Capital Budgeting

1. Capital Budgeting Arguing for your project.

2. 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.

3. Growing perpetuity

4. 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?

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

6. 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...

7. 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))

8. 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%).

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

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

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

12. Uses of measures • Project acceptance • Mutually exclusive alternatives.

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

14. Survey of use of measures by corporations

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

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

17. 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.

18. 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.

19. Payback merits • Based on cash flows

20. 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.

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

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

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

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

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

26. 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.

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

28. Project

29. IRR =23.37 48.685 .1 NPV(r) Figure 6.4: NPV(r)=0 at r=23.37% NPV NPV(.1) = 48.68520 100 r

30. Figure 6.4 • NPV (r) = 0 at r = 23.37%

31. 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.

32. 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.

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

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

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

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

37. Multiple IRR's

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

39. IRR’s at r=1 and r=2. NPV 100% 200% r

40. 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%

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

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

43. Scale problem in IRR One canyon, one dam.

44. 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.

45. 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.

46. Scale problems in IRR

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

48. Big dam, little dam For hurdle rates below r*, the big dam is preferred. NPV NPV of the big dam 500 NPV of the small dam 100 r 1 r* .5 r* = .4444...