69 316.41 5

5 3164.06 3,164.06 949.22 6


Working 2 - Maintenance

Amount Tax Saving

$100 per Year (100 x 30%) = $30

Working 3 - Discount Rate

Pre-tax Borrowing Rate 14.28%

Tax Rate 30%

Post Tax Borrowing Rate 14.28 x (1 - 0.3) = 10%

Working 4 - NPV

Period 0 1 2 3 4 5 6

Capital -10,000

WDA Tax Saving (W1)

750 562 422 316 949

Maintenance -100 -100 -100 -100 -100

Maintenance Tax Saving (W2)

30 30 30 30 30

Total Cash Flows -10,000 -100 680 492 352 246 979


1 0.909 0.826 0.751 0.683 0.621 0.564

PV Cash Flows -10,000 -91 562 369 240 153 552

NPV -8,214


Lease

Period 0 1 2 3 4 5 6

Capital -2200 -2200 -2200 -2200 -2200

Tax Saving on Lease Payment

660 660 660 660 660

Total Cash Flows -2200 -2200 -1540 -1540 -1540 660 660


1 0.909 0.826 0.751 0.683 0.621 0.564

PV Cash Flows -2,200 -2000 -1272 -1157 -1052 410 372

NPV -6,898

Based on the above, the company should lease the machine.


Equivalent Annual Cost - Illustration 4

Machine Cost 30,000

Running costs

Year 1 10,000

Year 2 11,500

Residual Value (if sold after..)

Year 1 19,000

Year 2 16,000

Cost of capital = 10%

Is it better to replace the machine every year or to replace it every 2 years?


Solution

NPV for replacement after one year

Period 0 1


Running Costs -10,000

Residual Value 19,000

Cash Flows -30,000 9,000

Discount Rate 10% 1 0.909

PV Cash Flows -30,000 8,181

NPV -21,819

Annuity Factor from tables (1yr at 10%)

0.909

Equivalent Annual Cost (NPV / Annuity Factor) = (-21,819 / 0.909) = -$24,003Equivalent Annual Cost (NPV / Annuity Factor) = (-21,819 / 0.909) = -$24,003Equivalent Annual Cost (NPV / Annuity Factor) = (-21,819 / 0.909) = -$24,003

NPV for replacement after two years

Period 0 1 2


Running Costs -10,000 -11,500

Residual Value - 16,000

Cash Flows -30,000 -10,000 4,500

Discount Rate 10% 1 0.909 0.826

PV Cash Flows -30,000 -9,090 3,717

NPV -35,373

Annuity Factor from tables (2yrs at 10%)

1.736

Equivalent Annual Cost (NPV / Annuity Factor) = (-35,373 / 1.736) = -$20,376Equivalent Annual Cost (NPV / Annuity Factor) = (-35,373 / 1.736) = -$20,376Equivalent Annual Cost (NPV / Annuity Factor) = (-35,373 / 1.736) = -$20,376Equivalent Annual Cost (NPV / Annuity Factor) = (-35,373 / 1.736) = -$20,376


Test Your Knowledge


1. A business is considering 2 different projects. The likely profit made from each project is outlined below:

Project 1Project 1 Project 2Project 2



$12,000 10% $12,000 15%

$16,000 30% $16,000 25%

$25,000 40% $25,000 30%

$30,000 20% $30,000 30%




$12,000 12% $12,000 18%

$16,000 35% $16,000 30%

$25,000 44% $25,000 30%

$30,000 9% $30,000 22%

Which of the projects should be chosen on the basis of the Expected Values?

A Project 1B Project 2C Project 3D Project 4

Answer C



Projected Profit

Percentage Likely-hood

Projected Profit


$12,000 10% $1,200 $12,000 15% $1,800

$16,000 30% $4,800 $16,000 25% $4,000

$25,000 40% $10,000 $25,000 30% $7,500

$30,000 20% $6,000 $30,000 30% $9,000

$22,000 $22,300


Projected Profit


Projected Profit


$12,000 12% $1,440 $12,000 18% $2,160

$16,000 35% $5,600 $16,000 30% $4,800

$25,000 44% $11,000 $25,000 30% $7,500

$30,000 9% $2,700 $30,000 22% $6,600

$20,740 $21,060


2. A company is considering investing in a project with an expected life of four years. The project has a positive net present value of $280,000 when cash flows are discounted at 12% per annum. The project’s estimated cash flows include net cash inflows of $320,000 for each of the four years. No tax is payable on projects of this type.

What is the sensitivity margin of the cash inflows of the project?

A 87.5%

B 21.9%

C 3.5%

D 28.8%

Answer D

Net Present Value of the project = $280,000

Present value of the annual cash inflow = $320,000 x 3.037 = $971,840

Sensitivity = $280,000/$971,840 = 28.8%

3. A five year investment project has a positive net present value of $320,000 when discounted at the cost of capital of 10% per annum. The project includes annual net cash inflows of $100,000 which occur at the end of each of the five years.

What is the sensitivity margin of the cash inflows of the project?

A 31.25%

B 118.5%

C 84.4%

D 18.5%

Answer C

Discounted value of cash inflow = $100k x 3.791 = $379.1k

Sensitivity = $320k / $379.1k = 84.4%


4. Davos Co. intends to lease a machine on a 5 year operating lease for a payment of $3,500 payable in advance. The tax rate is 30%. The pre-tax cost of borrowing is 15.71%.

What is the present value cost to the business of leasing the machine?

A. $9,440B. $10,480C. $10,864D. $10,974

Answer C

Period 0 1 2 3 4 5 6

Capital -3,500 -3,500 -3,500 -3,500 -3,500

Tax Saving on Lease Payment

1,050 1,050 1,050 1,050 1,050

Total Cash Flows -3,500 -3,500 -2,450 -2,450 -2,450 1,050 1,050

Discount Rate 11% 15.71 x (1 - 0.3)

1 0.901 0.812 0.731 0.659 0.593 0.535

PV Cash Flows -3,500 -3154 -1989 -1791 -1615 623 562

NPV -10,864

5. Davos Co. intends to buy a machine a payment of $2m. Tax allowable depreciation is allowable over 5 years at 25% reducing balance. The tax rate is 30%. The pre-tax cost of borrowing is 17.14%. Maintenance costs of $65,000 are payable each year.

What is the present value cost to the business of buying the machine?

A. -$1,786B. -$1,615C. -$1,849D. -$2,172

Answer A



Period

1 2000 500 150 2

2 1500 375 113 3

3 1125 281 84 4

4 844 211 63 5

5 633 633 190 6

Period 0 1 2 3 4 5 6

Capital -2,000

WDA Tax Saving 150 113 84 63 190

Maintenance -65 -65 -65 -65 -65

Maintenance Tax Saving 19.5 19.5 19.5 19.5 19.5

Total Cash Flows -2,000 -65 104.5 67.5 38.5 17.5 209.5

Discount Rate 12% (17.14% x (1 - 0.3)) 1 0.893 0.797 0.712 0.636 0.567 0.507

PV Cash Flows -2,000 -58 83 48 24 10 106

NPV -1,786


6. Kevlar Co. has a piece of machinery which cost $40,000 and is trying to decide how often to replace it based on the Equivalent Annual Cost (EAQ). The following information relates to the machine.

Machine Cost 40,000

Running costs

$12,000 per year

Residual Value (if sold after..)

Year 1 19,000

Year 2 16,000

Year 3!! 14,000

Year 4!! 14,000

Cost of capital = 12%

When is best to replace the machine based on the EAQ?

A. At the end of year 1B. At the end of year 2C. At the end of year 3D. At the end of year 4

Answer D

Year Cost Costs Residual Value

NPVCost

Annuity Factor EAC

1 40,000 12,000 x 0.893 10,716 19,000

x 0.893 16,976 33,740 0.893 37,783

2 40,000 12,000 x 1.690 20,820 16,000

x 0.797 12,752 48,068 1.690 28,443

3 40,000 12,000 x 2.402 28,824 14,000

x 0.712 9,968 58,856 2.402 24,503

4 40,000 12,000 x 3.102 37,224 14,000

x 0.636 6,996 70,228 3.102 22,640



1. What is the difference between risk and uncertainty?

Risk can be quantified whereas uncertainty cannot.

2. How can we deal with each of risk and uncertainty in investment appraisal?

Risk can be quantified using probabilities. This enables us to calculate an expected value and use this in our investment appraisal.

3. What is an operating lease?

An operating lease is a leasing arrangement where a company does not take ownership of the item being leased but pays a periodic amount to use it. It will remain on the lessor’s balance sheet and they will be responsible for maintaining it.

4. Why might a company want to lease an item rather than buy it?

There may be tax benefits to leasing the item.The lessor retains the risk of obsolescence and maintenance.It can be used as a form of off-balance-sheet finance.There is no requirement to take out a loan to finance the item.

5. What are the relevant costs of buying the item?

The cost of the item.The residual value at the end of the useful life.Written down allowances against tax.Maintenance costs which will be incurred when the item is owned.Tax allowance on the maintenance costs (or any other tax allowable cost in a question).

6. What are the relevant costs of leasing the item?

The lease payments.Tax allowance on the lease payments.


7. If I have a pre-tax borrowing rate of 13% and the tax rate is 25% what is the post-tax borrowing rate?

0.13 x (1-T)0.13 x (1 - 0.25) = 0.975

Answer = 9.75%

8. What does the equivalent annual cost method tell us?

EAC tells us when best to replace assets as it shows us the cost per year to own and operate them.

9. What is the equation for the EAC?

NPV / Annuity factor.

10. I have an item of plant costing $30,000 new and $5,000 to maintain each year. The residual value after 3 years is $7,000 and after 4 years is $5,000. If I have a cost of capital of 10% after how long should I replace the asset?

EAC for replacing after 3 years

Period 0 1 - 3 3




Cash Flows -30,000 -5,000 7,000

Discount Rate 10% 1 2.487 0.751

PV Cash Flows -30,000 -12,435 5,257

NPV -37,178


2.487



EAC for replacing after 4 years

Period 0 1 - 4 4




Cash Flows -30,000 -5,000 7,000

Discount Rate 10% 1 3.170 0.683

PV Cash Flows -30,000 -15,850 4,781

NPV -41,069


3.170


It is better to replace the plant every 4 years as the EAC is lower.


December 2009 Q1 (a) & (b)December 2007 Q2 (c)

Now do it!


Lecture 13 Further Appraisal II


Profitability Index - Illustration 1

A business has identified the following projects. They have $200,000 to invest and the projects are divisible.

Project Investment NPV

A 90,000 15,000

B 110,000 25,000

C 50,000 10,000

D 75,000 22,000

E 70,000 -8,000

Which projects should the business undertake?

Solution

Project Investment NPV PI (NPV / Investment)

Rank

A 90,000 15,000 17% 4%

B 110,000 25,000 23% 2%

C 50,000 10,000 20% 3%

D 75,000 22,000 29% 1%

E 70,000 -8,000 -

Investment

Project Investment

All of D 75,000

All of B 110,000

30% of C (50,000 x 0.3) 15,000

Total Investment 200,000


Investment Choices - Illustration 2

A business has identified the following projects. They have $200,000 to invest and the projects are non-divisible.


A 90,000 15,000

B 110,000 25,000

C 50,000 10,000

D 75,000 22,000

Which projects should the business undertake?

Solution

Project Investment NPV Rank

A + B 90,000 + 110,000 = 200,000 15,000 + 25,000 = 40,000 2

A + C 90,000 + 50,000 = 140,000 15,000 + 10,000 = 25,000 6

A + D 90,000 + 75,000 = 165,000 15,000 + 22,000 = 37,000 3

B + C 110,000 + 50,000 = 160,000 25,000 + 10,000 = 35,000 4

B + D 110,000 + 75,000 = 185,000 25,000 + 22,000 = 47,000 1

C + D 50,000 + 75,000 = 125,000 10,000 + 22,000 = 32,000 5

The business should undertake projects B and D as these will yield the highest NPV.The business should undertake projects B and D as these will yield the highest NPV.The business should undertake projects B and D as these will yield the highest NPV.The business should undertake projects B and D as these will yield the highest NPV.


Equivalent Annual Annuity - Illustration 3

! ! ! ! NPV Duration

Project 1 300 5 yrs

Project 2 200 3 yrs

Project 3 350 6 yrs

Calculate the EEA of each project given a cost of capital of 10%

Solution

Project NPV Annuity Factor

Working (NPV / Annuity Factor)

EAA

1 300 3.791 300 / 3.791 79.13

2 200 2.487 200 / 2.487 80.42

3 350 4.355 350 / 4.355 80.37

Project 3 has the highest EAA.Project 3 has the highest EAA.Project 3 has the highest EAA.Project 3 has the highest EAA.Project 3 has the highest EAA.


Test Your Knowledge


1. An investment project requires an initial investment of $500,000 and has a residual value of $130,000 at the end of five years. The net present value of the project is $140,500 after discounting at the company’s cost of capital of 12% per annum.

The profitability index of the project is:

A 0.38 B 0.54 C 0.28 D 0.26

Answer C

The profitability index= net present value of the investment / initial investment = $140,500 / $500,000= 0.281


2. A company has a maximum of $80 million available for investment and seven independent projects in which it could invest as follows:


A 10 4.20

B 40 6.10

C 20 8.50

D 40 13.70

E 50 3.80

F 20 4.90

G 20 4.33

None of the projects can be carried out more than once. Each project is divisible therefore investment in part of a project can be undertaken.

What is the maximum NPV that could be achieved from investing the $80m using the Profitability Index?

A. $28.85B. $31.3mC. $45.53mD. $26.4m

Answer A

Project Investment

NPV PI Rank Cumulative Inv.

Cumulative NPV

C 20 8.50 0.43 1 20 8.5

A 10 4.20 0.42 2 30 12.7

D 40 13.70 0.34 3 70 26.4

F 20 4.90 0.25 4 80 28.85

G 20 4.33 0.22 5 - -

B 40 6.10 0.15 6 - -

E 50 3.80 0.08 7 - -


3. Which of the following best describes ‘hard’ capital rationing?

A. A limited amount of capital is available to the company due to external factors such as banks unwillingness to lend.

B. A limited amount of capital is available to the company due to internal factors such as management unwillingness to take more risk.

C. Extra capital is available to the company due to external factors such as banks who are keen to lend.

D. Extra capital is available to the company due to internal factors such as excess cash from operations.

Answer A

4. Which of the following best describes ‘soft’ capital rationing?

A. A limited amount of capital is available to the company due to external factors such as banks unwillingness to lend.

B. A limited amount of capital is available to the company due to internal factors such as management unwillingness to take more risk.

C. Extra capital is available to the company due to external factors such as banks who are keen to lend.

D. Extra capital is available to the company due to internal factors such as excess cash from operations.

Answer B



1. What is the difference between divisible and non-divisible projects?

For divisible projects, the company can do a proportion of one project if they do not have the capital to do it all.

Non divisible projects cannot be split i.e. they are all or nothing.

2. If the projects are divisible,which method should be used to decide which projects to undertake?

Profitability index.

3. How do we calculate the Profitability Index?

NPV of project / Cost of investment.

4. If projects are non divisible how do we make a decision?

Trial and error.

5. What is the equivalent annual benefit?

The EAB tells us what the NPV of the project would be the equivalent to as an annual amount.

6. What is capital rationing?

Capital rationing refers to the fact that companies do not have an unlimited amount of capital available to invest.

7. What is hard capital rationing?

Hard capital rationing is externally imposed by factors outside of the organisation.


8. What is soft capital rationing?

Soft capital rationing is imposed by factors internal to the organisation.


December 2009 Q1 (c) & (d)

Now do it!


Lecture 14 Business Valuations


Net Assets Valuation Method Illustration 1

Non Current Assets 550,000

Current Assets 170,000

Current Liabilities -80,000

Share Capital 300,000

Reserves 200,000

10% Loan Notes 150,000

The Market Value of property in the Non Current Assets is $50,000 more than the book value.The Market Value of property in the Non Current Assets is $50,000 more than the book value.

The Loan Notes are redeemable at a 5% premium.The Loan Notes are redeemable at a 5% premium.

What is the value of a 70% holding using the net assets valuation basis?

Solution

Working $

Non Current Assets 550,000 + 50,000 (Property value) 600,000



10% Loan Notes 150,000 x 105% -157,500

532,500

Value of 70% 532,500 x 70% 372,750


DVM - Illustration 2

ABC pays a constant dividend of 45c. It has 3m ordinary shares.

The shareholders require a return of 15%.

What is the Value of the business?

Solution

Working

Constant Dividend In Question 45c

Required Return (Cost of Equity or Ke) In Question 15%

Share Price (Dividend / Ke) 45 / 0.15 300c

No. Ordinary Shares In Question 3m

Value of the business 300c x 3m $9m


DVM - Illustration 3

A business has Share Capital made up of 50c shares of $3 millionDividend per share (just paid) 30cDividend paid four years ago 22cRequired Return = 12%

Calculate the Value of the business using the dividend valuation method.

Solution

Working 1 - Dividend GrowthWorking 1 - Dividend Growth

Dividend Paid Now 30c

Dividend Paid 4 Years Ago 22c

Dividend Growth (4√(30 / 22))=1.08=8%

Working 2 - Business ValuationWorking 2 - Business Valuation

Dividend Paid 30c

Required Return (Ke) 12%

Dividend Growth 8%

Share Price (Dividend (1+g)) / (Ke - g) (30 x 1.08) / (0.12 - 0.08) = 810c

No Ordinary Shares ($3m / 0.5) = 6m

Value of business (6m x 810c) = $48.6m


P/E Ratio Method - Illustration 4

X1 X2 X3

$‘000 $‘000 $‘000

Revenue 3000 3500 4200

COS 2000 2400 3200




PBIT 500 500 300


Tax 120 90 50




Industry P/E Average 13 12 14

Calculate the Value of the Company for each of the 3 years using the P/E Ratio method.

Solution

Year Industry P/E Ratio Total Earnings Value of Company

1 13 280,000 (13 x 280,000) = $3.64m

2 12 260,000 (12 x 260,000) = $3.12m

3 14 30,000 (14 x 30,000) = $420,000


P/E Ratio Method - Illustration 5

X1 X2 X3

$‘000 $‘000 $‘000

Revenue 3200 3800 4800

COS 2000 2400 3200




PBIT 700 800 900


Tax 120 90 50




Industry P/E Average 17 15 18

Number of Shares 3m 3m 3m

Calculate the Earnings Per Share for each of the 3 years

Calculate the Value of the Company for each of the 3 years using the EPS you calculate.


Solution

Year Earnings No. Shares EPS (Earnings / No. Ordinary Shares)

1 480,000 3m 16c

2 560,000 3m 18.66c

3 630,000 3m 21c

Year Industry P/E Ratio

EPS Share Price(EPS x P/E Ratio)

Value of Company

1 17 16c $2.72 (2.72 x 3m) = $8.16m

2 15 18.66c $2.80 (2.80 x 3m) = $8.4m

3 18 21c $3.78 (3.78 x 3m) = $11.34m


Earnings Yield - Illustration 6

X1 X2 X3

$‘000 $‘000 $‘000

Revenue 3100 3700 4600

COS 2000 2400 3200




PBIT 600 700 700


Tax 120 90 50




Earnings Yield 0.15 0.18 0.17

Number of Shares 4m 4m 4m

Calculate the Earnings Per Share for each of the 3 years and the share price using the earnings yield.

Solution

Year Earnings No. Shares

EPS (Earnings / No. Ordinary

Shares)

Earnings Yield

Share Price(EPS / Earnings

Yield)

1 380,000 4m 9.5c 0.15 63.33c

2 460,000 4m 11.5 0.18 63.88c

3 430,000 4m 10.75 0.17 63.23c


Present Value of Future Cash Flows - Illustration 7

ABC Company earned $100,000 in cash inflows this year.

They expect this to increase in each of the next 5 years by 5% and after that to increase by 2% forever.

The company uses a cost of capital of 10%.

Calculate the value of the company using the present value of future cash flows method.

Solution

Period 1 2 3 4 5 6

Cash Inflows 105,000 110,250 115,763 121,551 127,628(127,628 x 1.02) / (0.10 - 0.02)= 1,627,257

Discount Rate 10% 0.909 0.826 0.751 0.683 0.621 0.621

PV Cash Flows 95,445 91,067 86,938 83,019 79,257 1,010,527

Total 1,446,2521,446,2521,446,2521,446,2521,446,2521,446,252


Test Your Knowledge


1.

Non Current Assets 700,000



Share Capital 500,000

Reserves 300,000

10% Loan Notes 200,000

The Market Value of property in the Non Current Assets is $100,000 more than the book value.The Market Value of property in the Non Current Assets is $100,000 more than the book value.

The Loan Notes are redeemable at a 10% premium.The Loan Notes are redeemable at a 10% premium.

What is the value of a 80% holding using the net assets valuation basis?

A. $730,000B. $664,000C. $584,000D. $444,000

Answer C


Solution

Working $

Non Current Assets 700,000 + 100,000 800,000



10% Loan Notes 200,000 x 1.1 -220,000

730,000

Value of 70% 730,000 x 80% 584,000

2. ABC Co. has Share Capital made up of 50c shares of $5 million. They have just paid a dividend per share of 50c and paid a dividend per share four years ago of 35c.The cost of capital is 14%.

Calculate the Value of the business using the dividend valuation method.

A. $343.6mB. $389.3mC. $109.3mD. $54.65m

Answer C

Solution

Working 1 - Dividend GrowthWorking 1 - Dividend Growth

Dividend Paid Now 50c

Dividend Paid 4 Years Ago 35c

Dividend Growth (4√(50 / 35))=1.09=9%


Dividend Paid 50c



Required Return (Ke) 14%

Dividend Growth 9%

Share Price (Dividend (1+g)) / (Ke - g) (50 x 1.09) / (0.14 - 0.09) = 1093c

No Ordinary Shares ($5m / 0.5) = 10m

Value of business (10m x 1093c) = $109.3m

3. SKV Co has paid the following dividends per share in recent years:

Year 2013 2012 2011 2010

Dividends 36.0 33.8 32.8 31.1

The dividend for 2013 has just been paid and SKV Co has a cost of equity of 12%.

Using the geometric average historical dividend growth rate and the dividend growth model, what is the market price of SKV Co shares to the nearest cent on an ex dividend basis?

A $4·67 B $5·14 C $5·40 D $6·97

Answer C

The geometric average dividend growth rate is (36·0/31·1)1/3 – 1 = 5%

The ex div share price = (36·0 x 1·05)/(0·12 – 0·05) = $5·40


4. The following information relates to Stovie Co.

$‘000

Revenue 3000

COS 2000

Gross Profit 1000

Op. Costs 500

Net Profit 500

Number of Shares 1m

Share Price $5

Industry P/E Average 15

What is the the Value of the Company Using the P/E ratio calculation?

A. $5m B. $7.5mC. $8mD. $5.5m

Answer B

Solution

Year Industry P/E Ratio Total Earnings Value of Company

1 15 500,000 $7.5m


5. Archie Company expects to earn $100,000 in cash inflows this year.

They expect this to increase in each of the following 4 years by 8% and after that to increase by 4% forever.


Calculate the value of the company to the nearest $‘000 using the present value of future cash flows method.

A. $1,902,000B. $2,795,000C. $1,340,000D. $3,675,000

Answer A

Solution

Period 1 2 3 4 5 Post Yr 5

Cash Inflows 100 108 117 126 136136(1.04) / (0.1 - 0.04)

= 2,357

Discount Rate 10% 0.909 0.826 0.751 0.683 0.621 0.621

PV Cash Flows 91 89 88 86 84 1,464

Total 1,902


6. Archie Company expects to earn $500,000 in cash inflows this year.

They expect this to increase in each of the following 4 years by 7% and after that to increase by 3% forever.


Calculate the value of the company to the nearest $‘000 using the present value of future cash flows method.

A. $7,569,000B. $9,638,000C. $8,137,000D. $11,790,000

Answer C

Solution

Period 1 2 3 4 5 Post Yr 5

Cash Inflows 500 535 572 613 655655(1.03) / (0.1 - 0.03)

= 9,638

Discount Rate 10% 0.909 0.826 0.751 0.683 0.621 0.621

PV Cash Flows 455 442 430 418 407 5,985

Total 8,137



1. When is it appropriate to use the Net Assets Valuation method?

To value a property investment company.As the minimum price in a takeover.If asset stripping a company.

2. What are the downsides of using the Net Assets Valuation method?

It ignores intangibles that are not shown on the balance sheet.It is not based on earnings which is usually the reason for buying a business.It will often lead to an under-valuation.

3. A company pays a constant dividend of 50c and has a cost of capital of 13%. Calculate the share price using DVM.

50 / 0.13 = $3.85

4. A company pays a dividend of 50c and paid a dividend of 40c 4 years ago. The company has a cost of capital of 13%. Calculate the share price using DVM.

Growth = [4√(50 / 40)] -1 = 0.057 (5.7%)

Share Price = 50 (1+0.057) / (0.13 - 0.057) = $7.24

5. What are the downsides of using DVM?

It assumes constant growth in the dividends.The future growth is estimated from historic data.The model is very sensitive to changes in any of the variables.

6. Why do we use a proxy P/E Ratio when valuing a business with this method?

To base our valuation on what the business should be achieving based on the industry it is in, rather that what it is achieving. If we buy the business we will intend to improve it’s performance at least to the industry average.

7. When and how can we adjust the P/E Ratio used?


When we are valuing a risky company or an unlisted company we may adjust the P/E ratio down by say 10% to reflect this.

8. The industry average P/E ratio for the fashion industry is 13. We are valuing an unlisted fashion business who have an EPS of 22c and 12m shares in issue. What is the value of the firm?

A fashion business is risky as fashion changes and it is also unlisted so let’s adjust the P/E ratio down to 12 and say:

22c x 12m = Total earnings of $2.64m

$2.64 x 12 = $31.68

9. What are the downsides of using the P/E ratio method?

Using a proxy company may be inaccurate.it is based on earnings which may be manipulated or include one-off items which distort the resulting valuation.The P/E ratio will be dependent on the view of the market which is not always correct.

10. A business is expected to earn $250,000 this year that is expected to grow at 4% forever. What is the value of the business using the present value of future cash flows if their cost of capital is 14%?

We can use the growth formula in the DVM model to calculate this:

250,000 (1 + 0.04) / (0.14 - 0.04) = $2,600,000


December 2007 Q1 (a)June 2008 Q2 (a) & (b)December 2008 Q1

Now do it!


Lecture 15 WACC I


Cost of Equity using DVM - Illustration 1

ABC Company has just paid a dividend of 35c.

The current share price is $3.25.

Calculate the Cost of Equity (Ke) using DVM.

Solution

Dividend 35

Share Price 325

Cost of Equity (Dividend / Share Price) (35 / 325) = 10.76%


Cost of Equity using DVM - Illustration 2

ABC Company has just paid a dividend of 35c.

The dividend paid has grown by 4% per year for the past 5 years.


Calculate the Cost of Equity (Ke) using DVM.

Solution

Dividend 35

Share Price 325

Dividend Growth 4%

Cost of Equity (Dividend (1+g) / Share Price) +g

((35 x 1.04) / 325) + 0.04 = 0.152= 15.2%


Cost of Equity using CAPM - Illustration 3

Company A has a Beta of 1.2.

Government bonds are currently trading at 4%.

The average return than investors in the market can expect is 15%.

Calculate the Cost of Equity using CAPM.

Solution

Rf (Risk Free Rate) 4

Rm (Ave Return on the Market) 15

Beta 1.2

Ke = Rf + β(Rm - Rf) (4 + 1.2(15 - 4)) = 17.2%


Cost of Equity using CAPM - Illustration 4


Company B has a Beta of 1.


The average return than investors in the market can expect is 12%.

Calculate the Cost of Equity using CAPM for each company.

Solution

Company A Company B

Rf (Risk Free Rate) 5 5

Rm (Ave Return on the Market)

12 12

Beta 1.2 1

Ke = Rf + β(Rm - Rf) (5 + 1.2(12 - 5)) = 13.4% (5 + 1(12 - 5)) = 12%

Notice that when Beta is 1 (Company B) Ke is 12% which is the same as the average return on the market.Notice that when Beta is 1 (Company B) Ke is 12% which is the same as the average return on the market.Notice that when Beta is 1 (Company B) Ke is 12% which is the same as the average return on the market.

Also notice that a higher Beta of 1.2 gives a higher Ke of 13.4% showing that a higher Beta means higher risk.Also notice that a higher Beta of 1.2 gives a higher Ke of 13.4% showing that a higher Beta means higher risk.Also notice that a higher Beta of 1.2 gives a higher Ke of 13.4% showing that a higher Beta means higher risk.


Cost of Equity using CAPM Illustration 5


Company B has a Beta of 1.2.


The average market risk premium is 6%.

Calculate the Cost of Equity using CAPM for each company.

Solution

Company A Company B

Rf (Risk Free Rate) 5 5

Rm - Rf (Ave Market Risk Premium)

6 6

Beta 1.3 1.2

Ke = Rf + β(Rm - Rf) (5 + 1.3(6) = 12.8% (5 + 1.2(6)) = 12.2%

Remember to look out for the market risk PREMIUM as this is always (Rm - Rf) rather than Rm (Average return on the market)Remember to look out for the market risk PREMIUM as this is always (Rm - Rf) rather than Rm (Average return on the market)Remember to look out for the market risk PREMIUM as this is always (Rm - Rf) rather than Rm (Average return on the market)

Again notice that a higher Beta leads to a higher Ke i.e. more risk.Again notice that a higher Beta leads to a higher Ke i.e. more risk.Again notice that a higher Beta leads to a higher Ke i.e. more risk.


Test Your Knowledge


1. Entrie Company has just paid a dividend of 75c. The dividend paid has grown by 3% per year for the past 4 years. The current share price is $6.54

What is the cost of equity using the dividend growth model?

A. 12%B. 15%C. 7%D. 11%

Answer B

Dividend 75

Share Price 654

Dividend Growth 3%

Cost of Equity (Dividend (1+g) / Share Price) +g

((75 x 1.03) / 654) + 0.03 = 0.15= 15%

2. Company Alpha has a Beta of 1.1.Government bonds are currently trading at 4%. The average market risk premium is 7%.

What is the cost of equity using the capital assets pricing model?

A. 12.2%B. 11.7%C. 7.3%D. 11.4%

Answer B


3. Which of the following statements about ‘systematic risk’ are correct when referring to the capital assets pricing model?

A. Systematic risk affects the overall market, not just a particular stock or industry. B. Systematic risk is company or industry specific risk.C. Systematic risk is risk that can be diversified away by investors.D. Systematic risk is determined by the gearing of the company.

Answer A

4. Which of the following statements about ‘unsystematic risk’ are correct when referring to the capital assets pricing model?

A. Systematic risk affects the overall market, not just a particular stock or industry. B. Systematic risk is company or industry specific risk.C. Systematic risk is risk that can be diversified away by investors.D. Systematic risk is determined by the gearing of the company.

Answer B

5. Which of the following are assumptions made by the capital asset pricing model (CAPM) are correct?

1. It assumes that investors can borrow at the risk free rate.2. It assumes a capital market with high transaction costs.3. It assumes that all investors are diversified.4. It assumes that the risk free rate is 5%


Answer B


6. Which of the following are downsides of the capital assets pricing model (CAPM) are correct?

1. The Beta used is calculated using historic data.2. The dividend growth is based on historic data.3. The assumptions it makes are not necessarily reflected in reality.4. The share price fluctuates on a daily basis.


Answer B



1. What is the weighted average cost of capital?

Each item of capital that a company has e.g. debt and equity has a cost.

The cost for debt will be the interest that the company has to pay and the cost for equity will be the dividends paid.

There may be more equity than debt so to get the average cost of these capital sources we need to weight the average based on the market value of each.

2. Set out the creditors hierarchy.

Type Cost

1 Fixed Charge Creditors Interest Paid

2 Floating Charge Creditors Interest Paid

3 Unsecured Creditors Interest Paid

4 Preference Shareholders Pref. Dividend

5 Ordinary Shareholders Ord. Dividend

3. Why is debt cheaper to service than equity (2 reasons!)?

Debt holders take less risk as they are higher on the creditors hierarchy.Interest payments on debt are tax deductible.

4. If a company has a dividend of 40c and a share price of $3.45 what is the cost of equity?

40 / 345 = 11.59%

5. If the dividend in question 4 is growing at a rate of 5% what is the cost of equity?

[40 (1+0.05) / 345] + 0.05 = 17.17%


6. What are the two types of risk mentioned in the CAPM lecture?

Systematic Risk & Unsystematic Risk.

7. Why can we ignore unsystematic risk?

Unsystematic risk can be diversified away by the diversification of investors portfolios.

8. What type of risk is CAPM a measure of?

The systematic risk of a particular company.

9. What does Beta tell us?

How the shares of a company have historically fluctuated with the average of all the shares in the market.

10. What are the assumptions of CAPM?

CAPM assumes that you can borrow at the risk free rate.CAPM assumes a perfect capital market with no transaction costs.CAPM assumes that all investors are diversified (so we can ignore unsystematic risk).

11. A company has a Beta of 1.3. The market risk premium is 6% and government bonds are trading at 4%. Calculate the cost of equity using CAPM.

Ke = Rf + β(Rm - Rf)Ke = 4 + 1.3(6)Ke = 11.8

12. Is a company with a Beta of 1.2 a more risky or less risky investment than a company with a Beta of 1.6?

The company with a Beta of 1.6 is more risky than the one with 1.2.


13. How is Beta calculated?

Beta is calculated by plotting the historic data as to how that share price has fluctuated in the past on a graph against the average share price in the market.

The past fluctuations are projected into the future.

14. What are the downsides of CAPM?

Beta is based on historic data.CAPM is really supposed to be used for one period only and we may use it to evaluate a 5 year project.The assumptions it makes are not necessarily reflected in reality (see Q10)

If you’ve successfully answered all of the above questions then you’re ready to do the exam questions below:You’re not Ready Yet - Do the next lecture!

Now do it!


Lecture 16 WACC II


Irredeemable Debt - Illustration 1

A company has issued 10% irredeemable debt.

The market value of the debt is $90.

The tax rate is 30%

Calculate the cost of debt (Kd).

Solution

Interest paid (Per $100 nominal) $10

Tax Rate 30%

After tax interest (Amount Paid (1 - t)) $10 x (1 - 0.30) = $7

Market Value of Debt (Per $100 nominal) $90

Cost of Debt (After tax interest / Market Value of Debt) (7 / 90) = 7.7%


Redeemable Debt - Illustration 2

A Company has issued debt which is redeemable in 5 years time.

Interest is payable at 8%.

The current market value of the debt is $102.

Ignore taxation.

Calculate the Cost of Debt (Kd).

Solution

Period

Item $ DR 5% PV DR 15% PV

1 -5 Interest 8 4.329 34.63 3.352 26.82

5 Capital 100 0.784 78.40 0.497 49.70

Market Value -102 -102

11.03 -25.48

IRR Calculation: 5 + (11.03 / (11.03 - (25.48)) (15 - 5) = 8.02%IRR Calculation: 5 + (11.03 / (11.03 - (25.48)) (15 - 5) = 8.02%IRR Calculation: 5 + (11.03 / (11.03 - (25.48)) (15 - 5) = 8.02%IRR Calculation: 5 + (11.03 / (11.03 - (25.48)) (15 - 5) = 8.02%IRR Calculation: 5 + (11.03 / (11.03 - (25.48)) (15 - 5) = 8.02%IRR Calculation: 5 + (11.03 / (11.03 - (25.48)) (15 - 5) = 8.02%IRR Calculation: 5 + (11.03 / (11.03 - (25.48)) (15 - 5) = 8.02%


Redeemable Debt - Illustration 3

A Company has issued debt which is redeemable in 5 years time.



Tax is payable at 30%.


Solution

Period


1 -5 Interest (10 x (1 - 0.3)

7 4.329 30.30 3.352 23.46

5 Capital 100 0.784 78.40 0.497 49.70


4.70 -30.84



Convertible Debt - Illustration 4

A Company has issued debt which is convertible in 5 years time.



On conversion, investors will have a choice of either:

I. Cash at a 15% premium; or

II. 18 shares per loan note.

The current share price is $6 and it is expected to grow in value by 4% per year.

Tax is payable at 30%.


Solution

Working 1 - Cash or Convert?

Working

Cash (15% Premium) 100 x 1.15 $115

Shares

Current Value $6

Value in 5 years with 4% growth

6 x (1.04 to the power of 5) $7.30

Number of shares per $100 18

Conversion Value 7.30 x 18 $131.40

The conversion value is higher than the cash so the investors will choose to convert.The conversion value is higher than the cash so the investors will choose to convert.The conversion value is higher than the cash so the investors will choose to convert.

Do an IRR the same as for redeemable but filling $131.40 into the capital repaidDo an IRR the same as for redeemable but filling $131.40 into the capital repaidDo an IRR the same as for redeemable but filling $131.40 into the capital repaid


Cost of Debt

Period


1 -5 Interest (10 x (1 - 0.3) 7 4.329 30.30 3.352 23.46

5 Conversion Value 131.4 0.784 103.02 0.497 65.31


13.32 -31.23

IRR Calculation: 5 + (13.32 / (13.32 - (31.23)) (15 - 5) = 8%IRR Calculation: 5 + (13.32 / (13.32 - (31.23)) (15 - 5) = 8%IRR Calculation: 5 + (13.32 / (13.32 - (31.23)) (15 - 5) = 8%IRR Calculation: 5 + (13.32 / (13.32 - (31.23)) (15 - 5) = 8%IRR Calculation: 5 + (13.32 / (13.32 - (31.23)) (15 - 5) = 8%IRR Calculation: 5 + (13.32 / (13.32 - (31.23)) (15 - 5) = 8%IRR Calculation: 5 + (13.32 / (13.32 - (31.23)) (15 - 5) = 8%

Preference Shares - Illustration 5

A company has issued 8% preference shares with a nominal value of $1.

The market value of the shares is 80c.


Calculate the cost of the preference shares (Kd).

Solution

Interest Paid 8

Market Value of share 80

Cost (Kd) (Interest Paid / Market Value) (8 / 80) = 10%


Bank Debt - Illustration 6

A company has a bank loan of $2m at an interest rate of 10%.


Calculate the cost of debt (Kd).

Solution

Interest Rate before Tax 10

Tax Rate 30%

After Tax Cost of Debt (10 x (1 - 0.3)) 7%


WACC - Illustration 7

Company A is funded as follows:

Item Capital Structure Cost

Equity 85% 15%

Debt 15% 7%

Calculate the Weighted Average Cost of Capital.

Solution

Item Capital Structure Cost Ave

Equity 85% 15 12.75

Debt 15% 7 1.05

WACC 13.8




Balance Sheet Extract

Ordinary Shares (50c) 3000

Loan Notes 2000

Bank Loan 1000

The cost to the company of each of the above items has been calculated as:

Ordinary Shares 13%

Loan Notes 8%

Bank Loan 5%

The Loan notes are currently trading at $94.

The current share price is $1.50


Solution

Working 1 - Calculate Cost of Capital for each item.

Given in the QuestionGiven in the Question

Ordinary Shares 13%

Loan Notes 8%

Bank Loan 5%


Working 2 - Calculate the Market Value of Debt and Equity.

SFP Market Value

Ordinary Shares (50c)

3000 No. of shares (3000 / 0.50) = 6000Share Price = $1.50

(6000 x $1.50) = 9000

Loan Notes 2000 Loan Notes nominal value (on SFP) = 100Market Value = 94

(2000 x (94 / 100) = 1880

Bank Loan 1000 No market for this so use SFP value

1000

Working 3 - Calculate the weighting of each item.

Item Market Value Weighting

Equity 9000 (9000 / 11,880) = 75.75%

Loan Notes 1880 (1880 / 11,880) = 15.82%

Bank Loan 1000 (1000 / 11,880) = 8.41%

11880

Working 4 - Weighted Average Cost of Capital

Item Market Value

Weighting Cost (W1)

Ave

Equity 9000 (9000 / 11,880) 13 (9000 / 11,880) x 13 = 9.85

Loan Notes 1880 (1880 / 11,880) 8 (1880 / 11,880) x 8 = 1.27

Bank Loan 1000 (1000 / 11,880) 5 (1000 / 11,880) x 5 = 0.42

11880 WACC 11.54%






12% Loan Notes 1500

8% Preference Shares ($1) 500

Bank Loan 750

Details on these are as follows.

The company has an equity beta of 1.2. Government bonds are currently trading at 6% and the average market risk premium is 7%.

The Loan notes are currently trading at $106 and are redeemable at par in 5 years time.

The preference shares are trading at 92c.

The bank loan has an interest rate of 10%.





Solution

Working 1 - Calculate Cost of Capital for each item.

Cost of Equity using CAPM


(Rm - Rf)(Ave market risk premium) 7

Beta 1.2

Ke = Rf + β(Rm - Rf) (6 + 1.2(7)) = 14.4%

Cost of 12% Loan Notes

Period


1 -5 Interest (12 x (1 - 0.3)

8.4 4.329 36.36 3.352 28.16

5 Capital 100 0.784 78.40 0.497 49.70


8.76 -28.14


Cost of Preference Shares

Interest Paid 8

Market Value of share 92

Cost (Kd) (Interest Paid / Market Value) (8 / 92) = 8.7%


Cost of Bank Debt

Interest Rate before Tax 10

Tax Rate 30%

After Tax Cost of Debt (10 x (1 - 0.3)) 7%


SFP Market Value



(4000 x $1.25) = 5000

12% Loan Notes

1500 Loan Notes nominal value (on SFP) = 100Market Value = 106

(1500 x (106 / 100) = 1590

8% Preference Shares ($1)

500 Preference shares nominal value (on SFP) = $1Market Value = 92c

(500 x (92 / 1)) = 460

Bank Loan 750 No market for this so use SFP figure

750

Working 3 - Calculate the weighting of each item.

Item Market Value Weighting

Equity 5000 (5000 / 7800)

Loan Notes 1590 (1590 / 7800)

Preference Shares 460 (460 / 7800)

Bank Loan 750 (750 / 7800)

7800


Working 4 - Weighting & Weighted Average Cost of Capital

Item Market Value

Weighting Cost (W1)

Ave

Equity 5000 (5000 / 7800) 14.4 (5000 / 7800) x 14.4 = 9.23

Loan Notes 1590 (1590 / 7800) 7.37 (1590 / 7800) x 7.37 = 1.50

Preference Shares

460 (460 / 7800) 8.7 (460 / 7800) x 8.7 = 0.51

Bank Loan 750 (750 / 7800) 7 (750 / 7800) x 7 = 0.67

7800 WACC 11.91%


Test Your Knowledge


1. Avecas Co. has irredeemable debt in issue that interest at a rate of 12%. The market value of the debt is $84 and the tax rate is 30%.

What is the cost of debt?

A. 14%B. 12%C. 10%D. 11%

Answer C

Interest paid (Per $100 nominal) $12

Tax Rate 30%

After tax interest (Amount Paid (1 - t)) $12 x (1 - 0.30) = $8.40

Market Value of Debt (Per $100 nominal) $84

Cost of Debt (After tax interest / Market Value of Debt) (8.4 / 84) = 10%

2. A company has 10% irredeemable debt in issue at a market value of $97. If the tax rate is 30% what is the cost of the debt?

A. 7.2%B. 9.7%C. 6.5%D. 8.2%

Answer A

10 (1-0.3) / 97 = 7.2%


3. A Company has issued debt which is redeemable in 5 years time. Interest is payable at 12%. The current market value of the debt is $102. Tax is payable at 30%.

What is the cost of debt (kd) using linear extrapolation and discount rates of 5% and 15% in the calculation?

A. 12.00%B. 8.47%C. 9.00%D. 7.24%

Answer B

Period


1 -5 Interest (12 x (1 - 0.3)

8.4 4.329 36.36 3.352 28.16

5 Capital 100 0.784 78.40 0.497 49.70


12.76 -24.14



4. A company has 5 year 8% redeemable debt in issue at a market value of $103. The tax rate is 25%.

What is the cost of debt (kd) using linear extrapolation and discount rates of 5% and 15% in the calculation?

A. 6.26%B. 5.95%C. 7.19%D. 5.4%

Answer D

Period Item $ DR 5% PV DR 15% PV

1 -5 Interest (8 x (1 - 0.25)) 6 4.329 25.97 3.352 20.11

5 Capital 100 0.784 78.40 0.497 49.70


1.37 -33.19

IRR Calculation: 5 + (1.37 / (1.37 - (33.19) (15 - 5) = 5.4%IRR Calculation: 5 + (1.37 / (1.37 - (33.19) (15 - 5) = 5.4%IRR Calculation: 5 + (1.37 / (1.37 - (33.19) (15 - 5) = 5.4%IRR Calculation: 5 + (1.37 / (1.37 - (33.19) (15 - 5) = 5.4%IRR Calculation: 5 + (1.37 / (1.37 - (33.19) (15 - 5) = 5.4%IRR Calculation: 5 + (1.37 / (1.37 - (33.19) (15 - 5) = 5.4%IRR Calculation: 5 + (1.37 / (1.37 - (33.19) (15 - 5) = 5.4%


5. Jeeves Company has issued debt which is convertible in 5 years time. Interest is payable at 12% and the current market value of the debt is $108.

On conversion, investors will have a choice of either:

Cash at a 10% premium; or

14 shares per loan note.

The current share price is $7 and it is expected to grow in value by 3.5% per year.

Which of the following statements is correct?

A. Based on the information available, investors would be better off choosing to take the cash option by $6.39.

B. Based on the information available, investors would be better off choosing to take the conversion option by $6.39.

C. Based on the information available, investors would be indifferent between the cash and conversion option.

D. Based on the information available, investors would be better of choosing to take the cash option by $8.94.

Answer B

6. A company has 8% preference share in issue at a current value of 94c. The tax rate is 30%. What is the cost of the preference shares?

A. 8.5%B. 6.0%C. 8.0%D. 5.6%

Answer A

8 / 94 = 8.5%

7. A company has a bank loan of $7m at a rate of 6%. The tax rate is 35%. What is the cost of the bank debt?

A. 6.0%B. 2.1%C. 3.9%D. 4.2%

Answer C

6 (1-T) = 6 (1 - 0.35) or 3.9%


8. Company A is funded as follows:



Loan Notes 1000

Bank Loan 500

The cost to the company of each of the above items has been calculated as:

Ordinary Shares 17%

Loan Notes 7%

Bank Loan 6%

The Loan notes are currently trading at $98.

The current share price is $3.50

What is the Weighted Average Cost of Capital?

A. 11.56%B. 16.19%C. 13.34%D. 17.24%

Answer B



SFP Market Value



(5000 x $3.50) = 17,500

Loan Notes 1000 Loan Notes nominal value (on SFP) = 100Market Value = 98

(1000 x (98 / 100) = 980

Bank Loan 500 No market for this so use SFP value

500

Working 2 - Weighted Average Cost of Capital

Item Market Value

Weighting Cost (W1)

Ave

Equity 17,500 (17,500 / 18,980) 17 (17,500 / 18,980) x 17=15.67

Loan Notes 980 (980 / 18,980) 7 (980 / 18,980) x 7= 0.36

Bank Loan 500 (500 / 18,980) 6 (500 / 18,980) x 6= 0.16

18980 WACC 16.19%



1. What is the nominal value of issued debt?

$100

2. What is convertible debt convertible into?

Shares.

3. What is the calculation for irredeemable debt?

Annual Interest (1-T) / Market Value of debt

4. A company has 10% irredeemable debt in issue at a market value of $97. If the tax rate is 30% what is the cost of the debt?

10 (1-0.3) / 97 = 7.2%

5. A company has 5 year 8% redeemable debt in issue at a market value of $103. The tax rate is 25%. What is the cost of the debt?

Period Item $ DR 5% PV DR 15% PV

1 -5 Interest (8 x (1 - 0.25)) 6 4.329 25.97 3.352 20.11

5 Capital 100 0.784 78.40 0.497 49.70


1.37 -33.19

IRR Calculation: 5 + (1.37 / (1.37 - (33.19) (15 - 5) = 5.4%IRR Calculation: 5 + (1.37 / (1.37 - (33.19) (15 - 5) = 5.4%IRR Calculation: 5 + (1.37 / (1.37 - (33.19) (15 - 5) = 5.4%IRR Calculation: 5 + (1.37 / (1.37 - (33.19) (15 - 5) = 5.4%IRR Calculation: 5 + (1.37 / (1.37 - (33.19) (15 - 5) = 5.4%IRR Calculation: 5 + (1.37 / (1.37 - (33.19) (15 - 5) = 5.4%IRR Calculation: 5 + (1.37 / (1.37 - (33.19) (15 - 5) = 5.4%

6. A company has 10% convertible debt in issue at a market value of $111 that is redeemable in 5 years at either cash or 5 shares per nominal. The current share price is $18 and is expected to grow at 2%. The tax rate is 30%. What is the cost of debt?



Working

Cash $100

Shares

Current Value $18

Value in 5 years with 4% growth

18 x (1.02 to the power of 5)

$19.87


Conversion Value 19.87 x 5 $99.35

The conversion value is lower than the cash so the investors will choose not to convert.The conversion value is lower than the cash so the investors will choose not to convert.The conversion value is lower than the cash so the investors will choose not to convert.

Cost of Debt

Period


1 -5 Interest (10 x (1 - 0.3) 7 4.329 30.30 3.352 23.46

5 Conversion Value 100 0.784 78.40 0.497 49.70


-2.30 -37.84



7. A company has 8% preference share in issue at a current value of 94c. What is the cost of the preference shares.

8 / 94 = 8.5%

8. A company has a bank loan of $7m at a rate of 6%. The tax rate is 35%. What is the cost of the bank debt?

6 (1-T) = 6 (1 - 0.35) or 3.9%

9. The company has each of the types of debt in questions 4 to 6 on their balance sheet at a book value of $10m for each of them except for the bank debt which is on the balance sheet at $7m. If the company has a market value of $110m with a cost of equity of 14% then what is the company’s weighted average cost of capital?


SFP Market Value

Ordinary Shares

10m Market Value given will be the value of the shares

110m

Irredeemable Debt

10m 10m x 97/100 9.7m

Redeemable Debt

10m 10m x 103/100 10.3m

Convertible Debt

10m 10m x 111/100 11.1m


10m 10m x 94/100 9.4m

Bank Loan 7m No market for this so use SFP figure

7m


Item Market Value

Weighting Cost Ave

Ordinary Shares

110 (110 / 157.5) 14 9.78

Irredeemable Debt

9.7 (9.7 / 157.5) 7.2 0.44

Redeemable Debt

10.3 (10.3 / 157.5) 5.4 0.35

Convertible Debt

11.1 (11.1 / 157.5) 5.57 0.39


9.4 (9.4 / 157.5) 8.5 0.51

Bank Loan 7 (7 / 157.5) 3.9 0.17

157.5 WACC 11.65

10. What if the company has each of the types of debt in questions 4 to 6 on their balance sheet at a book value of $8m for each of them except for the bank debt which is on the balance sheet at $7m. If the company has a market value of $99m with a cost of equity of 12% then what is the company’s weighted average cost of capital?


SFP Market Value

Ordinary Shares

8m Market Value given will be the value of the shares

99m

Irredeemable Debt

8m 8m x 97/100 7.76m

Redeemable Debt

8m 8m x 103/100 8.24m

Convertible Debt

8m 8m x 111/100 8.88m


8m 8m x 94/100 7.52m

Bank Loan 7m No market for this so use SFP figure

7m


Item Market Value

Weighting Cost Ave

Ordinary Shares

99 (99 / 138.4) 14 10.01

Irredeemable Debt

7.76 (7.76 / 138.4) 7.2 0.40

Redeemable Debt

8.24 (8.24 / 138.4) 5.4 0.32

Convertible Debt

8.88 (8.88 / 138.4) 5.57 0.36


7.52 (7.52 / 138.4) 8.5 0.46

Bank Loan 7 (7 / 138.4) 3.9 0.20

138.4 WACC 11.76

If you’ve successfully answered all of the above questions then you’re ready to do the exam questions below:December 2008 Q3 (a)June 2010 Q2June 2008 Q1

Now do it!


Lecture 17 Capital Structure


Capital Structure - Illustration 1

A company has total capital of $1,000 with debt making up $300 and equity making up $700 of the total. The company’s cost of debt is 5% and cost of equity is 14%.

I. Calculate the company’s current WACC.II. Calculate the WACC if the company substitutes $200 of equity for $200 of debt

causing their cost of equity to rise to 16%.III. Calculate the WACC if the company substitutes $300 of equity for $300 of debt

causing their cost of equity to rise to 25%.

Solution

I.

Item Market Value Weighting Cost WACC

Debt 300 300 / 1000 5% 1.5

Equity 700 700 / 1000 14% 9.8

1000 11.3

II.


Debt 500 500 / 1000 5% 2.5

Equity 500 500 / 1000 16% 8

1000 10.5

III.


Debt 600 600 / 1000 5% 3

Equity 400 400 / 1000 25% 10

1000 13


Test Your Knowledge


Which of the following statements concerning capital structure theory is correct?

A. In the traditional view, there is a linear relationship between the cost of equity and financial risk

B. Modigliani and Miller said that, in the absence of tax, the cost of equity would remain constant

C. Pecking order theory indicates that preference shares are preferred to convertible debt as a source of finance

D. Business risk is assumed to be constant

Answer D

2. Which of the following statements concerning capital structure theory is correct?

A. The traditional view of capital structure suggests that the company can minimise their weighted average cost of capital

B. Modigliani and Miller said that, incorporating tax, the weighted average cost of capital would remain constant

C. Pecking order theory indicates that preference shares are preferred to convertible debt as a source of finance

D. Modigliani and Miller said that, incorporating tax, as gearing levels increase so the value of the company will decrease

Answer A

3. Which of the following are assumptions that Modigliani and Miller made in their ‘no tax’ model?

1. No risk of bankruptcy no matter how much debt the company has.2. High transaction charges.3. The company is able to borrow at the risk free rate.4. The company has no debt in it’s capital structure.


Answer B


4. What does the M&M model with tax suggest a company should do with their capital structure?

A. As there is greater financial risk at high levels of gearing the company should have as little debt as possible.

B. As the transaction costs will be high the company should retain their current capital structure for as long as possible.

C. As taking on more debt reduces the weighted average cost of capital the company should increase their gearing levels.

D. The company should find the optimum capital structure at which it can minimise its weighted average cost of capital.

Answer C



1. What is capital structure?

How much debt and equity a company has.

2. What does the traditional view suggest you can do with the WACC?

Minimise it.

3. Why would you want to do this?

The WACC is a cost to the business - as with any cost the company will wish to minimise it.

4. What other assumptions did M & M make in their ‘no tax’ model?

No risk of bankruptcy no matter how much debt the company has.No transaction charges.The company is able to borrow at the risk free rate.

5. What does the M&M model with tax suggest we should do with our capital structure?

As the interest on debt is tax deductible and thus debt is cheaper, M&M suggested that a company should substitute Equity for Debt in order to take advantage of this fact.

This will also have the effect of increasing the value of the business using the PV of future cash-flows method as the WACC and thus the discount rate will be lower leading to a higher valuation.


Pilot Paper Q1 (b)June 2009 Q1 (c)

Now do it!


Lecture 18 Financing & Investment


Project Specific Discount Rate - Illustration 1

Company A intends to undertake a project in an unrelated industry.

The following details are relevant:

Item Company A Proxy Company

Equity Beta (βe) 1.2 1.4

Value of Equity 1000 800

Value of Debt 400 500

The risk free rate is 4%.

The average return on the market is 12%.

Calculate a project specific discount rate.

Ignore Tax

Solution

Working 1 - Un-gear the proxy βe to get βa.

Proxy Equity Beta 1.4

Value of Equity of Proxy 800

Value of Debt of Proxy 500

βa = βe(Ve / (Ve + Vd)) 1.4 (800 / (800 + 500)) = 0.86


Working 2 - Re-gear βa with our capital structure

βa 0.86

Value of Equity of Company A 1000

Value of Debt of Company A 400

βe = βa (Ve + Vd ) / Ve) 0.86 ((1000 + 400) / 1000) = 1.20

Working 3 - Fill into CAPM


Rm (Ave return on the market) 12

Beta 1.2

Ke = Rf + β(Rm - Rf) (4 + 1.2(12 - 4)) = 13.6%


Project Specific Discount Rate - Illustration 2

Company A intends to undertake a project in an unrelated industry.

The following details are relevant:

Item Company A Proxy Company

Equity Beta (βe) 1.1 1.3

Value of Equity 1200 900

Value of Debt 500 450

The risk free rate is 4%.

The average return on the market is 12%.


Calculate a project specific discount rate.

Solution





βa = βe(Ve / (Ve + (Vd x 1-t)) 1.3 (900 / (900 + (450 x 0.7)) = 0.96



βa 0.96



βe = βa (Ve + (Vd x 1-t) / Ve) 0.96 ((1200 + (500 x 0.7)) / 1200) = 1.24




Beta 1.24

Ke = Rf + β(Rm - Rf) (4 + 1.24(12 - 4)) = 13.92%


Test Your Knowledge


Company Alpha is financed with $1,000 of equity and $400 of debt and intends to undertake a project in an unrelated industry. They have identified Horizon Co. as a company in the new industry with $700 of equity and $300 of debt. Alpha Co. has a Beta of 1.3 whereas Horizon Co. has a Beta of 1.2. The risk free rate is 4% and the average return on the market is 12%. The tax rate is 30%.

Which of the following would be the project specific discount rate for Alpha Co. when entering the new industry?

A. 12.34%B. 10.25%C. 11.12%D. 13.42%

Answer DWorking 1 - Un-gear the proxy βe to get βa.




βa = βe(Ve / (Ve + (Vd x 1-t)) 1.2 (700 / (700 + (300 x 0.7)) = 0.92


βa 0.92



βe = βa (Ve + (Vd x 1-t) / Ve) 0.92 ((1000 + (400 x 0.7)) / 1000) = 1.18





Beta 1.18

Ke = Rf + β(Rm - Rf) (4 + 1.18(12 - 4)) = 13.42%


2. Company Alpha is financed with 60% equity and 40% debt and intends to undertake a project in an unrelated industry. They have identified Horizon Co. as a company in the new industry with 75% equity and 25% debt. Alpha Co. has a Beta of 1.1 whereas Horizon Co. has a Beta of 1.4. The risk free rate is 6% and the average return on the market is 14%. The tax rate is 30%.


A. 19.38%B. 18.00%C. 17.20%D. 16.32%

Answer A





βa = βe(Ve / (Ve + (Vd x 1-t)) 1.4 (75 / (75 + (25 x 0.7)) = 1.14


βa 1.14



βe = βa (Ve + (Vd x 1-t) / Ve) 1.14 ((60 + (40 x 0.7)) / 60) = 1.67





Beta 1.67

Ke = Rf + β(Rm - Rf) (6 + 1.67(14 - 6)) = 19.38%


3. Company Alpha is financed with debt/equity of 1/4 and intends to undertake a project in an unrelated industry. They have identified Horizon Co. as a company in the new industry with debt/equity 1/3. Alpha Co. has a Beta of 1.05 whereas Horizon Co. has a Beta of 1.24. The risk free rate is 6% and the average return on the market is 14%. The tax rate is 30%.


A. 16.23%B. 15.49%C. 17.26%D. 18.28%

Answer B





βa = βe(Ve / (Ve + (Vd x 1-t)) 1.24 (3 / (3 + (1 x 0.7)) = 1.01


βa 1.01



βe = βa (Ve + (Vd x 1-t) / Ve) 1.01 ((4 + (1 x 0.7)) / 4) = 1.19





Beta 1.19

Ke = Rf + β(Rm - Rf) (6 + 1.19(14 - 6)) = 19.38%



1. What are the two types of risk included in a company’s equity Beta?

Business risk & financial risk.

2. When do we use the WACC as a discount rate?

For a project in the same business area as the current business.No change in capital structure i.e. no issue of debt or equity to finance the project.The project is small in relation to the size of the company.The project has the same risk profile as the company.

3. What is capital structure?

How much debt & equity a firm has.

4. What are the steps to calculate a project specific discount rate?

Select a ‘proxy’ company with the same business risk as the new project area.Un-gear the equity beta of the proxy to remove it’s financial risk and get the ‘asset beta’ which just includes the business risk of the new project area.Re-gear the asset beta with our company’s financial risk to get a new ‘equity beta’ for that project.Fill the new equity beta into CAPM.


5. Our business has a Beta of 1.2, debt with a market value of 100 and equity with a market value of 400. If the proxy has a Beta of 1.4, debt with a market value of 100 and equity with a market value of 200 calculate a project specific discount rate. The risk free rate is 4% and the average market risk premium is 7%. Ignore tax.





βa = βe(Ve / (Ve + (Vd x 1-t)) 1.4 (200 / (200 + 100)) = 0.93


βa 0.93



βe = βa (Ve + (Vd x 1-t) / Ve) 0.93 ((400 + 100 / 400) = 1.163




Beta 1.24

Ke = Rf + β(Rm - Rf) (4 + 1.24(12 - 4)) = 13.92%


6. What are the 3 types of market efficiency?

Weak form, semi-strong form and strong form.

7. Describe weak form market efficiency.

The share price reflects public data as well as historic data.

Investors cannot therefore ‘beat the market’ as the price responds only to new information that investors do not have.


December 2008 Q3 (c)June 2010 Q3 (c) (iii)December 2010 Q1 (c)

Now do it!


Lecture 19 More Debt


December 07 Exam Question (6 marks)

Phobis Co has in issue 9% bonds which are redeemable at their par value of $100 in five years’ time.

Alternatively, each bond may be converted on that date into 20 ordinary shares of the company. The current ordinary share price of Phobis Co is $4·45 and this is expected to grow at a rate of 6·5% per year for the foreseeable future. Phobis Co has a cost of debt of 7% per year.

Required: Calculate the following current values for each $100 convertible bond: (i) market value; (ii) floor value; (iii) conversion premium.

Solution

i. Market Value


Working

Cash $100

Shares

Current Value $4.45

Value in 5 years with 6.5% growth

4.45 x (1.065 to the power of 5)

$6.10


Conversion Value 6.10 x 20 $122

Answer

Period Item $ DR 7% PV

1 - 5 Interest 9 4.1 36.90

5 Conversion Value 122 0.713 86.99

123.89

II. Floor Value



1 - 5 Interest 9 4.1 36.90

5 Minimum Redemption 100 0.713 71.30

108.20

III. Conversion Premium

Working Amount

Current Conversion Value 4.45 x 20 89

Expected Value in 5 years (W1) 123.89

Premium 34.89

Premium Per share 34.89 / 20 1.74


Test Your Knowledge


1. Luke Co has 8% convertible loan notes in issue which are redeemable in five years’ time at their nominal value of $100 per loan note. Alternatively, each loan note could be converted after five years into 70 equity shares with a nominal value of $1 each.

The equity shares of Luke Co are currently trading at $1·25 per share and this share price is expected to grow by 4% per year. The before-tax cost of debt of Luke Co is 10% and the after-tax cost of debt of Luke Co is 7%.

What is the current market value of each loan note to the nearest dollar?

A. $92 B. $96 C. $104 D. $109

Answer B

Working

Cash $100

Shares

Current Value $1.25

Value in 5 years with 6.5% growth 1.25 x (1.04 to the power of 5) $1.52


Conversion Value $106.40


1 - 5 Interest 8 3.791 30.33

5 Conversion Value 106.4 0.621 66.07

96.40


2. A bond has a coupon rate of 8.5% per annum. The next interest payment will be made in one year’s time. The bond will repay the par value of $100 when it matures in seven years’ time. The before-tax cost of debt is 7% and the after-tax cost of debt is 5%.

What is the the expected current market price of the bond to the nearest dollar?

A. $98 B. $93 C. $108 D. $106

Answer C


1 - 7 Interest 8.5 5.389 45.81

7 Redemption 100 0.623 62.30

108.11

3. A bond has a coupon rate of 6% per annum and will repay its face value of $100 on its maturity in four years’ time. The yield to maturity on similar bonds is 4% per annum. The annual interest has just been paid for the current year.


A. $96 B. $92 C. $110 D. $107

Answer D


1 - 4 Interest 6 3.546 21.28


106.78


4. Angus Co has 8% convertible loan notes in issue which are redeemable in five years’ time at their nominal value of $100 per loan note. Alternatively, each loan note could be converted after five years into 35 equity shares with a nominal value of $1 each. The tax rate is 30%

The equity shares of Angus Co are currently trading at $2·25 per share and this share price is expected to grow by 6% per year. The before-tax cost of debt of Luke Co is 10% and the after-tax cost of debt of Luke Co is 7%.

What is the current market value of each loan note to the nearest dollar?

A. $87 B. $96 C. $98 D. $108

Answer C


Working

Cash $100

Shares

Current Value $2.25

Value in 5 years with 6.5% growth 2.25 x (1.06 to the power of 5) $3.01


Conversion Value $105.35

Answer


1 - 5 Interest (8 x 0.7) 5.6 4.1 22.96

5 Conversion Value 105.35 0.713 75.11

98.07


5. A $100 bond has a coupon rate of 8% per annum and is due to mature in four years time. The next interest payment is due in one year’s time. Similar bonds have a yield to maturity of 10%.


A. $96 B. $94 C. $110 D. $100

Answer B


1 - 4 Interest 8 3.170 25.36


93.66



1. How is the market value of convertible debt calculated?

The present value of the interest and capital paid to debt holders, discounted at the cost of debt.

2. What will the capital repaid figure in the IRR calculation be the higher of?

Cash or conversion value.

3. What is the floor value of convertible debt?

The minimum value that the debt should ever be.

4. How is the floor value calculated?

Discount the interest and the nominal capital to be repaid at the cost of the debt.

5. What is the conversion premium?

The difference between the expected conversion value and the current conversion value.


Now do it!


Lecture 20 Currency Risk I


Buy or Sell Currency - Illustration 1

You have an invoice to pay to a US business of $1250 and you are a UK business.

The rate offered by the bank is $:£ 1.2500 - 1.3500

How many £ will it take to pay the $125?

Solution

Bank sells low We want to buy $ with our £ and the bank will sell them to us at the low rate of 1.2500

For a receipt use the rate on the right

We are making a payment so we use the rate on the left i.e. 1.2500

Cost of $ (Amount of $ / FX Rate)

($1250 / 1.25) = £1,000


Buy or Sell Currency - Illustration 2

You have issued an invoice to a US customer of $2000 and you are a UK business.

The rate offered by the bank is $:£ 1.4500 - 1.5500

How many £ will you receive for the $2000?

Solution

Bank sells low We want to sell the $ we will receive. The bank will buy them from us at the high rate of 1.5500

For a receipt use the rate on the right

This is a receipt so use the rate on the right of 1.5500

Value of $ (Amount of $ / FX Rate)

($2000 / 1.55) = £1,290


Purchasing Power Parity Theory - Illustration 3

The current exchange rate is 2$ per £.

Inflation in the US is 6%.

Inflation in the UK is 8%.

What will the FX rate be in 1 years time?

Solution

Current Spot Rate 2

Inflation in Counter (US) 6%

Inflation in Base (UK) 8%

Forecast (Spot Rate Counter x (1 + Inf in Counter / 1 + Inf in Base)

2 x ((1 + 0.06) / (1 + 0.08)) = 1.96


Interest Rate Parity Theory - Illustration 4

The current exchange rate is 2$ per £.

The interest rate in the US is 3%.

The interest rate in the UK is 2%.

What will the FX rate be in 1 years time?

Solution

Current Spot Rate 2

Interest rate in Counter (US) 3%

Interest rate in Base (UK) 2%

Forecast (Spot Rate Counter x (1 + Int in Counter / 1 + Int in Base)

2 x ((1 + 0.03) / (1 + 0.02)) = 2.02


Forward Rate - Illustration 5

ABC Company has entered into a contract whereby they will receive $500,000 from a US customer in 3 months.

ABC is a UK company.

A 3 month forward rate is available at $:£ 1.6000 +/- 0.0500.

Calculate the amount of £ ABC would receive under the forward contract.

Solution

A rate quoted at $:£ 1.6000 +/- 0.0500 is the same as saying $:£ 1.5500 - 1.6500A rate quoted at $:£ 1.6000 +/- 0.0500 is the same as saying $:£ 1.5500 - 1.6500

Rate to use (For a receipt use the one on the right)

1.6500

Convert ($ amount / Forward rate) (500,000 / 1.6500) = £303,030


Money Market Hedge - Illustration 6

A UK business needs to pay $350,000 to a US supplier in 3 months time.

Exchange rate now: $:£ 1.6500 - 1.7000

Deposit rates UK 4% annual US 6% annual

Borrowing rates UK 5% annual US 6.5% annual

How much £ will the transaction cost using a money market hedge?

Solution

Step 1 - How much Foreign Currency?

Amount of $ to pay 350,000

We will deposit the money in the US where it will earn interest so that in 3 months we have $350,000.We will deposit the money in the US where it will earn interest so that in 3 months we have $350,000.

Deposit Rate in US per year 6%

Deposit Rate for 3 months (Annual rate x 3/12)

6 x (3/12) = 1.5%

Amount to deposit (Total $ discounted at 1.5%)

350,000 x (100 / 101.5) = $344,827

We will deposit $344,827 in the US where it will earn interest of 1.5% over the 3 months making it worth $350,000 when the payment becomes due.We will deposit $344,827 in the US where it will earn interest of 1.5% over the 3 months making it worth $350,000 when the payment becomes due.

We transfer the money now so that there is no more FX risk. The transfer is made at the spot rate.We transfer the money now so that there is no more FX risk. The transfer is made at the spot rate.


Step 2 - Convert using the Spot Rate

Amount to Transfer (Step 1) $344,827


Spot rate (We are making a payment) 1.6500

Convert ($ Amount / Spot Rate) (344,827 / 1.6500) = £208,986

Step 3 - Borrow the Home Currency

Amount to Borrow (Step 2) £208,986

We will have to pay interest on the amount we have borrowed for 3 months.We will have to pay interest on the amount we have borrowed for 3 months.

Borrowing Rate per year in UK 5%

Borrowing Rate for 3 months (Annual Rate x 3/12)

(5 x 3/12) = 1.25%

Total Cost of transaction

Amount transferred to US £208,986

Interest on borrowings in UK (£ amount x 3 month UK borrowing rate)

(208,986 x 1.25%) = £2,612

Total Cost (Amount transferred + interest incurred)

(208,986 + 2,612) = £211,589


Money Market Hedge Illustration 7

A UK business will receive $350,000 from a US supplier in 3 months time.

Exchange rate now: $:£ 1.6500 - 1.7000

Deposit rates UK 4% annual US 6% annual

Borrowing rates UK 5% annual US 6.5% annual

How much £ will the business receive using a money market hedge?

Solution

Step 1 - How much foreign currency?

Amount of $ to receive 350,000

We will borrow the money in the US now and transfer it home.We will borrow the money in the US now and transfer it home.

Borrowing Rate in US per year 6.5%

Borrowing Rate for 3 months (Annual rate x 3/12)

6.5 x (3/12) = 1.625%

Amount to borrow (Total $ discounted at 1.625%)

350,000 x (100 / 101.625) = $344,403

We will borrow $344,403 in the US where it will earn interest of 1.625% over the 3 months making it worth $350,000 when the receipt becomes due. We will borrow $344,403 in the US where it will earn interest of 1.625% over the 3 months making it worth $350,000 when the receipt becomes due.

We will pay off the loan in the US when we receive the $350,000 in 3 months.We will pay off the loan in the US when we receive the $350,000 in 3 months.



Step 2 - Convert into home currency using spot rate.



Spot rate (We are receiving the foreign currency)

1.7000


Step 3 - Place the money on deposit in the UK

Amount to Deposit (Step 2) £202,590

We will receive interest on the money we deposit.We will receive interest on the money we deposit.

Deposit Rate per year in UK 4

Deposit Rate for 3 months (Annual Rate x 3/12)

(4 x 3/12) = 1%

Total Receipt

Amount transferred to UK £202,590

Interest on deposit in UK (£ Amount x 3 month UK borrowing rate)

(202,590 x 1%) = £2,026

Total Receipt (Amount transferred + interest received)

(202,590 + 2,026) = £204,616


Test Your Knowledge


1. The home currency of ACB Co is the dollar ($) and it trades with a company in a foreign country whose home currency is the Dinar. The following information is available:

Home Country Foreign Country

Spot Rate 20.00 Dinar per $

Interest Rate 3% per year 7% per year

Inflation Rate 2% per year 5% per year

What is the six-month forward exchange rate?

A 20·39 Dinar per $ B 20·30 Dinar per $ C 20·59 Dinar per $ D 20·78 Dinar per $

Answer A

Using interest rate parity, six-month forward rate

= 20·00 x (1·07/1·03)0·5 = 20·39 Dinar per $

2. What is the impact of a fall in a country’s exchange rate?

1 Exports will be given a stimulus 2 The rate of domestic inflation will rise

A 1 only B 2 only C Both1 and 2 D Neither 1 nor 2

Answer C


3. The date is 31 January 2014 and Avecas Co. has entered into a contract whereby they will receive $300,000 from a US customer on 01 April 2014. Avecas Co. is a UK company.

The following forward rates are available:

2 Month Rate $:£ 1.6000 +/- 0.0500.3 Month Rate $:£ 1.5000 +/- 0.0500.6 Month Rate $:£ 1.4000 +/- 0.0500.

What amount in £ will Avecas Co. receive under the appropriate forward contract to the nearest £.?

A. £181,818B. £193,548C. £206,897D. £495,000

Answer A

4. Hilasys Co. is a UK business that needs to pay $250,000 to a US supplier in 3 months time. The spot rate now is: $:£ 1.6500 - 1.7000. Deposit rates in the UK are 5% annual and in the US are 7% annual. Borrowing rates in the UK are 3% annual and in the US are 4.5% annual.

What will the transaction cost Hilasys Co. to the nearest £ using a money market hedge?

A. £181,818B. £245,700C. £148,909D. £150,026

Answer D


Deposit Rate in US per year 7%

Deposit Rate for 3 months (Annual rate x 3/12) 7 x (3/12) = 1.75%

Amount to deposit (Total $ discounted at 1.75%) 250,000 x (100 / 101.75) = $245,700

Convert at Spot Rate ($245,700 / 1.65) £148,909

Borrow at home (Annual rate x 3/12) 3 x (3/12) = 0.75%

Total Cost (£148,909 x 1.0075) £150,026


5. Varys Co is a UK business that will receive $500,000 from a US supplier in 3 months time. The spot rate now is: $:£ 1.6500 - 1.7000. Deposit rates in the UK are 5% annual and in the US are 6.5% annual. Borrowing rates in the UK are 3% annual and in the US are 4% annual

How much to the nearest £ will the Varys receive using a money market hedge?

A. £256,732B. £294,846C. £291,206D. £495,050

Answer B

Amount of $ to receive 500,000

Borrowing Rate in US per year 4%

Borrowing Rate for 3 months (Annual rate x 3/12) 4 x (3/12) = 1%

Amount to Borrow (Total $ discounted at 1%) 500,000 x (100 / 101) = $495,050

Convert at Spot Rate ($495,050 / 1.7) £291,206

Deposit at home (Annual rate x 3/12) 5 x (3/12) = 1.25%

Total Cost (£291,206 x 1.0125) £294,846



1. $/£ 1.35 - 1.45 which currency is the counter currency?

The dollar.

Remember this as the base is always on the right or that this is dollars (plural) to the pound (singular).

2. UK company receiving $500. Spot rate is $/£ 1.35 - 1.45. How many £ will the company receive?

500 / 1.45 = £344

For a receipt of foreign currency use the rate on the right.

3. UK inflation is 5%, US inflation is 2%. The spot rate is $/£ 1.35. What will the FX rate be in one year’s time?

Future rate = spot rate x (1 + inf in the counter) / (1 + inf in the base)

Future rate = 1.35 x (1.02 / 1.05) = 1.31

4. What are the internal methods of hedging currency risk?

Invoicing in the home currency.Leading - paying up front.Lagging - paying when the rate is favourable.Offsetting receipts & payments in a foreign bank account.

5. What are the disadvantages of a forward contract?

Contractual commitment that you cannot renege upon.Can’t take advantage of favourable movements in the currency.

6. How many £ will a company receive if they take a forward contract at a rate of $/£ 1.55 +/- 0.05 for an amount of $400,000?

Rate to use: 1.55 + 0.05 = 1.6

$400,000 / 1.6 = £250,000


7. How does a money market hedge eliminate the foreign currency risk?

The transfer is made today at the spot rate so no more exposure to the risk.

8. A UK company is going to pay $400,000 to a US supplier in 3 months time. The UK deposit rate is 4.5% and the borrowing rate is 5.5%. The US deposit rate is 5.5% and the borrowing rate is 6.5%. The spot rate is $/£ 1.5 +/- 0.025. Calculate the cost of the payment if the company uses a money market hedge?

Step 1 - How much Foreign Currency?


We will deposit the money in the US where it will earn interest so that in 3 months we have $350,000.We will deposit the money in the US where it will earn interest so that in 3 months we have $350,000.

Deposit Rate in US per year 5.5%

Deposit Rate for 3 months (Annual rate x 3/12)

5.5 x (3/12) = 1.375%

Amount to deposit (Total $ discounted at 1.375%)

400,000 x (100 / 101.375) = $394,575

We will deposit $394,575 in the US where it will earn interest of 1.375% over the 3 months making it worth $400,000 when the payment becomes due.We will deposit $394,575 in the US where it will earn interest of 1.375% over the 3 months making it worth $400,000 when the payment becomes due.


Step 2 - Convert using the Spot Rate



Spot rate (We are making a payment) 1.475



Step 3 - Borrow the Home Currency

Amount to Borrow (Step 2) £267,508

We will have to pay interest on the amount we have borrowed for 3 months.We will have to pay interest on the amount we have borrowed for 3 months.

Borrowing Rate per year in UK 5.5%

Borrowing Rate for 3 months (Annual Rate x 3/12)

(5.5 x 3/12) = 1.375%

Total Cost of transaction

Amount transferred to US £267,508

Interest on borrowings in UK (£ amount x 3 month UK borrowing rate)

(267,508 x 1.375%) = £3,678

Total Cost (Amount transferred + interest incurred)

(267,508 + 3,678) = £271,186


Pilot Paper Q2 (All except part (a))December 2008 Q4 (a), (b) & (c)

Now do it!


Lecture 21 Currency Risk II


Test Your Knowledge


1. ‘There is a risk that the value of our foreign currency-denominated assets and liabilities will change when we prepare our accounts.’

To which risk does the above statement refer? A Translation risk B Economic risk C Transaction risk D Interest rate risk

Answer A

2. Which of the following are advantages of a using a futures contract to hedge foreign exchange risk?

1. High transaction costs.2. It can be traded and thus closed out at any time.3. It is an effective hedge.4. The company can take advantage of “upside risk”.


Answer C


3. Which of the following are disadvantages of a using a futures contract to hedge foreign exchange risk?

1. They can be arranged for standard contract sizes only2. They are available for a a wide range of currencies3. There is no upside risk if the currency movement is in your favour4. There is a large premium to pay on the contract.


Answer B

4. Which of the following are advantages of a using an option on a currency to hedge foreign exchange risk?

1. High transaction costs.2. It can be traded and thus closed out at any time.3. It is an effective hedge.4. The company can take advantage of “upside risk”.


Answer C

5. Which of the following are disadvantages of a using an option on a currency to hedge foreign exchange risk?

1. They can be arranged for standard contract sizes only2. They are available for a a wide range of currencies3. There is no upside risk if the currency movement is in your favour4. There is a large premium to pay on the contract.


Answer D



1. What are the 3 types of FX risk?

Translation.Transaction.Economic.

2. Explain each of the 3.

Translation risk is the risk that losses will be incurred in translating foreign assets or liabilities in the balance sheet at the year end.

Transaction risk is the risk that in the period between agreeing a transaction and settling it fluctuations in currency rates lead to a loss.

Economic risk is long term transaction risk i.e. the risk that your operations in a foreign currency make FX losses over the long term.

3. What is a futures contract?

A futures contract is a contract to buy or sell currency in the future. It is exchange traded and can be closed out at any time for a profit or a loss. They operate on 3 monthly cycles and are for specific contract sizes of currency.

4. What are the advantages of a future?

Low transaction costs.Can be traded and thus closed out at any time.It is an effective hedge.

5. What are the disadvantages of a future?

They can be arranged for standard contract sizes only.They are available for a limited range of currencies.There is no upside risk if the currency movement is in your favour.

6. How do you undertake a future contract?

Call up the exchange.Buy or sell the future depending on the risk you wish to hedge.Pay the initial margin required.Top up the margin daily if required.


Close out the transaction by trading in the opposite direction.Receive your profit or pay the loss accrued.

7. What is an option?

An option is the right but not the obligation to buy or sell a currency at a certain price in the future.

8. What is the main advantage of an option?

The user of an option can take advantage of upside risk if the currency movement is favourable to them by choosing not to exercise the option.

9. Are there any downsides to an option?

The premium is expensive and has to be paid whether the option is exercised or not.Options are available for relatively few currencies.

10.What type of risk will an option hedge?

Transaction risk.


Pilot Paper Q2 (a)December 2008 Q4 (d)

Now do it!


Lecture 22 Interest Rate Risk


Test Your Knowledge


1. In relation to hedging interest rate risk, which of the following statements is correct?

A. The flexible nature of interest rate futures means that they can always be matched with a specific interest rate exposure

B. Interest rate options carry an obligation to the holder to complete the contract at maturity

C. Forward rate agreements are the interest rate equivalent of forward exchange contracts D. Matching is where a balance is maintained between fixed rate and floating rate debt

Answer C

2. Which of the following are disadvantages of using an interest rate swap to hedge interest rate risk?

1. There is a risk that one of the parties fails to pay their side of the swap.2. It is a reversible agreement.3. The decision to move into the swap may be the wrong decision as interest rates may

change unexpectedly.4. The transactions costs can be very high.


Answer B

3. Which of the following statements are correct in reference to using an ‘over the counter’ interest rate option to manage interest rate risk?

A. It constitutes an contract with a bank to secure a specific interest rate no matter what happens.

B. It is an agreement with a bank that ensures that the company can take advantage of low rates, but secure against high rates.

C. It is an exchange traded contract that can be closed out at any time.D. It enables the company to swap from a fixed interest rate to a floating rate or vice-versa.

Answer B


4. In relation to hedging interest rate risk, which of the following statements is correct?

A. The flexible nature of interest rate futures means that they can always be matched with a specific interest rate exposure

B. Interest rate options carry an obligation to the holder to complete the contract at maturity

C. Forward rate agreements are the interest rate equivalent of money market hedging of foreign exchange risk

D. Smoothing is where a balance is maintained between fixed rate and floating rate debt

Answer D

5. Which of the following statements about the yield curve is correct?

1. In normal circumstances the curve is upward sloping.2. Liquidity preference theory explains the yield curve on the basis that investors generally

prefer cash.3. Expectations theory explains the yield curve as the market generally expects interest

rates to be lower in the future.4. The yield curve can be used to predict interest rates.

A 1, 2 and 3 only B 1 and 3 only C 2 and 3 only D 1, 2 and 4 only

Answer D



1. What internal methods may a firm use to manage interest rate risk?

Smoothing.Matching.Netting.

2. What is an FRA?

A forward rate agreement. Effectively this is a forward interest rate agreed with a bank.

3. Why might a firm use an interest rate option to manage interest rate risk?

It means that they can take advantage of low rates, but secure against high rates.

4. What is an Interest Rate Swap?

Sn arrangement organised through a bank whereby two parties swap interest rate commitments.

5. What are the disadvantages of an interest rate swap?

There is a risk that one of the parties fails to pay their side of the swap.It is a binding agreement.The decision to move into the swap may be the wrong decision as interest rates may change unexpectedly.The transactions can be complex.

6. What does a Yield Curve plot?

Interest rates against the length of time or term of the debt.

7. In what way does a Yield Curve slope?

In normal circumstances the curve is upward sloping.


8. What are the three ways in which theorists have sought to explain the slope of the yield curve?

Expectations theory states that if debt is to be held for longer terms it is more likely that it won’t get paid back so higher interest rates are demanded to compensate so as the term gets longer the interest rate rises = upward sloping curve.

Liquidity preference theory states that because investors prefer cash, if they are going to tie capital up by lending it out for the longer term they will demand higher interest rates to compensate = upward sloping curve.

Market segmentation theory suggests that different investors have different requirements based on their own circumstances and that long term investors want higher yields leading to the upward sloping curve.


Now do it!


Lecture 23 Islamic Finance


Test Your Knowledge

If you can’t answer all of the questions below without looking at the answer then you need to do some more work on this area!Multiple Choice

1. In relation to Islamic Finance, which of the following statements is correct?

A. It is possible under certain circumstances to charge interest on an Islamic Finance product.

B. There is a lot of use of partnerships and joint ventures under Islamic Finance.C. It is not possible for a financial product to be compatible with Sharia law.D. Islamic Finance is only available to those of the muslim faith.

Answer B


1. What is the main principle behind islamic finance?

Money should not generate money i.e. no interest is allowed.

2. What should money only be generated by?

Labour.

3. What are the Islamic terms for ‘forbidden’ and ‘permitted’?

Forbidden - haraam.Permitted - halaal.

4. How will a mortgage work under islamic financial principles?

The lender will own the property and the borrower will pay a rental amount and a capital repayment amount until the asset is owned.

5. What is the islamic term for a bank loan?


Murabaha transaction.

6. How will lease finance (ijara) work under islamic finance?

Party A will let party B use the asset.Rent will be paid from B to A.A is responsible for the major maintenance of the asset.B takes care of minor maintenance.

7. What must debt finance relate to under islamic finance principles?

An asset.

8. What is the islamic finance term for a joint venture?

Musharaka.


Now do it!


Documents

ACCA F9 Workbook Lecture 1 Financial Strategy