Robert Uberman, Financial Management, KA im Frycza Modrzewskiego 7

Robert Uberman, Financial Management, KA im Frycza ModrzewskiegoRobert Uberman, Financial Management, KA im Frycza Modrzewskiego

77


Session SeSession Seveven Topicsn Topics

Introducing interrelation between time and Introducing interrelation between time and money money

Discounting money streamsDiscounting money streams Key problems with proper discountingKey problems with proper discounting

Brealey, Myers: the chapter titled: “Present Value Brealey, Myers: the chapter titled: “Present Value … “ (pp. 11-56)… “ (pp. 11-56)


Time Value of MoneyTime Value of Money

1 USD today 1 USD today does notdoes not equal 1 USD equal 1 USD tomorrow!tomorrow!

FV = PV * (1+r)FV = PV * (1+r)nn where: where: r represents a returnr represents a return n represents number of periods (quite often n represents number of periods (quite often

years)years) PV = FV/ (1+r)PV = FV/ (1+r)nn


Theoretical fundaments of relation between Theoretical fundaments of relation between time and valuetime and value

Risk Risk of a return different from the planned one (Mind you: of a return different from the planned one (Mind you: also bigger also bigger !!!)!!!)

LiquidityLiquidity: investor converts cash, which is the most : investor converts cash, which is the most universal value transponder into less liquid assets universal value transponder into less liquid assets (Opportunity Cost of Capital),(Opportunity Cost of Capital),

Purchasing PowerPurchasing Power: universal (inflation, see Brealey, : universal (inflation, see Brealey, Myers, pp. 642-645), individual (ultimate goal in investing)Myers, pp. 642-645), individual (ultimate goal in investing)

Intrinsic value of money (per se)Intrinsic value of money (per se):– J.M. Keynes’ theory. :– J.M. Keynes’ theory.


CapitalisationCapitalisation

ttt rCFFV )1(0

FVFVt t – – Future Value of a given sumFuture Value of a given sum CFCF0 0 – – present value of a given sumpresent value of a given sum rrt t – – interest rate in period interest rate in period t t (most often annual)(most often annual) tt – – capitalisation periodcapitalisation period

Brealey, Myers pp. 11-56Brealey, Myers pp. 11-56


Capitalisation rateCapitalisation rate

tnt n

rCFFV )1(0

The most common way of expressing a capitalisation rate is The most common way of expressing a capitalisation rate is an annual one, marked withan annual one, marked with r r letterletter without without index tindex t

However quite often a real capitalisation period is different However quite often a real capitalisation period is different – interests are added to a capital after each month, quarter – interests are added to a capital after each month, quarter or so. Then the previously mentioned equitation is or so. Then the previously mentioned equitation is converted into:converted into:

Capitalisation rate 10%Present Value 1 000,00 Capitalisation period A 12 monthsValue after 1 year A 1 100,00 Capitalisation period B 1 monthValue after 1 year B 1 104,71


Key equationsKey equations

nn

r

CFPV

)1(

(1)

where:

CFn – Year n cash flow,

R – discount rate.

n – Subsequent year

It is useful to convert a discount rate into a discount factor:

nn rd

)1(

1

(2)

And then calculate Present Value as:

nn dCFPV (3)


Present Value as dependence on a discount Present Value as dependence on a discount raterate

Discount rate 8% 10% 12% 15% 20%

Discounting Period Present value of 50 000 USD due at the period’s end

PV,25 yrs 7 301 4 615 2 941 1519 524

PV,75 yrs 156 39 10 1,40 0,06

PV, infinity 0 0 0 0 0


Present Value as dependence on a discount Present Value as dependence on a discount raterate

Discount rate 8% 10% 12% 15% 20%

Discounting PeriodPresent value of 50 000 USD annuity for

the given period

PV,25 yrs

533

739

453

852

392

157

323

207

247 379

PV,75 yrs

623

054

499

607

416

582

333

324

250 000

PV, infinity

625

000

500

000

416

667

333

333

250 000


Various approaches to set an interest Various approaches to set an interest (discount) rate(discount) rate

There is a huge variety of theories and models covering the issue. There is a huge variety of theories and models covering the issue. The list below indicates a subjective selection of most commonly The list below indicates a subjective selection of most commonly used ones:used ones:

Alternative capital costAlternative capital cost Risk-free alternativeRisk-free alternative Debt costDebt cost WACCWACC Historical rate of returnHistorical rate of return Risk Adjusted Discount Rate (RADR)Risk Adjusted Discount Rate (RADR) Hurdle rateHurdle rate Social rate of returnSocial rate of return

Discount rate Discount rate quite often is presented as: quite often is presented as:

risk-free rate + risk adjustmentrisk-free rate + risk adjustment


Concept of riskConcept of risk

Financial and insurance meaning of riskFinancial and insurance meaning of risk Individual attitudes towards risk: Individual attitudes towards risk:

averse, averse, neutral, neutral, Seeker.Seeker.


HomeworkHomework

If the PV of 150 USD to be paid in one year is 130 USD, what is a discount rate? (Brealey, Myers, Chapter 2, Q 2)

You have come to a bank in order to make 1000 PLN deposit for 5 years, with 7% interest and half-year capitalisation (period). An financial advisor has stepped in with an offer of shares which over last 5 years period brought 40 % return. What would be your decision?


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Session Session EightEight Topics Topics

Investment vs Capital Budgeting Decisions Investment vs Capital Budgeting Decisions NPVNPV I(nternal) R(ate of) ReturnI(nternal) R(ate of) Return PIPI Payback (discounted)Payback (discounted)

Brealey, Myers: Chapter titled “Why Net Present Brealey, Myers: Chapter titled “Why Net Present Value Leads to Better Investment Decisions …” Value Leads to Better Investment Decisions …” (pp. 85-112)(pp. 85-112)


Investment vs. Capital Investment vs. Capital Budgeting DecisionsBudgeting Decisions

Investment = money committed or Investment = money committed or property acquired for future incomeproperty acquired for future income

Capital budgeting is planning capital Capital budgeting is planning capital outlays for purchasing new fixed assets to outlays for purchasing new fixed assets to get additional profit thus it means planning get additional profit thus it means planning investmentsinvestments

Intra-corporate investment process is Intra-corporate investment process is usually much more complicated ro evaluate usually much more complicated ro evaluate than financial investments (share, bonds) than financial investments (share, bonds) since cash flows are not easily definedsince cash flows are not easily defined


Examples of Capital Budgeting Examples of Capital Budgeting DecisionsDecisions

Equipment selection decisionEquipment selection decision.. Plant expansion aimed at:Plant expansion aimed at:

increase in sales;increase in sales; backward integration.backward integration.

Equipment replacement decision caused Equipment replacement decision caused by aging machine park.by aging machine park.

New equipment purchase aimed at cost New equipment purchase aimed at cost reduction.reduction.


Commonly used measures of Commonly used measures of investment efficiencyinvestment efficiency

Payback (straight)Payback (straight) I(nternal) R(ate of) ReturnI(nternal) R(ate of) Return NPVNPV PIPI Payback (discounted)Payback (discounted)


PaybackPayback (period) (period)

TheThe payback period estimates the time payback period estimates the time required to recover the principal amount required to recover the principal amount of an investment.of an investment.

It is often defined as a length of time It is often defined as a length of time needed for an investment's net cash needed for an investment's net cash receipts to cover completely the initial receipts to cover completely the initial outlay expended in acquiring the outlay expended in acquiring the investmentinvestment


Payback (example)Payback (example) A&B Enterprises is trying to select the best investment from among three A&B Enterprises is trying to select the best investment from among three

alternatives. Each alternative involves an initial investment of $100,000. alternatives. Each alternative involves an initial investment of $100,000. Their cash flows follow:Their cash flows follow:

Which investment will you select using the payback method? Why? (Brealey, Myers)

Year A B C

1 $ 10,000 $ 50,000 $ 25,000

2 $ 20,000 $ 40,000 $ 25,000

3 $ 30,000 $ 30,000 $ 25,000

4 $ 40,000 - $ 25,000

5 $ 50,000 - $ 25,000


Payback – key issuesPayback – key issues

What is an investment?What is an investment? Capital expenditureCapital expenditure Increase in NWCIncrease in NWC OtherOther

How one defines a pay back itself?How one defines a pay back itself? Net profit Net profit Net cash flowNet cash flow


Payback - limitationsPayback - limitations

The payback period method ignores: The payback period method ignores: any benefits that occur after the investment is repaid any benefits that occur after the investment is repaid the time value of moneythe time value of money

risk-free cost of moneyrisk-free cost of money riskrisk

Therefore payback period: Therefore payback period:

is useless for ranking purposesis useless for ranking purposes can be used only in relation to near certain can be used only in relation to near certain

flowsflows


NPVNPV


IRRIRR

IRR vs Yield to MaturityIRR vs Yield to Maturity IRR algorithmIRR algorithm IRR useIRR use Disadvantages of IRRDisadvantages of IRR


IRR - definitionsIRR - definitions


IRR vs NPVIRR vs NPV IRR:IRR:

can be calculated only if a cash flow break even only once – can be calculated only if a cash flow break even only once – which is typical for many simple investments;which is typical for many simple investments;

is directly comparable to benchmarks like interests on deposits;is directly comparable to benchmarks like interests on deposits; quite often is calculated simultaneously with NPVquite often is calculated simultaneously with NPV can be used as a ranking tool but with attention to various trapscan be used as a ranking tool but with attention to various traps

(see Brealey, Myers, pp. 94-101(see Brealey, Myers, pp. 94-101..

NPV NPV in practice it is calculated to get IRR;in practice it is calculated to get IRR; it can be applied to streams not to be assessed using IRR;it can be applied to streams not to be assessed using IRR; it can not be used as a ranking tool (unless all investments are it can not be used as a ranking tool (unless all investments are

equal)equal)


PI (Profitability Index)PI (Profitability Index)


Discounted Payback (Period)Discounted Payback (Period)

The discounted payback period estimates the time The discounted payback period estimates the time required to recover the principal amount of an required to recover the principal amount of an investment but applying discounting. investment but applying discounting.

It is often defined as a length of time needed for an It is often defined as a length of time needed for an investment's net cash receipts to cover completely investment's net cash receipts to cover completely the initial outlay expended in acquiring the the initial outlay expended in acquiring the investment with consideration of time value of investment with consideration of time value of money concept.money concept.

It is quite often used as an indicator of a risk levelIt is quite often used as an indicator of a risk level


HomeworkHomework

An owner of a successful retail business of a traditional handmade An owner of a successful retail business of a traditional handmade wool clothes in Krynica considers opening a new outlet in Warsaw. wool clothes in Krynica considers opening a new outlet in Warsaw. There are two options as far as location is concerned and they can There are two options as far as location is concerned and they can be characterised as stated below in terms of key economic be characterised as stated below in terms of key economic parameters. Please select the most efficient one using measures parameters. Please select the most efficient one using measures presented before. Apply 15 % discount/hurdle rate when needed.presented before. Apply 15 % discount/hurdle rate when needed.

Location(PLN)

Cost/month

Monthly turnover

Mark up

Days in stock

Days payable

Initial investment

Premium 10 000

50 000 50 % 30 60 90 000

Subarbian

6 000

35 000 30 % 45 60 30 000

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Robert Uberman, Financial Management, KA im Frycza Modrzewskiego 7