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Capital Budgeting Plus some stocks and bonds

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Review question A bond has a coupon rate of 8%. It sells today at par, that is, for $1000. What is the yield? 8% Prove it. Calculate value at 8%. Maturity can be anything.

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Growing perpetuity

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Example: share of stock The market expects a dividend of $4 in one year. It expects the dividend to grow by 5% per year The discount rate for such firms is 16%. What is the price of a share?

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Solution PP=4*(1/(.16-.05)) ==36.3636...

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Decomposition of value Absent growth, as a cash cow, value = 4*(1/.16) = 25. Remaining value of 36.3636… - 25 is net present value of growth opportunities (NPVGO). =11.3636...

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Example: whole firm The market expects $30M in one year and growth of 2% thereafter. Discount rate = 17%. Value of the firm is $200M. That is 30M*(1/(.17-.02))

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continued A new line of business for the firm is discovered. The market expects $20M in a year, with growth at 7% thereafter. Value of the new growth opportunity is $200M (at r = 17%).

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Whole value: 400M = 200M + 200M Note that the value is gross, not net. Share price? Divide by the number of shares.

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Arguing for your project Capital budgeting CFO receives proposals from divisions Projects described by cash flows

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Arguing means applying measures Net present value is the right measure. Many smart people use the wrong ones. Alternative ways to the same end.

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Uses of measures Project acceptance Mutually exclusive alternatives.

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Capital Budgeting Techniques Kim, Crick, and Kim, Management Accounting Nov. 1986, p. 49-52

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Survey of use of measures by corporations

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Make no mistake NPV is the right measure always. Others work sometimes. NPV measures value to owners, their wealth.

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Objectives of a good measure Value cash flows. Respond to the market.

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NPV’s merits Values cash flows as the market does. Responsive because the discount rate is the current market rate. Measures increase in shareholder value.

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Payback period is The time required for undiscounted cash flows to add up to the initial investment. e.g., build a Wendy’s if it “pays for itself” in two years or less.

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Payback merits Based on cash flows

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Payback defects No market response. When r is high, the satisfactory payback period should be shorter. Subtracts time-t dollars from time-0 dollars, a cardinal sin. Ignores cash flow after payback. Ignores timing during payback.

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Defects are not necessarily fatal Repeated, similar investments. Stable financial conditions.

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The well-informed capital budgeter knows When to accept payback period as a measure. When it is likely to fail.

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Accounting rate of return Doesn’t value cash flows No market response Ignores market values Scaling problems: melons or malls

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Merits of accounting r.o.r. Easily understood. Sometimes okay in stable markets. Smart application can overcome defects.

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Internal rate of return Definition: IRR is the discount rate that makes NPV = 0 That is, IRR is the r such that

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Internal rate of return Definition: IRR is the discount rate that makes NPV(r) = 0. NPV(r) is a function. RWJ Figures 6.4 and 6.5.

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IRR is almost the same as bond yield Bond yield is r such that

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Project

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Figure 6.4: NPV(r)=0 at r=23.37% NPV r 100 NPV(r) NPV(.1) = 48.68520.1 IRR =23.37 48.685

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Figure 6.4 NPV (r) = 0 at r = 23.37%

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Applications of IRR measure Hurdle rate = market rate Project acceptance: Accept a project if IRR > hurdle rate. Mutually exclusive projects: Take the one with the highest IRR (> hurdle rate)????? Don’t rely on it.

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Project acceptance: NPV and IRR give the same conclusion when... Cash flows have one sign change. In the example: IRR = 23.37% > hurdle = 10% for an investment project. IRR = 23.37% < hurdle rate = 30% for a financing or “borrowing from nature” project.

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Merits Uses cash flows. Responds to the market when the hurdle rate changes

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Objective Learn to recognize the times when NPV and IRR are the same. and also the problems with IRR

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Defects of IRR -- project acceptance Lending to nature or borrowing from her? Multiple IRR's may occur.

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Financing (borrowing from nature) Seek IRR < hurdle rate Same as NPV > 0

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Multiple IRR's

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IRR’s at r = 1 and r = 2 100% per decade = 7.17735% per year. 200% per decade = 11.61232% per year.

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IRR’s at r=1 and r=2. NPV r 100% 200%

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Descartes’ Rule The number of internal rates of return is no more than the number of sign changes. The number of positive roots of a polynomial with real coefficients is at most equal to the number of sign changes in the coefficients. Interest rates are more than -100%

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Defects of IRR -- mutually exclusive projects Ignores market values. Scale problems -- melons or malls.

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Typical hour exam question What is the scale problem in using IRR to choose between mutually exclusive projects?

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Scale problem in IRR One canyon, one dam.

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Sketch of answer The smaller dam has the higher IRR. The big dam has higher value. The big dam extends consumption possibility of owners more than the little dam does. It is wrong to take the higher IRR in this case.

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Capital Budgeting Jiu Jitsu Consider the project of replacing the little dam by the big dam. Cash flows are -900, +1300. IRR of the project is 4/9 =.4444 >.1 NPV is 281.8181… So replace the little dam. Capital budgeting jiu jitsu.

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Scale problems in IRR

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r NPV 50%100% 100 500 Big dam Little dam IRR

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Big dam, little dam NPV NPV of the big dam NPV of the small dam 500 100.5 1 r r* For hurdle rates below r*, the big dam is preferred. r* =.4444...

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