# Capital Budgeting Plus some stocks and bonds Review question  A bond has a coupon rate of 8%.  It sells today at par, that is, for \$1000.  What is.

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Capital Budgeting Plus some stocks and bonds

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.

Growing perpetuity

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?

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

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...

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))

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%).

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

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

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

Uses of measures  Project acceptance  Mutually exclusive alternatives.

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

Survey of use of measures by corporations

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

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

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.

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.

Payback merits  Based on cash flows

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.

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

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

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

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

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

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.

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

Project

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

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

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.

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.

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

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

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

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

Multiple IRR's

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

IRR’s at r=1 and r=2. NPV r 100% 200%

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%

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

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

Scale problem in IRR One canyon, one dam.

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.

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.

Scale problems in IRR

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

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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