last study topics opportunity cost of capital – rate of an alternative investment opportunity...

Last Study Topics

• Opportunity Cost of Capital– Rate of an Alternative investment opportunity

having a similar risk.

• Investment vs. Consumption– Manager finds it difficult to reconcile the different

objectives of the shareholders.

11/16/2014 Instructor: Mr. Wajid Shakeel Ahmed

Topics Covered

• Calculations of NPV & ROR• Managers and the Interests of Shareholders• Fundamental Study Result• Valuing Long-Lived Assets• PV Calculation Short Cuts

Calculation of NPV and ROR• The opportunity cost of capital is 20 percent for all four

investments.Initial Cash Cash Flow

Investment Flow, C0 in Year 1, C11 10,000 18,0002 5,000 9,0003 5,000 5,7004 2,000 4,000

a. Which investment is most valuable?b. Suppose each investment would require use of the same parcel of land. Therefore you can take only one. Which one?


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• Answer to question ‘a’; – Investment 1, since this investment with respect

to others has generate highest NPV with Max rate of return.

• Answer to question ‘b’; – Investment 1, since this investment with respect

to others has highest contributed net value.


Decision Rules

• Here then we have two equivalent decision rules for capital investment;

– Net present value rule; Accept investments that have positive net present values.

– Rate-of-return rule; Accept investments that offer rates of return in excess of their opportunity costs of capital.


Fundamental Result• Our justification of the present value rule was

restricted to two periods and to a certain cash flow.

• However, the rule also makes sense for uncertain cash flows that extend far into the future. The argument goes like this:

• 1- A financial manager should act in the interests of the firm’s owners, its stockholders.


Continue• 2- Stockholders do not need the financial

manager’s help to achieve the best time pattern of consumption.

• 3- How then can the financial manager help the firm’s stockholders? – There is only one way: by increasing the market

value of each stockholder’s stake in the firm.


Continue• Despite the fact that shareholders have

different preferences, they are unanimous in the amount that they want to invest in real assets.

• This means that they can cooperate in the same enterprise and can safely delegate operation of that enterprise to professional managers.


Continue• These managers do not need to know

anything about the tastes of their shareholders and should not consult their own tastes.

• Their task is to maximize net present value. If they succeed, they can rest assured that they have acted in the best interest of their shareholders.


Managers and Shareholder Interests

• Do managers really looking after the interests of shareholders?

• This takes us back to the principal–agent problem.

– Several institutional arrangements that help to ensure that the shareholders’ pockets are close to the managers’ heart.


Continue• Utilizing their Voting power;– If shareholders believe that the corporation is

underperforming and that the board of directors is not sufficiently aggressive in holding the managers to task, they can try to replace the board in the next election.

• E.g; chief executives of Eastman Kodak, General Motors, Xerox, Lucent, Ford Motor, etc were all forced to step aside.


Continue• As a result the stock price tumbles. – This damages top management’s reputation and

compensation.• Part of the top managers’ paychecks comes

from bonuses tied to the company’s earnings or from stock options, which pay off if the stock price rises but are worthless if the price falls below a stated threshold. – This should motivate managers to increase

earnings and the stock price.


Continue• If managers and directors do not maximize

value, there is always the threat of a hostile takeover.

• The further a company’s stock price falls, due to lax management or wrong-headed policies, the easier it is for another company or group of investors to buy up a majority of the shares.– The old management team is then likely to find

themselves out on the street and their place is taken by a fresh team.


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• Should managers look after the interests of shareholders?

• For this question we need to understand that In most instances there is little conflict between doing well (maximizing value) and doing good.– Profitable firms are those with satisfied customers

and loyal employees and vice versa;


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• Ethical issues do arise in business as in other walks of life.– when we say that the objective of the firm is to

maximize shareholder wealth, we do not mean that anything goes.

• In business and finance, as in other day-to-day affairs, there are unwritten, implicit rules of behavior.

• To work efficiently together, we need to trust each other.


How to Calculate Present Values

Principles of Corporate FinanceBrealey and Myers Sixth Edition

Chapter 3

©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill11/16/2014 Instructor: Mr. Wajid Shakeel Ahmed

Present Values

Discount Factor = DF = PV of $1

Discount Factors can be used to compute the present value of any cash flow.


Present Values

Discount Factor = DF = PV of $1


DFr t

1

1( )


Present Values


DFr t

1

1( )

1

11 1 r

CCDFPV


Present Values

Replacing “1” with “t” allows the formula to be used for cash flows that exist at any point in time.

t

tt r

CCDFPV

1


Present ValuesExample

Suppose you will receive a certain cash inflowof $100 next year (C1 = $100) and the rate of interest on one-year U.S. Treasury

notes is 7 percent (r1 = 0.07). What would be the present value of Cash inflow ?

94$)07.1(100

)1(1 rCPV



Suppose you will receive a certain cash inflowof $100 in two year (C2 = $100) and the rate of interest on two-year U.S. Treasury

notes is 7.7 percent (r1 = 0.077). What would be the present value of year 2 Cash inflow ?

21.86$)077.1(100

)1(1 rCPV



You just bought a new computer for $3,000. The payment terms are 2 years same as cash. If you can earn 8% on your money, how much money should you set aside today in order to make the payment when due in two years?



You just bought a new computer for $3,000. The payment terms are 2 years same as cash. If you can earn 8% on your money, how much money should you set aside today in order to make the payment when due in two years?

PV 30001 08 2 572 02

( . )$2, .


Present Values PVs can be added together to evaluate

multiple cash flows.

PV C

r

C

r

1

12

21 1( ) ( )....


Present Values PVs can be added together to evaluate

multiple cash flows, and called as discounted cash flow or (DCF) formula;

tt

t

rCPV

)1(


Present Values• If a dollar tomorrow is worth less than a

dollar today, one might suspect that a dollar the day after tomorrow should be worth even less.

• But, lets assume - given two dollars, one received a year from now and the other two years from now, the value of each is commonly called the Discount Factor. Assume r1 = 20% and r2 = 7%.


Present Values• Given two dollars, one received a year from now

and the other two years from now, the value of each is commonly called the Discount Factor. Assume r1 = 20% and r2 = 7%.

87$.

83$.

2

1

)07.1(00.1

2

)20.1(00.1

1

DF

DF


Continue• If First we lend $1,000 for one year at 20

percent, we have;– FV = PV (1+rt)t

=

• Go to the bank and borrow the present value of this $1,200 at 7 percent interest, we have;– PV = FV / (1+rt)t

=


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• If we going to find out the net present value of our investment we get,

– NPV = PV – Investment = $1121 - $1200

“Just imagine in this game of lending and borrowingHow much money you can earn without taking risks”


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• Of course this story is completely fanciful.– “There is no such thing as a money machine.”

• In well-functioning capital markets, any potential money machine will be eliminated almost instantaneously by investors who try to take advantage of it.



Assume that the cash flows from the construction and sale of an office building is as follows. Given a 7% required rate of return, create a present value worksheet and show the net present value.

000,300000,100000,150

2Year 1Year 0Year


Present ValuesExample - continued

Assume that the cash flows from the construction and sale of an office building is as follows. Given a 7% required rate of return, create a present value worksheet and show the net present value.

400,18$

900,261000,300873.2

500,93000,100935.1

000,150000,1500.10Value

Present

Flow

Cash

Factor

DiscountPeriod

207.11

07.11

TotalNPV11/16/2014 Instructor: Mr. Wajid Shakeel Ahmed

NPV FormulaMathematically; PV @ 7%

∑PV = PV of C1+ PV of C2

= -$93,500 + $261,900= $168,400

NPV = ∑ PV - INV= $168,400 - $150,000= $18,400


Summary

• Calculations of NPV & ROR• Managers and the Interests of Shareholders• Fundamental Study Result• Valuing Long-Lived Assets

Short Cuts

• Sometimes there are shortcuts that make it very easy to calculate the present value of an asset that pays off in different periods.

• These tolls allow us to cut through the calculations quickly.


Short CutsPerpetuity - Financial concept in which a cash flow is theoretically received forever.

PV

Cr

cashflow

luepresent va

Return


Short CutsPerpetuity - Financial concept in which a cash

flow is theoretically received forever.

r

CPV 1

ratediscount

flow cash FlowCash of PV


Case : Investment A• An investment costs $1,548 and pays $138 in

perpetuity. If the interest rate is 9 percent, what is the NPV?– PV = C / r

= $1533.33

– NPV = PV - INV = $1533.33 - $1548

= -$ 14.67


Short CutsAnnuity - An asset that pays a fixed sum each

year for a specified number of years.

trrrC

1

11annuity of PV


Case: leasing a carExample

You agree to lease a car for 4 years at $300 per month. You are not required to pay any money up front or at the end of your agreement. If your opportunity cost of capital is 0.5% per month, what is the cost of the lease?


ContinueExample - continued

You agree to lease a car for 4 years at $300 per month. You are not required to pay any money up front or at the end of your agreement. If your opportunity cost of capital is 0.5% per month, what is the cost of the lease?

10.774,12$

005.1005.

1

005.

1300Cost Lease 48

Cost


Case: Endowment FundsExample - Suppose, for example, that we begins to wonders what it would cost to contribute in a endowment fund with an amount of $100,000 a year for only 20 years?

400,851$

10.110.

1

10.

1000,100Cost Lease 20

Cost


Alternatively• We can simply look up the answer in the annuity table given on the next slide. • This table gives the present value of a dollar to be received in each of t periods. • In our example t = 20 and the interest rate r = .10, and therefore;• We look at the twentieth number from the top in the 10 percent column. It is 8.514. Multiply 8.514 by $100,000, and we have our answer,$851,400.11/16/2014 Instructor: Mr. Wajid Shakeel Ahmed

Compound Interest

• There is an important distinction between compound interest and simple interest.– When money is invested at compound interest,

each interest payment is reinvested to earn more interest in subsequent periods.

– In contrast, the opportunity to earn interest on interest is not provided by an investment that pays only simple interest.


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