Financial Management Calculations

7/28/2019 Financial Management Calculations

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Bond Prices DTO Inc, Inc.

Coupon Rate 8%

Number of Periods Remaining 10

Payments per year 1

YTM 6%Assumed Face Value $1,000

Coupon Value $80

Current Bond Price $1,147.20

OR Using Built In Excel Functions

Settlement Date: 1/1/2000

Maturity Date: 1/1/2010

Annual Coupon rate: 0.08

Yield to Maturity: 0.06

Face Value (% of par): 100

Coupons per year: 1

Bond Price (% of par) 114.72

Bond Price ($) $1,147.20 Check


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Bond Yields Aragon Co.

Coupon Rate 9%

Number of Periods Remaining 9Payments per year 1

Current Price $884.50

Assumed Face Value $1,000

Coupon Value $90

Yield to Maturity (YTM) 11.0935%

OR Using Built In Excel Functions

Settlement Date: 1/1/2000Maturity Date: 1/1/2009

Annual Coupon rate: 0.09

Bond Price (% of par) 88.45


Coupons per year: 1

Yield to Maturity: 11.0935% Check


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YTM Worksheet (By trial error try to find the YTM):

Calculated Bond Price: $884.50 Target: $884.50 $1,769.00

Estimated YTM (Guess): 11.0935% Try different values and try to get

Bond Price to find YTM


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iven


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Calculating Real Rates of Returnr=real rate of interest

R=nominal interest rate

T-Bills are paying: 6.00% h= inflation rate

Inflation Rate: 4.50%

Approximate Real Rate of Interest: 1.50% Formula: r=R-h (approximate)

Exact Real Rate of Interest: 1.44% Formula: r=(R-h)/(1+h)


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Inflation and Nominal Returns

r=real rate of interest

R=nominal interest rate

Real Interest Rate (r): 4.00% h= inflation rate

Inflation Rate (h): 2.50%

T-Bills should be expected to pay: 6.60% Formula: R=(1+r) x (1+h) - 1


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Bond Yields

Coupon Rate: 8.40%

Years to Maturity: 9

Payment freq.: 2

Payment % of PAR: 104

Assumed face value: $1,000Current Price: $1,040

Annual Coupon: $84

Current Yield: 8.08%

YTM: 7.76%

Effective Annual Yield: 7.91%

OR Using Excel Built In Functions: YTM Calculation Workshe

Make Estimate 3.88% 1.0409077404

Settlement Date: 1/1/2000

Maturity Date: 1/1/2009 Since this pays twice a year:

Annual Coupon rate: 0.084 YTM = 2 * 6 month rate =Bond Price (% of par) 104


Coupons per year: 2

Yield to Maturity: 7.77%


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t:

Target: 1.04 (104% of PAR)

7.76%


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Bond Prices versus Yields

Part a: Bond Price = C x [1 - 1/(1 + r)^t]/r + F/(1 + r)^t

where:

C = Coupon Paid Each Periodr = rate per period

t = number of periods

F = Bond's face value

Part b: Why do some bonds sell at a premium over par value while other bonds sell at a discount?

Bond value is determined in two parts. One part takes into account the cash flows due to the annuit

based on the "coupons" that are paid periodically. The Annuity present value is = C * (1 - (1/1 + r)^t)

and r is the yield to maturity

A second component is the Lump Sum or face value that is paid at some point in the future. This isPV = F/(1 + r)^t where F is the face value of the bond and r is the yield to maturity

The cash flows from a bond remain constant while interest rates fluctuate. Therefore investors wil

they will pay for an investment based on the current interest rates and weigh the risk/reward of inve

bond. Because of this the price of the bond will fluctuate. The bond's Yield to Maturity r is the inter

The relationship between the Coupon Rate and the YTM for premium bonds:

The coupon rate is simply the annual coupon value of the bond divided by the face value. It never ch

On a premium bond, YTM is less than the coupon rate

The relationship between the Coupon Rate and the YTM for discount bonds:

On a discount bond, YTM is greater than the coupon rate

For bonds selling at PAR value the Coupon Rate equals the YTM


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Part c: What is the relationship between the current yield and YTM for premium bonds?

The current yield on a premium bond is higher than the Yield to Maturity for premium bonds becausinto account the fact that there is a built-in loss on premium bonds. The current yield only reflects t

In fact: Coupon Rate > Current Yield > YTM for Premium Bonds

What is the relationship between the current yield and YTM for discount bonds?

The current yield on a discount bond is lower than the Yield to Maturity for the discount bond becau

into account the fact that there is a built-in gain on discount bonds. The current yield only reflects th

In fact: Coupon Rate < Current Yield < YTM for Premium Bonds

What is the relationship between the current yield and YTM for bonds selling at PAR value?

The current yield on a bond selling at PAR/FACE value is equal to the Yield to Maturity for the bond

In fact: Coupon Rate = Current Yield = YTM for Premium Bonds


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component of the bond. This is

/r where C is the coupon value

calculated as follows:

l decide how much

ting in the

st rate required by the market for the cash flows the bond produces

nges. YTM will fluctuate with interest rates.


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the current yield does not takee coupon portion of the return.

e the current yield does not take

e coupon portion of the return.

.


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Stock Values MUG Inc.

Dividend Amount $3.10 D

Growth Rate 5.00%


Therefore:

Required Rate of Return 11.46%

P0=

D1

( Rg)

1D

g

0P

R=D

1

P0+g

R


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Stock Values Warren Corporation

Dividend Amount $3.60 D

Growth Rate 4.50%

Required Return 13.00%


P0=

D1

( Rg)

1D

g

0P

R


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Nonconstant Growth Metallica Bearings, Inc.

Starting in Year 10:

Dividend Amount $8.00

Growth Rate 6.00%


Price in Year 10 $114.29

Price today $38.04

start 1 2 3 4 5 6

P9=

D10

( Rg)

g

R

PV=FV

(1+R )9

D10

P9


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etc.

107 8 9

Starting in year 10 an $8 dividendwill be paid that will increase by 6%each year thereafter.


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Supernormal Growth Rizzi Corporation

Divendend Workshe

NOTE: Start from Year 0: Year 0 $2.80

Year 1 $3.50Year 2 $4.38

Initial Dividend Amount $2.80 Year 3 $5.47

Year 4 $5.85

Growth Rate 25.00% Year 5 $6.26

Year 6 $6.70

Etc.

Starting in Year 3:

Year 3 Dividend $5.47

Growth Rate 7.00%


Price in Year 3 $97.53

Price today $77.90

g

R

P3=D

3(1+g)

Rg

D4

P0= D1(1+R )

+ D2(1+R )2

+ D3(1+R )3

+ P3(1+R )3

P3

g

D0


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t:

25% Growth Starts from here

7% Growth Starts from here

D1

D2

D3


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NPV versus IRR

Year Cash Flow (X) Cash Flow (Y) Discount Rate

0 -$5,000.00 -$5,000.00 0% $1,700.001 $2,700.00 $2,300.00 5% $1,100.21

2 $1,700.00 $1,800.00 10% $587.53

3 $2,300.00 $2,700.00 15% $145.56

20% -$238.43

IRR 16.82% 16.60% 25% -$574.40

Done by built in Excel Function

13.28% $290.48

IRR Check

Formula for IRR Project X:

$0.00 16.82%

Formula for IRR Project Y:

$0.00 16.60%

NPVProject X

0=5000+2700

(1+IRR)+1700

(1+IRR)2+2300

(1+IRR)3

0=5000+2300

(1+IRR)+1800

(1+IRR)2+2700

(1+IRR)3


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$1,800.00$1,155.49

$607.06 We can see that the crossover occurs somewhere here

$136.35 This is because NPV-X is > NPV-Y whereas before

-$270.83 NPV-X was less than NPV-Y

-$625.60

$290.47 Using Trial and Error we find the correct value with guess

NPVProject Y

This checkis done byplugging inthe IRRcalculatedabove into

the formula

This checkis done byplugging inthe IRR

calculatedabove intothe formula


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s between 10 and 15 percent


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Problems with IRR

Year Cash Flow

0 -$28,000,000.00 Return Required:

1 $53,000,000.00

2 -$8,000,000.00

a. If the company requires a 10 percent return on its investments, should it accept t

First calculate the NPV for the project: $13,570,248

$13,570,248

b. Compute the IRR for this project.

This must be done by trial error. With the formula above guesses must be made:

Guess IRR One -83.46046% $0.06 Close to Zero

Guess IRR Two 72.74617% $0.07 Close to Zero

How many IRRs are there? We know there will be two IRRs because

If you apply the IRR decision rule, should you accept the project or not?

In this case, the IRR decision is ambiguous since there are two IRRs and t

should not use the IRR to make a decision in this case.

NPV=28,000.000+53, 000, 000

(1+. 1)

8,000, 000

(1+ .1)2

0=28,000.000+53,000,000

(1+IRR )

8,000,000

(1+IRR )2


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10%

his project? Why?

Check

IRR Guess NPV

-99% -$74,728,000,000.00

-90% -$298,000,000.00 Sign Change: IRR is b

-80% $37,000,000.00

-70% $59,777,777.78

-60% $54,500,000.00

-50% $46,000,000.00

-40% $38,111,111.11

-30% $31,387,755.10

-20% $25,750,000.00

-10% $21,012,345.68

f the sign change. 0% $17,000,000.00

10% $13,570,247.9320% $10,611,111.11

30% $8,035,502.96

40% $5,775,510.20

50% $3,777,777.78

60% $2,000,000.00

70% $408,304.50 Sign Change: IRR is b

80% -$1,024,691.36

erefore one 90% -$2,321,329.64

99% -$3,386,985.18

Yes since NPV is > 0 the company should accept this project


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etween -80% and -90%

etween 70% and 80%


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Comparing Investment Criteria

Year Cash Flow (A) Discounted (A) Cash Flow (B) Discounted (B) Required

0 -$210,000.00 -$210,000.00 -$21,000.00 -$21,000.00

1 $15,000.00 $13,043.48 $11,000.00 $9,565.22

2 $30,000.00 $22,684.31 $9,000.00 $6,805.293 $30,000.00 $19,725.49 $11,000.00 $7,232.68

4 $370,000.00 $211,548.70 $9,000.00 $5,145.78

a. If you apply the payback criterion, which investment will you choose? Why?

Project A Payback 3.36 Years

Project B Payback 2.09 Years Project B

b. If you apply the discounted payback criterion, which investment will you choose? Why

Project A Payback 3.73 Years

Project B Payback 2.64 Years Project B

c. If you apply the NPV criterion, which investment will you choose? Why?

Project A NPV $57,001.98 Project A

Project B NPV $7,748.97

d. If you apply the IRR criterion, which investment will you choose? Why?

Project A IRR 22.97%

Project B IRR 32.73% Project B

e. If you apply the profitability index criterion, which investment will you choose? Why?

Profitability Index A 1.27

Profitability Index B 1.37 Project B

f. Based on your answers in (a) through (e), which project will you finally choose? Why?

Even though project B was deemed superior in all comparisons except for NPV,

Choose Project A. First, although project B wins with IRR and Profitability In

Second, the payback rules seem to indicate that Project B is superior, however,

that the NPV is so much higher for Project A, I would choose project A.

of these measures are not considered to be accurate forMutally Exclusive Proj


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eturn: 15%

ould be chosen because it has the smaller payback period

?

ould be chosen because it has the smaller dicounted payback period

ould be chosen because it has the higher NPV

ould be chosen because it has the higher IRR

ould be chosen because it has the higher Profitability Index

I would still

ex, both

due to the fact

cts.


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Portfolio Expected Return

Stock Expected Return Percent Invested

X 11% 50%

Y 17% 30%

Z 14% 20%

Expected Portfolio Return 13.4% Formula: Expected Return * Percent Invested


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Calculating Returns and Standard Deviations

Expected Return

Stock A

Recession 0.1 0.06 0.60% -2.10%

Normal 0.6 0.07 4.20% -1.10%

Boom 0.3 0.11 3.30% 2.90%

8.10%

Stock B

Recession 0.1 -0.2 -2.00% -35.70%

Normal 0.6 0.13 7.80% -2.70%

Boom 0.3 0.33 9.90% 17.30%

15.70%

State ofEconomy

Probability ofState ofEconomy

Rate of ReturnIf State Occurs

Return Deviationfrom ExpectedReturn

Expected Return

Stock A

Expected ReturnStock


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0.000441 0.0000441

0.000121 0.0000726

0.000841 0.0002523

0.000369 1.92% Stock A

0.127449 0.0127449

0.000729 0.0004374

0.029929 0.0089787

0.022161 14.89% Stock B

Squared ReturnDeviation fromExpected Return

Product ofProbabilityState ofEconomy andSquaredReturnDeviation

StandardDeviation

gmaSquaredDeviation

For Stock A

SquaredDeviationFor Stock B


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Calculating Portfolio Betas

Stock Beta

Q 25% 0.6R 20% 1.7

S 15% 1.15

T 40% 1.34

1.20 Sum of (Percent Portfolio * Beta) for each stock

PortfolioPercent

PortfolioBeta


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Using CAPM

Beta 1.3

14%

5%

16.70%

ExpectedMarketReturn

RiskFreeRate

ExpectedReturn

E(R i )=R f+[E(RM)R f ]i


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Using CAPM

6%

14%

4%

Beta 1.67

MarketRiskPremium

StockExpectedReturn

RiskFreeRate


i=E( Ri )

[ E( R M)


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therfore:

Denominator is Market Risk Premium

f

f ]


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Using CAPM

Beta 0.85

11%

6%

11.97%

Therefore:

StockExpectedReturn

RiskFreeRate

ExpectedReturn


E(RM)=[ E(Ri )Rf ]

i+Rf


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Financial Management Calculations