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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?
11/16/2014 Instructor: Mr. Wajid Shakeel Ahmed
Continue
• 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.
11/16/2014 Instructor: Mr. Wajid Shakeel Ahmed
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.
11/16/2014 Instructor: Mr. Wajid Shakeel Ahmed
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.
11/16/2014 Instructor: Mr. Wajid Shakeel Ahmed
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.
11/16/2014 Instructor: Mr. Wajid Shakeel Ahmed
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.
11/16/2014 Instructor: Mr. Wajid Shakeel Ahmed
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.
11/16/2014 Instructor: Mr. Wajid Shakeel Ahmed
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.
11/16/2014 Instructor: Mr. Wajid Shakeel Ahmed
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.
11/16/2014 Instructor: Mr. Wajid Shakeel Ahmed
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.
11/16/2014 Instructor: Mr. Wajid Shakeel Ahmed
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.
11/16/2014 Instructor: Mr. Wajid Shakeel Ahmed
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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;
11/16/2014 Instructor: Mr. Wajid Shakeel Ahmed
Continue
• 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.
11/16/2014 Instructor: Mr. Wajid Shakeel Ahmed
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.
11/16/2014 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.
DFr t
1
1( )
11/16/2014 Instructor: Mr. Wajid Shakeel Ahmed
Present Values
Discount Factors can be used to compute the present value of any cash flow.
DFr t
1
1( )
1
11 1 r
CCDFPV
11/16/2014 Instructor: Mr. Wajid Shakeel Ahmed
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
11/16/2014 Instructor: Mr. Wajid Shakeel Ahmed
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
11/16/2014 Instructor: Mr. Wajid Shakeel Ahmed
Present ValuesExample
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
11/16/2014 Instructor: Mr. Wajid Shakeel Ahmed
Present ValuesExample
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?
11/16/2014 Instructor: Mr. Wajid Shakeel Ahmed
Present ValuesExample
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
( . )$2, .
11/16/2014 Instructor: Mr. Wajid Shakeel Ahmed
Present Values PVs can be added together to evaluate
multiple cash flows.
PV C
r
C
r
1
12
21 1( ) ( )....
11/16/2014 Instructor: Mr. Wajid Shakeel Ahmed
Present Values PVs can be added together to evaluate
multiple cash flows, and called as discounted cash flow or (DCF) formula;
tt
t
rCPV
)1(
11/16/2014 Instructor: Mr. Wajid Shakeel Ahmed
Present Values• If a dollar tomorrow is worth less than a
dollar today, one might suspect that a dollar the day after tomorrow should be worth even less.
• But, lets assume - given two dollars, one received a year from now and the other two years from now, the value of each is commonly called the Discount Factor. Assume r1 = 20% and r2 = 7%.
11/16/2014 Instructor: Mr. Wajid Shakeel Ahmed
Present Values• Given two dollars, one received a year from now
and the other two years from now, the value of each is commonly called the Discount Factor. Assume r1 = 20% and r2 = 7%.
87$.
83$.
2
1
)07.1(00.1
2
)20.1(00.1
1
DF
DF
11/16/2014 Instructor: Mr. Wajid Shakeel Ahmed
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
=
11/16/2014 Instructor: Mr. Wajid Shakeel Ahmed
Continue
• If we going to find out the net present value of our investment we get,
– NPV = PV – Investment = $1121 - $1200
“Just imagine in this game of lending and borrowingHow much money you can earn without taking risks”
11/16/2014 Instructor: Mr. Wajid Shakeel Ahmed
Continue
• Of course this story is completely fanciful.– “There is no such thing as a money machine.”
• In well-functioning capital markets, any potential money machine will be eliminated almost instantaneously by investors who try to take advantage of it.
11/16/2014 Instructor: Mr. Wajid Shakeel Ahmed
Present ValuesExample
Assume that the cash flows from the construction and sale of an office building is as follows. Given a 7% required rate of return, create a present value worksheet and show the net present value.
000,300000,100000,150
2Year 1Year 0Year
11/16/2014 Instructor: Mr. Wajid Shakeel Ahmed
Present ValuesExample - continued
Assume that the cash flows from the construction and sale of an office building is as follows. Given a 7% required rate of return, create a present value worksheet and show the net present value.
400,18$
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
11/16/2014 Instructor: Mr. Wajid Shakeel Ahmed
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.
11/16/2014 Instructor: Mr. Wajid Shakeel Ahmed
Short CutsPerpetuity - Financial concept in which a cash flow is theoretically received forever.
PV
Cr
cashflow
luepresent va
Return
11/16/2014 Instructor: Mr. Wajid Shakeel Ahmed
Short CutsPerpetuity - Financial concept in which a cash
flow is theoretically received forever.
r
CPV 1
ratediscount
flow cash FlowCash of PV
11/16/2014 Instructor: Mr. Wajid Shakeel Ahmed
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
11/16/2014 Instructor: Mr. Wajid Shakeel Ahmed
Short CutsAnnuity - An asset that pays a fixed sum each
year for a specified number of years.
trrrC
1
11annuity of PV
11/16/2014 Instructor: Mr. Wajid Shakeel Ahmed
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?
11/16/2014 Instructor: Mr. Wajid Shakeel Ahmed
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
11/16/2014 Instructor: Mr. Wajid Shakeel Ahmed
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
11/16/2014 Instructor: Mr. Wajid Shakeel Ahmed
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.
11/16/2014 Instructor: Mr. Wajid Shakeel Ahmed