Last Study Topics What Is A Corporation? - All large and medium-sized businesses are organized as corporations. The Role of The Financial Manager - Capital

Last Study Topics• What Is A Corporation?- All large and medium-sized businesses are organized as

corporations.• The Role of The Financial Manager- Capital Budgeting vs Financing Decision.• Who Is The Financial Manager?- Anyone responsible for a significant investment or

financing decisions.• Separation of Ownership and Management• Financial Markets

11/14/2014 Instructor: Mr. Wajid Shakeel Ahmed 1

Present Value and The Opportunity Cost of Capital

Principles of Corporate FinanceBrealey and Myers Sixth Edition

©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill

Topics Covered

• Present Value (PV)• Net Present Value (NPV)• NPV Rule• Rate Of Return Rule• Opportunity Cost of Capital• Managers and the Interests of Shareholders

11/14/2014 3Instructor: Mr. Wajid Shakeel Ahmed

Introduction• COMPANIES INVEST IN a variety of real assets.- Tangible Assets: such as plant and machinery.- Intangible Assets: such as management

contracts and patents.• Object of investment is to find real assets that

are worth more than they cost.• Companies are always searching for assets

that are worth more to them than to others.


Continue• Suppose you own a warehouse.• The odds are that your appraiser’s estimate of

its value will be within a few percent of what the building would actually sell for.

• The appraiser’s stock-in-trade is knowledge of the prices at which similar properties have recently changed hands.

• Problem of valuing real estate is simplified by the existence of an active market. Or Is it not?


Continue• Answer to that would be;• First, it is important to know how asset values

are reached in an active market. • Second, it is important to understand why

that warehouse is worth, say, $250,000 and not a higher or lower figure.

• Thirdly, the market for most corporate assets is pretty thin.


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• In other words, you need a theory of value.• Should you invest to build a new office

building in the hope of selling it at a profit next year?

• Finance theory endorses investment if net present value is positive, that is, if the new building’s value today exceeds the required investment.


Understanding the Present Value

• The present value of $400,000 one year from now must be less than $400,000.

• “A dollar today is worth more than a dollar tomorrow” - first basic principle of finance.


1factordiscount =PV C

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Present Value

Value today of a future cash

flow.

Discount Rate

Interest rate used to compute

present values of future cash flows.

Discount Factor

Present value of a $1 future payment.


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Discount Factor = DF = PV of $1

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

DFr t

1

1( )


Case: Office Building

• Warehouse has burned down. You consider rebuilding, but your real estate adviser suggests putting up an office building instead. The construction cost would be $300,000, and there would also be the cost of the land, which might otherwise be sold for $50,000. new building would fetch $400,000 if you sold it after an year. Is it worth to go ahead with the investment plan? or not?


Valuing an Office Building

Step 1: Forecast cash flows (,000)

Cost of building = C0 = $350

Sale price in Year 1 = C1 = $400

• Assuming for the moment that the$400,000 payoff is a sure thing.


ContinueStep 2: Estimate opportunity cost of capitalIf equally risky investments in the capital marketoffer a return of 7%, how much would you haveto invest in them in order to receive $400,000 at the end of the year?

Lets find out!


Valuing an Office Building

Step 3: Discount future cash flows (,000)

• Since the property will be worth $400,000 in a year, investors would be willing to pay $374,000 for it today.

374)07.1(400

)1(1 r

CPV


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• We have discounted expected payoffs by the rate of return offered by equivalent investment alternatives in the capital market, i.e. offer a return of 7%.

• This rate of return is often referred to as the discount rate, hurdle rate, or opportunity cost of capital.


Net Present Value

r

C

1C=NPV

investment required-PV=NPV

10


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Step 4: Go ahead if PV of payoff exceeds investment

• NPV = PV - required investment = 374,000 - 350,000 = $24,000.

• In other words, your office development is worth more than it costs—it makes a net contributionto value.


Risk and Present Value• Higher risk projects require a higher rate of

return.• Higher required rates of return cause lower

PVs.

374.071

400PV

7%at $400 C of PV 1


Risk and Present Value

• Suppose you believe the project is as risky as investment in the stock market and that stock market investments are forecasted to return 12 percent.

• Then 12 percent becomes the appropriate opportunity cost of capital.

• That is what you are giving up by not investing in equally risky securities.


Risk and Present Value

374.071

400PV

7%at $400 C of PV 1

357.121

400PV

12%at $400 C of PV 1


Re-compute;

NPV = PV-350 =$7

Rate of Return Rule• Accept investments that offer rates of return

in excess of their opportunity cost of capital


Rate of Return Rule• Accept investments that offer rates of return

in excess of their opportunity cost of capital.

Example

In the project listed below, the foregone investment opportunity is 12%. Should we do the project?

14%or .14350,000

350,000400,000

investment

profitReturn


Explanation

• One cannot be certain about future values of office buildings.

• The $400,000 represents the best forecast, but it is not a sure thing.

• A safe dollar is worth more than a risky one.• Most investors avoid risk when they can do so

without sacrificing return.


Case: Motel Building

• Aparcel of land costs $500,000. For an additional $800,000 you can build a motel on the property. The land and motel should be worth $1,500,000 next year. Suppose that common stocks with the same risk as this investment offer a 10 percent expected return. Would you construct the motel? Why or why not?


Valuing a Motel Building

Step 1: Forecast cash flows (,000)

Cost of building = C0 = $1300

Sale price in Year 1 = C1 = $1500

• Assuming for the moment that the$1500,000 payoff is a sure thing.


ContinueStep 2: Estimate opportunity cost of capitalA Common Stock with a same risk as this investments in the capital market offer a return of 10%, how much would you have to invest in them in order to receive $1500,000 at the end Of the year?

Lets find out!


Continue

• To calculate present value, we discount expected payoffs by the rate of return offered by equivalent investment alternatives in the capital market, i.e. offer a return of 10%.

• This rate of return is often referred to as the discount rate, hurdle rate, or opportunity cost of capital.


Valuing an Motel Building

Step 3: Discount future cash flows (,000)

• Since the property will be worth $1500,000 in a year, investors would be willing to pay $1364,000 for it today

1364)10.1(1500

)1(1 r

CPV


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Step 4: Go ahead if PV of payoff exceeds investment

• NPV = PV - required investment = 1364,000 - 1300,000 = $64,000.

• In other words, your motel development is worth more than it costs—it makes a net contribution to value.


Alternative

• we can compute r as follows:

r = ($1,500,000/$1,300,000) – 1 = 0.1538 = 15.38%

• Since - Rate of Return is > Cost of Capital, you would still construct the motel.


Understanding NPV and ROR

• Let INV = investment required at time t = 0 (i.e., INV = -C0) and let x = rate of return.

• Then x is defined as:x = (C1 – INV)/INV

• Therefore:C1 = INV(1 + x)


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• It follows that:NPV = C0 + {C1/(1 + r)}

NPV = -INV + {[INV(1 + x)]/(1 + r)}

NPV = INV {[(1 + x)/(1 + r)] – 1}


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a. When x equals r, then:[(1 + x)/(1 +r)] – 1 = 0and NPV is zero.

b. When x exceeds r, then:[(1 + x)/(1 + r)] – 1 > 0and NPV is positive.


Case: Pakistan Treasury security

• What is the net present value of a firm’s investment in a Pakistan Treasury security with the face value of Rs. 1000 yielding 5 percent and maturing in one year?

• Solution: NPV = C0 + [C1/(1 + r)] = Rs. -1000 + (1050/1.05) = Rs. 0


Explanation

• This is not a surprising result, because 5 percent is the opportunity cost of capital, i.e., 5 percent is the return available in the capital market.

• If any investment earns a ‘rate of return’ equal to the ‘opportunity cost of capital’, the NPV of that investment is zero.


Net Present Value Rule

• Accept investments that have positive net present value.

Example

Suppose we can invest $50 today and receive $60 in one year. Should we accept the project given a 10% expected return?

55.4$1.10

60+-50=NPV


Summary• Present Value (PV)– “A dollar today is worth more than a dollar

tomorrow”

• Net Present Value (NPV)– If your investment makes a net contribution to

value

• NPV Rule• Rate Of Return Rule


Documents

Last Study Topics What Is A Corporation? - All large and medium-sized businesses are organized as corporations. The Role of The Financial Manager - Capital