fina2303 topic 02 time value of money and valuation

8/18/2019 FINA2303 Topic 02 Time Value of Money and Valuation

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Topic 2: Time Value of Money and

Valuation


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Topic 2 Time Value of Money and Valuation M K Lai Page 2

Learning Outcomes

cost-benefit analysis

valuation principletime value of moneyfuture value and compoundingpresent value and discountingcash flow streams

annuities and perpetuitiescompounding frequency

interest rate quotes


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Learning Outcomes

application: discount rates and loans

determinants of interest ratesopportunity cost of capital


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Cost-Benefit Analysis

a financial manager needs to identify the costsand benefits of a financial decision in terms ofcash flows

costs as cash outflows

benefits as cash inflowshe needs the help of the other departments (suchas marketing, production, etc.) to quantify the

costs and benefitscost-benefit analysis helps him make the bestfinancial decision among a number of

alternatives



Cost-Benefit Analysis

when benefits exceed costs, it adds value to acompany and hence increases its shareholders’wealth



Role of Competitive Market Price

a competitive market is a market in which a goodcan be bought and sold at the same “market”price

in a competitive market, the market pricedetermines the value of a good (value inexchange) – which has nothing to do with thepersonal preferences of a consumer (value in use)or his assessment of its fair value

what do you do if the market price of an item

is $10 and its assessed fair value is $12?



Role of Competitive Market Price

source: ABCI Securities

fair value of stockstock price



Role of Market Price

in finance, we are more concerned with marketvalue of an item than its book value in thefinancial statements

e.g. a concert ticket with a face value of $100

can be sold at $250 in the marketthe book value is $100the market value is $250



Valuation Principle

“The value of a commodity or an asset to the firmor its investors is determined by the competitivemarket price . The benefits and costs of a decisionshould be evaluated using those market prices.

When the value of the benefits exceeds the valueof the costs, the decision will increase the marketvalue of the firm .”


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Example: Valuation Principle

You are the operations manager of a firm. Due toa pre-existing contract, you have the discretion todecide whether to acquire 200 barrels of oil for$16,000. The current market price of oil is $90

per barrel. You believe that the value of oil wouldplummet to $70 over the next month. Should youor should you not buy the oil at the contract price

of $16,000?


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Example: Valuation Principle

market value of 200 barrels of oil (benefit) = .

cost = .

decision: .

$16,000

$18,000

buy 200 barrels


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Law of One Price and Arbitrage

law of one price (no-arbitrage condition) : incompetitive markets, securities with the samecash flows (and risk) should have the same pricearbitrage : the practice of simultaneous buying

and selling equivalent goods in two markets totake advantage of a price discrepancy (buy low,sell high)

arbitrage opportunity : any situation in which it ispossible to make a profit without taking any riskor making any investment

may take time


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Given that there are no transaction costs, an itemis sold at $1,000 in one market and $1,200 inanother market, what do you do?

1.

2.

3.

buy it at $1,000

resell it at $1,200

make a profit of $200


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if a lot of people rush to buy in the undervaluedmarket , the market price will rise

if a lot of people rush to sell in the overvalued

market , the market price will fall

sooner or later, the market prices will converge tothe same level and the law of one price holdsagain

does not hold


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source: The Economist


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Time Value of Money

cash flows appear to have different values to us ifthey occur in different time periods


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Time Value of Money

which of the following options do you choose?

receive $10,000 right away

will receive $10,000 in a year’s time


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Why Time Value of Money?

a dollar received today is worth more than adollar received later

better to receive money earlier and pay later

why?1.

2.

inflation

deferred consumption


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Effect of Inflation

inflation refers to a rise in general price levelit leads to a decline in the purchasing power ofmoney , i.e. the same amount of cash flows underinflation cannot buy the same quantity of goodsas the case without inflation

for example, you have $1,000if the price of an item is $100 each, you can

buy 10 unitsif the price of an item increases to $200each due to inflation, you can buy only 5

units


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Effect of Inflation

inflation rate : the change in the average pricelevel of a basket of goods over a period, usuallymeasured through the consumer price index (CPI)

consumer price index (CPI) is a measure of theaverage price of a basket of consumer goods andservices purchased by households

inflation rate at time t = (CPI at time t – CPI at

time t-1)/CPI at time t-1


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Example: Inflation Rate

source: Census andStatistics Department

inflation rate = (120.2-

115.1)/115.1 = 4.43%


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Example: Nominal and Real Interest

RatesIf the nominal interest rate on a financialinstrument is 5% and the expected inflation rateis 3%, what is the real interest rate?

real interest rate = (1+5%)/(1+3%) – 1 = 1.94%

real interest rate ≈ 5% - 3% = 2%


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Inflation

nowsource: hongkong.coach.com

inflation rate= 10%

in a year’s timesource: hongkong.coach.com


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Deferred Consumption

given that inflation rate = 0%

if we receive cash flows now, we can consumeright away ( current consumption )if we will receive cash flows in a year’s time,

we can only consume in the future ( futureconsumption )

other things being equal, people prefer toconsume now to later (time preference )


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that is why we demand for a rate of return or aninterest rate on an investment because we haveto postpone the current consumption to a laterperiod


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receive $4,400now

source: hongkong.coach.com

inflation rate= 0%

for a wholeyear!

will receive $4,400 in ayear’s time

source: ho ngkong.coach.com

H t C C h Fl i Diff t


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How to Compare Cash Flows in Different

Time Periods?which of the following options do you choose?

receive $10,000 right away

will receive $10,300 in a year’s time

what additional information is required to make adirect comparison?

H t C C h Fl i Diff t


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Time Periods?the trick is to convert all cash flows into acommon benchmark through interestrate/discount rate

present value : the value of a cash flowcomputed in terms of cash today

future value at a specified future date N: thevalue of a cash flow that is moved forward in

time to date N

Ho to Comp re C sh Flo s in Different


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Time Periods?interest rate or discount rate is the rate at whichmoney can be borrowed or lent over a givenperiodthe process of converting a future value into a

present value is known as discountingthe process of converting a present value into afuture value is known as compounding

present

value

future

value

discounting

compounding



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Time Periods?rule 1: it is only possible to compare or combinevalues at the same point in time

rule 2: compound a cash flow to calculate its

future value

rule 3: discount a cash flow to calculate itspresent value


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Timeline of Cash Flows

…0 1 2 N-2 N-1 N

-$100 $5 $5 $5 $5 $105

period

cashflow

now end of

period 2

beginning

of period 3

cashoutflow

cashinflows


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Present Value and Future Value

where PV = present value; FV N = future value at

time N; r = interest rate or discount rate and N =number of years(1+r) N is called the interest rate factor for N years

1/(1+r) N is called the discount factor for N yearsmathematically, as long as we know three out ofthese four variables (PV, r, N and FV N), we candetermine the fourth one

( ) NNN

N

)r1(

FVPVorr1*PVVF

+

=+=


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Future Value in a Single Period

suppose that the annual interest rate is 2%receive $10,000 now = will receive$10,000*(1+2%) = $10,200 in a year’stime = future value in a year’s time

will receive $10,300 in a year’s time =future value in a year’s time

decision : choose over0 1

$10,000

$10,300

year

cash flow

cash flow

$10,200


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Present Value in a Single Period

suppose that the annual interest rate is 2%

receive $10,000 now = present valuewill receive $10,300 in a year’s time =receive $10,300/(1+2%) = $10,098.04 now

= present valuedecision : choose over

0 1

$10,000

$10,300

year

cash flow

cash flow $10,098


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Simple Interest Rate

simple interest rate : earn interest on originalprincipal, e.g. principal = $10,000, simpleinterest rate = 3%

interest in year 1 = $10,000*3% = $300principal + total interest = $10,000*(1+3%) =$10,300interest in year 2 = $10,000*3% = $300principal + total interest in year 2 =

$10,000*(1+3%*2) = $10,600


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Simple Interest Rate

interest in year 3 = $10,000*3% = $300principal + total interest in year 3 =$10,000*(1+3%*3) = $10,900…


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Compound Interest Rate

compound interest rate : earn interest on theoriginal principal and interest on interest , e.g.principal = $10,000, compound interest rate =3%

interest in year 1 = $10,000*3% = $300principal + total interest over 1 year =$10,000*(1+3%) = $10,300

interest in year 2 = $10,000*3% + $300*3%= $309 ($300*3% = $9 is the interest oninterest effect)


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Compound Interest Rate

principal + total interest over two years =$10,000*(1+3%) 2 = $10,609interest in year 3 = $10,000*3% + $300*3%+ $309*3% = $318.27 ($300*3% + $309*3%

= $18.27 is the interest on interest effect)principal + total interest over three years =$10,000*(1+3%) 3 = $10,927.27…

the interest on interest effect is also called thecompounding effect


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Example: The Power of Compounding


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Example: The Power of CompoundingEffect

initial investment =$10,000; annual

interest rate = 5%;annual compounding

$0$20,000

$40,000$60,000

$80,000

$100,000

$120,000

0 10 20 30 40 50

accumulated wealth ($)

investment horizon (years)

$26,533$43,219

$70,400

$114,674

$16,289

Present Value and Future Value in More


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Than One Year

for long term investment, the investment horizonis usually longer than 1 year and we still use thesame basic formula where N > 1

where PV = present value; FV N = future value at

time N; i = interest rate and N = number of years

( ) NNN

N )r1(FV

PVorr1*PVVF +=+=

E l P V l


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Example: Present Value

You want to accumulate a wealth of $500,000 in10 year’s time so that you can afford to make thedown payment for a mortgage. If the interestrate is 5% and it is compounded on an annualbasis, how much do you need to put aside now?

63.956,306$%)51(000,500$

PV 10 =+

=

…0 1 2 8 9 10

$500,000

year

$306,957

E l F t V l


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Example: Future Value

You put $100,000 in a time deposit account forthree years with an interest rate of 3% perannum. If it is compounded on an annual basis,what will be the principal plus interest in threeyears’ time?

70.272,109$%)31(*000,100$FV 33 =+=

0 1 2

$100,000

year 3

$109,273

D t i i g th I t t R t


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Determining the Interest Rate

if we know about the present value, the futurevalue and the investment horizon, we candetermine the interest rate or the rate of returnon the investment

example: If the present value and future value inyear 3 are $100,000 and $135,000 respectively,

what is the interest rate?

%52.10r

)r1(*000,100$000,135$ 3

=

+=

Determining the In estment Hori on


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Determining the Investment Horizon

if we know about the present value, the futurevalue and the interest rate, we can determine theinvestment horizon

example: You have a lump sum of $50,000. Theinterest rate is 6% and it is compounded on anannual basis. Your financial objective is to save

$200,000 for your wedding. How many yearsdoes it take for your wedding to take place?

years79.23N

%)61(*000,50$000,200$ N

=

+=

Multiple Cash Flows Over Time:


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Additivity Principle

cash flows in the same time period t can beadded up or subtracted one from the other andthis is known as the additivity principle

the present value of the cash flow stream isthe sum of the present values of the individualcash flows over time

∑=

+=

N

1tt

t

)r1(C

PV

Multiple Cash Flows Over Time:


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Additivity Principle

the future value of the cash flow stream attime N is the sum of the future values of theindividual cash flows over time at time t

∑=−

+=

N

1t

tN

tN )r1(*CFV



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The winner of America’s Got Talent will get$1,000,000 in 40 annual installments, i.e.$25,000 annually in each of the coming 40 years.If the annual interest rate is 6%, what is thepresent value of this cash flow stream?

…0 1 2 38 39 40

$25,000

year

$25,000 $25,000 $25,000$25,000

$376,157

∑=

=+

=

40

1tt 42.157,376$%)61(

000,25$PV



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source: www.realityblurred.com



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You have just bought a financial instrumentwhich expects to generate $1,000, $1,000 and$11,000 in years 1, 2 and 3 respectively, e.g. a 3-year bond. If the interest rate is 4% and it iscompounded on an annual basis, what is thefuture value of this cash flow stream in year 3?

6.121,13$

000,11$%)41(*000,1$%)41(*000,1$FV 23

=

++++=

0 1 2

$1,000

year 3

$1,000 $11,000

$13,122

Special Cash Flow Patterns


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Special Cash Flow Patterns

annuity : a level stream of cash flows starting inyear 1 for a fixed period of time

perpetuity : an annuity in which the cash flowscontinue indefinitely

non-growing perpetuity : a constant stream of

cash flows that lasts forever

growing perpetuity : a growing stream of cash

flows at a constant rate that lasts forever

Annuity


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Annuity

5-year annuity with a constant cash flow of $100

0 1 2 3 4 5

$100 $100 $100 $100 $100

year

]1)r1[(*r1

*CFV

)r1( 11*r1*CPV

N

N

N

−+=

+−=

where FV N = future value at N; PV = present value;r = interest rate; N = number of years; C =constant cash flow in each year

Retirement Annuity Plan


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Retirement Annuity Plan

source: HSBC

Example: Present Value and Future


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Value of Annuity

Suppose that you are saving $100 at 5% in eachof the coming 5 years as an annuity. What is thepresent value of the annuity? What is the futurevalue of the annuity in year 5?

56.552$]1%)51[(*5%1*100$FV

95.432$%)51(

11*5%1*100$PV

55

5

=−+=

=+

−=

Example: Annuity Amount


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Example: Annuity Amount

If you borrow a loan of $100,000 at an annualinterest rate of 12% and have to repay it in fiveequal annual payments, what is the annuityamount of your payment? This is called anamortized loan.

97.740,27$C

%)121(1

1*12%

1*C000,100$ 5

=

+−=

C in an annuity is usually denoted by PMT in a

financial calculator or spreadsheet

Example: The Number of Payments


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Example: The Number of Payments

You have a credit balance of $10,000 on yourcredit card. You can only afford to pay theminimum payment of $200 per month. Theinterest rate on the credit card is 1.5% per month.How long will you need to pay off the credit?

years7.76ormonths11.93N%)5.11(

11*

1.5%1

*200$000,10$ N

=

+−=

Example: The Interest Rate


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p

An insurance company offers to pay you $10,000per year for 10 years if you will pay $70,000upfront. What rate is implicit in this 10-yearannuity policy?

%07.7r

)r1(11*

r1*000,10$000,07$ 10

=

+−=

Growing Annuity


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g y

5-year annuity with a first year cash flow of $100growing at 3%

0 1 2 3 4 5

$100 $103 $106.69 $109.27 $112.55

year

Growing Annuity


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g y

[ ]NN1N

N

1

)g1()r1(*

g -r

1*CFV

r1

g11*

g -r

1*CPV

+−+=

+

+−=

where FV N = future value at N; PV = present value;

r = interest rate; N = number of years; C 1 = cashflow in year 1

Example: Present Value and FutureV l f G i g A it


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Value of Growing Annuity

Suppose that you will start to save money in eachof the coming 5 years at an interest rate of 5%.In the first year, the saving is $100 which isexpected to grow at 3% in each year. What is thepresent value of the growing annuity? What is thefuture value of the growing annuity in year 5?

04.585$]*)31(%)51[(*3% -5%

1*100$FV

39.458$%51

%311*

3% -5%

1*100$PV

555

5

=+−+=

=

+

+−=

Perpetuity


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p y

non-growing perpetuity with a constant cash flowof $100

0 1 2 3 4

$100 $100 $100 $100

year …

…

growing perpetuity with a first year cash flow of$100 at a growth rate of 3% (discount rate >growth rate)

0 1 2 3 4

$100 $103 $106.69 $109.27

year …

…

Perpetuity


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g -r

CPV:perpetuitygrowing

rC

PV:perpetuitygrowing -non

1

1

=

=

where PV = present value; C 1 = cash flow in year1; r = interest rate; g = constant growth rate

Perpetual Bond


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source: Cbonds

Example: Non-Growing Perpetuity


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Suppose that you are receiving $100 each yearindefinitely. What is the present value of thiscash flow stream if the interest rate is 5%?

PV = $100/5% = $2,000

Example: Growing Perpetuity


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Suppose that you are receiving $100 next yearwhich will grow at an annual rate of 3%indefinitely. What is the present value of thiscash flow stream if the interest rate is 5%?

PV = $100/(5%-3%) = $5,000

Interest Rates in Financial Market


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different terminologies , e.g. interest rate,discount rate, yield, cost of capital, required rateof return, etc.

cost of using funds to a company

rate of return to an investor

usually annualized in percentage with atenor/(term to) maturity

interest income

cost of capital

of investing funds

interest rate will be affected by the term to maturity



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there are many interest rates in the financialmarkets, e.g. saving rate, 3-month time depositrate, prime rate, Hong Kong Interbank OfferedRate (HIBOR), base rate, etc.

interest rate reflects time value of money andrisk of an investment

interest rate with riskinterest rate usually over time

increase

total return: interim income:

increases



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change continuously depending on demand andsupply of funds in financial markets

demand for funds increase s, interest rate .

supply of funds increases , interest rate .decrease

increase

Demand And Supply Analysis of InterestRate


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Rate

consider the good as “availability of funds, F” andthe price as “(market) interest rate, r”

F

rS

Dr*

F*



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Rate

discuss the effect of the following factors on theinterest rate and the availability of funds in the

financial market

the central bank injects funds into the financialmarket

business organizations want to borrow moreloans as they expect better economic outlook



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Rate

F

iS

D0i0

F0

i1

F1

D1

F

iS0

D

i0

F0

S1

i1

F1

Annual Percentage Rate (APR)


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in the US

APR: the amount of interest earned in one yearwithout the compounding effect (simple

interest earned)

also called flat or quoted interest rate

monthly quoted rate = 1%; APR = 1%*12 =

12%

compound monthly basis --> 12 months



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in Hong Kong

APR: the amount of interest earned in a year,which is calculated based on Code of Banking

Practice

similar to effective annual rate to makepresent value of all relevant cash flows equalto zero

close to the actual interest rate you are paying

(consider compounding effect)

(including bank fees andcharges)



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source: DBS

APR in US = 0.31%*12 = 3.72%

APR in HK

Compounding Frequency


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the compounding frequency will affect the cashflows generated

rules for non-annual cash flows

the interest rate is specified as a periodic rate,e.g. monthly interest rate if it is compoundedon a monthly basisthe investment horizon is expressed in termsof the number of periods, e.g. 36 months if it iscompounded on a monthly basis

(divide US APR/12-->monthly interest rate)

for 3 years

Compounding Frequency


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mNN

mN

N

)m /APR1(FV

PVm

APR1*PVVF

+=

+=

where PV = present value; FV N = future value attime N; APR = annual percentage rate (in US); m

= number of periods in a year and N = number ofyears

half year-->2quarterly-->4monthly-->12

Effective Annual Rate (EAR)


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(1+APR/m) m - 1 is known as the effective annualrate (EAR) or annual percentage yield (APY)

show the actual interest rate you are paying ina year where APR/m is the periodic quotedrate, e.g. on a month basis, m = 12 and themonthly quoted rate = APR/12

in hk--> bank fees and charges are considered in EAR but notAPR

Example: Compounding Frequency


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suppose that the principal is $10,000, the quotedannual interest rate is 6% and the investment

horizon is 1 yearannual compounding

FV1 = $10,000*(1+6%) = $10,600annual flat rate = 6%EAR = (1+6%) – 1 = 6%

semi-annual compoundingFV1 = $10,000*(1+6%/2) 2*1 = $10,609semi-annual flat rate = 6%/2 = 3%

EAR = (1+6%/2) 2 – 1 = 6.09%

in US, EAR and APR arethe same if compund inannual basis

600-->interest

9-->interest on interesteffect

Example: Compounding Frequency


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quarterly compoundingFV1 = $10,000*(1+6%/4) 4*1 = $10,613.64quarterly flat rate = 6%/4 = 1.25%EAR = (1+6%/4) 4 – 1 = 6.14%

monthly compoundingFV1 = $10,000*(1+6%/12) 12*1 = $10,616.78

monthly flat rate = 6%/12 = 0.5%EAR = (1+6%/12) 12 - 1 = 6.17%

Example: Compounding Frequencyborrow loan****


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daily compoundingFV1 = $10,000*(1+6%/365) 365*1 =$10,618.31daily flat rate = 6%/365 = 0.02%

EAR = (1+6%/365)365

– 1 = 6.18%

continuous compoundingFV1 = $10,000*e 6%*1 = $10,618.36EAR = e 6%*1 - 1 = 6.18% (highest)

Equivalent n-Period Discount Rate


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equivalent n-period discount rate = (1+r) n – 1where n can be larger than 1 or less than 1 and r

= effective annual rate

when computing present value or future value,we should adjust the discount rate to matchthe time period of the cash flows

e.g. investment horizon: 3years,, total interest rate you earn?

n=3


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Application: Amortizing Loan(popular in HK) tax loan


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a bank loan is a major source of finance to acompany and whenever a bank grants a loan to a

borrower, some provision will be made for thepayment of interest and repayment of theprincipal

the borrower has to pay regular interestcalculated based on the beginning balance of theloan and repay parts of the principal amount over

time, usually quoted in APR e.g. tax loan,mortgage loan, and it is called an amortized loaninterest payments over time (why?)

principal repayments over time (why?)

decline

increase

Application: Amortizing Loan


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the cash flow stream is an annuity of even cashpayment of C in each period lasting for N periods

0 1 2 3 N-1 N

-C -C -C -C -C

year

loanbalance

…

usually, the credit officer of a bank prepares aloan amortization schedule to show a client therepayment schedule

Tax Loan


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source: DBS

Example: Loan Amortization Schedule


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Consider an amortized $50,000, two-year loan atan interest rate of 12%. Suppose that interest

payments are made on a monthly basis.

the first step is to determine the 24-monthannuity (monthly interest rate = 12%/12 = 1%)

67.353,2$C

%)11(1

1*1%1

*C000,50$ 24

=

+−=

every month



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the second step is to prepare the loanamortization schedule

increasing over timedecreasing over time

monthbeginning

loan balancemonthlypayment

interest payment =beginning loan balance *

monthly interest rate

principal repayment =monthly payment -interest payment

ending loan balance =beginning loan balance -

principal repayment1 $50,000.00 $2,353.67 $500.00 $1,853.67 $48,146.332 $48,146.33 $2,353.67 $481.46 $1,872.21 $46,274.12

3 $46,274.12 $2,353.67 $462.74 $1,890.93 $44,383.184 $44,383.18 $2,353.67 $443.83 $1,909.84 $42,473.345 $42,473.34 $2,353.67 $424.73 $1,928.94 $40,544.406 $40,544.40 $2,353.67 $405.44 $1,948.23 $38,596.177 $38,596.17 $2,353.67 $385.96 $1,967.71 $36,628.46

8 $36,628.46 $2,353.67 $366.28 $1,987.39 $34,641.079 $34,641.07 $2,353.67 $346.41 $2,007.26 $32,633.81

10 $32,633.81 $2,353.67 $326.34 $2,027.34 $30,606.4711 $30,606.47 $2,353.67 $306.06 $2,047.61 $28,558.8612 $28,558.86 $2,353.67 $285.59 $2,068.08 $26,490.78

i=1%



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increasing over timedecreasing over time

monthbeginning

loan balancemonthlypayment

interest payment =beginning loan balance *

monthly interest rate

principal repayment =monthly payment -interest payment

ending loan balance =beginning loan balance -

principal repayment

13 $26,490.78 $2,353.67 $264.91 $2,088.77 $24,402.0114 $24,402.01 $2,353.67 $244.02 $2,109.65 $22,292.3615 $22,292.36 $2,353.67 $222.92 $2,130.75 $20,161.6116 $20,161.61 $2,353.67 $201.62 $2,152.06 $18,009.5517 $18,009.55 $2,353.67 $180.10 $2,173.58 $15,835.9718 $15,835.97 $2,353.67 $158.36 $2,195.31 $13,640.6619 $13,640.66 $2,353.67 $136.41 $2,217.27 $11,423.3920 $11,423.39 $2,353.67 $114.23 $2,239.44 $9,183.9521 $9,183.95 $2,353.67 $91.84 $2,261.83 $6,922.1222 $6,922.12 $2,353.67 $69.22 $2,284.45 $4,637.6723 $4,637.67 $2,353.67 $46.38 $2,307.30 $2,330.3724 $2,330.37 $2,353.67 $23.30 $2,330.37 $0.00



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$0$5,000

$10,000

$15,000$20,000$25,000$30,000$35,000

$40,000$45,000$50,000

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24months

ending loan balance



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$0

$500

$1,000

$1,500

$2,000

$2,500

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

interest payment principal repayment

months

Opportunity Cost of Capital


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(opportunity) cost of capital : the best availableexpected return offered in the market on an

investment of comparable risk and term to thecash flow being discounted

it can also refer to the return an investorforegoes on an alternative investment ofequivalent risk and term when the investortakes on a new investmentit is the relevant interest rate used for aninvestment under consideration

Example: Opportunity Cost of Capital


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Suppose that you are considering making aninvestment of $100 in a financial instrument

which generates a return of $110 in a year’s time.An alternative investment available in the marketoffers a rate of return of 12% with the same risklevel. What do you do?



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rate of return on financial instrument = ($110-$100)/$100 = 10%

10% < the expected return of 12% on thealternative investment (opportunity cost ofcapital)

better not to invest in the financial instrumentand invest in the alternative investment



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alternatively, use the opportunity cost of capitalas discount rate and present value of financial

instrument = $110/(1+12%) = $98.21

no good to invest $100 in a financialinstrument with a present value of $98.21

better not to invest in the financial instrument,but to invest in the alternative investment

Notice


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so far, we assume that the interest rate ordiscount rate is constant over time

in reality, it can vary with the investment horizon;usually it increases with the investment horizon

Challenging Questions


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1. In financial principle, how important are ourpersonal preferences in valuing an investment

decision?2. Given that the exchange rate is CNY 10 for HKD

11.50. If the stock of Company XYZ sells at CNY10 in the A share market in Mainland China andsells at HKD 11.86 in Hong Kong. What do youdo to take advantage of the arbitrageopportunity ? sell CNY10 for HKD11.86,buy HKD11.5

0.36


h b k


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4. Give two reasons why arbitrage may not work inreal life.

A.B.

5. The value of a dollar today relative to the valueof a dollar in a year’s time tends to increase ifpeople put a weight on currentconsumption relative to future consumption and

the inflation rate is .6. If the observed interest rate of a security is 5%

and the expected inflation rate is 3%, what isthe nominal interest rate of the security? Explain.

govt restriction, the Exchangetransaction cost

positive

heavier


increase


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6. Nominal interest rate tends to with theexpected inflation rate . Who will benefit from a

higher inflation rate, the borrower or lender of aloan?

7. When the interest rate rises , the interest ratefactor is , the discount factor is and thepresent value is .

increase

higherlower

lower


f d $ h


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8. If a depositor puts $10,000 in a three-year timedeposit account and the annual compound

interest rate is 3%, what are the conditionsunder which the depositor can really earn the3% annual compound interest rate ?

A.B.

9. The present value of a future cash flow is higherif the interest rate is and the investmenthorizon is .

lower

keep all cash flows in the bank account

shorter

until the end of your investment horizon


10 If ’ i h f $1

True, because of compounding effects—growth on growth.


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10.If a company’s earnings per share grew from $1to $2 over a 10-year period, the total growth

would be 100%, but the annual growth ratewould be less than 10%. True or false? Explain.

11.Other things being equal, a borrower would liketo pay a interest rate on a loan while anlender would like to receive a interest ratefrom an investment. A borrower wants thecompounding frequency to be and a lenderwants the compounding frequency to be .

higher

lower

larger

smaller


12 Whi h f th f ll i fi i l i t t


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12.Which of the following financial instrumentshould offer the highest interest rate ?

A. the maturity is 10 years and the risk is lowB. the maturity is 5 years and the risk is low

C. the maturity is 10 years and the risk ishighD. the maturity is 5 years and the risk is high

13.Other things being equal, which is higher, APRor EAR? Explain why. Which is more relevant forfinancial decisions? compounding effect


14 I i f i t l


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14.In view of a recessionary economy, a centralbank may use an expansionary monetary policy

to stimulate it. It usually the money supplyso as to the general interest rate level. Insuch an interest rate environment, consumption

and investment tend to .

increase

lower

increase


15 An investment is expected to generate a rate of


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15.An investment is expected to generate a rate ofreturn of 16%. There are three alternative

investments with the same risk and the subjectinvestment with an expected rate of return of14%, 12% and 10% respectively in the market.

What is the opportunity cost of capital of thesubject investment?

14%--> highest valued option forgone

fina2303 topic 02 time value of money and valuation

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