1. 2-1 Copyright © 2006 McGraw Hill Ryerson Limited prepared by: Sujata Madan McGill University Fundamentals of Corporate Finance Third Canadian Edition

2. 2-2 Copyright © 2006 McGraw Hill Ryerson Limited Chapter 7 NPV and Other Investment Criteria Net Present Value (NPV) Other Investment Criteria Mutually Exclusive Projects Capital Rationing

3. 2-3 Copyright © 2006 McGraw Hill Ryerson Limited Net Present Value Capital Budgeting Decision  Which investments should the firm invest in?  Known as the capital budgeting decision or the investment decision.  This chapter discusses various criteria used to evaluate investments.

4. 2-4 Copyright © 2006 McGraw Hill Ryerson Limited Net Present Value Capital Budgeting Decision  Suppose you had the opportunity to buy a building for $350,000 today.  Assume that you could sell it for $400,000 guaranteed next year.

5. 2-5 Copyright © 2006 McGraw Hill Ryerson Limited Net Present Value Capital Budgeting Decision 0 1 $400,000 r% -$350,000 ? What discount rate do we use to value this stream of cash flows?  What else could we have done with the $350,000?  What other opportunity are we giving up by investing in the building?

6. 2-6 Copyright © 2006 McGraw Hill Ryerson Limited Net Present Value Capital Budgeting Decision 0 1 $400,000 7% -$350,000 Assume the interest rate on the risk-free T-bill is 7%. $4,000/(1+0.07) = $373,832 NPV = $23,832

7. 2-7 Copyright © 2006 McGraw Hill Ryerson Limited Net Present Value  Present value of cash flows minus initial investment. Opportunity Cost of Capital  Expected rate of return given up by investing in a project.

8. 2-8 Copyright © 2006 McGraw Hill Ryerson Limited Net Present Value NPV = PV - required investment where C t = Cash flow at time t r = Opportunity cost of capital

9. 2-9 Copyright © 2006 McGraw Hill Ryerson Limited Net Present Value Risk and Net Present Value  The discount rate used to discount a set of cash flows must match the risk of the cash flows.  Instead of being risk-free, if the building investment was estimated to be as risky as the stock market yielding 12%, the NPV would be: NPV= PV – C0C0 = [$400,000/(1+.12)] - $350,000 = $357,143 - $350,000 = $7,143

10. 2-10 Copyright © 2006 McGraw Hill Ryerson Limited Net Present Value Valuing long lived projects  The NPV rule works for projects of any duration.  The critical problems in any NPV problem are to determine:  The amount and timing of the cash flows.  The appropriate discount rate.

11. 2-11 Copyright © 2006 McGraw Hill Ryerson Limited Net Present Value Net Present Value Rule  Managers increase shareholders’ wealth by accepting all projects that are worth more than they cost.  Therefore, they should accept all projects with a positive net present value.

12. 2-12 Copyright © 2006 McGraw Hill Ryerson Limited Other Investment Criteria Net Present Value vs Other Criteria  Use of the NPV criterion for accepting or rejecting investment projects will maximize the value of a firm’s shares.  Other criteria are sometimes used by firms when evaluating investment opportunities.  Some of these criteria can give wrong answers!  Some of these criteria simply need to be used with care if you are to get the right answer!

13. 2-13 Copyright © 2006 McGraw Hill Ryerson Limited Other Investment Criteria Payback  Payback is the time period it takes for the cash flows generated by the project to cover the initial investment in the project. Payback Rule  Accept a project if its payback period is less than the specified cutoff period.

14. 2-14 Copyright © 2006 McGraw Hill Ryerson Limited Other Investment Criteria Payback  A company has the following three investment opportunities. The company accepts all projects with a 2 year or less payback period and uses a 10% discount rate. a Cash Flows in Dollars Project:C 0 C 1 C 2 C 3 A-2,000+1,000+$1,000+10,000 B-2,000+1,000+$1,000 - C-2,000 -+$2,000 -

15. 2-15 Copyright © 2006 McGraw Hill Ryerson Limited Other Investment Criteria Payback a Project: C 0 C 1 C 2 C 3 Payback NPV @10% A -2,000 +1,000 +$1,000 +10,000 2 $7,249 B -2,000 +1,000 +$1,000 - 2 -$ 264 C -2,000 - +$2,000 - 2 -$ 347

16. 2-16 Copyright © 2006 McGraw Hill Ryerson Limited Other Investment Criteria Payback a Project: C 0 C 1 C 2 C 3 Payback NPV @10% A -2,000 +1,000 +$1,000 +10,000 2 $7,249 B -2,000 +1,000 +$1,000 - 2 -$ 264 C -2,000 - +$2,000 - 2 -$ 347 Only Project A increases shareholder value and should be accepted!

17. 2-17 Copyright © 2006 McGraw Hill Ryerson Limited Other Investment Criteria Discounted Payback  Discounted payback is the time period it takes for the discounted cash flows generated by the project to cover the initial investment in the project.  Although better than payback, it still ignores all cash flows after an arbitrary cutoff date.  Therefore it will reject some positive NPV projects. a

18. 2-18 Copyright © 2006 McGraw Hill Ryerson Limited Other Investment Criteria Book Rate of Return  Book rate of return equals the company’s accounting income divided by its assets. a Book Rate of Return = Book Income / Book Assets Note: These components reflect historic costs and accounting income, not market values and cash flows. a

19. 2-19 Copyright © 2006 McGraw Hill Ryerson Limited Other Investment Criteria Internal Rate of Return (IRR)  IRR is the discount rate at which the NPV of the project equals zero. IRR Rule  Accept a project if it offers a rate of return higher than the opportunity cost of capital.

20. 2-20 Copyright © 2006 McGraw Hill Ryerson Limited Other Investment Criteria Internal Rate of Return (IRR)  Revisiting our building example, we discovered the following: Discount Rate NPV of Project 7%$23,382 12% $7,143 At what rate of return will the NPV of this project be equal to zero?

21. 2-21 Copyright © 2006 McGraw Hill Ryerson Limited Other Investment Criteria Internal Rate of Return (IRR)  If we solve for “r” in the equation below, we find the IRR for this project is 14.3%: NPV= [C 1 /(1+r)] - C0C0 0= [$400,000/(1+r)] - 350,000  r = 14.3% r

22. 2-22 Copyright © 2006 McGraw Hill Ryerson Limited Other Investment Criteria Internal Rate of Return (IRR)  Another way of solving for IRR is to graph the NPV at various discount rates.  The point where this NPV profile crosses the “x” axis will be the IRR for the project.

23. 2-23 Copyright © 2006 McGraw Hill Ryerson Limited IRR BY GRAPH NPV Profile for this Project ($20,000) ($10,000) $0 $10,000 $20,000 $30,000 $40,000 $50,000 $60,000 5%10%15%20% Discount Rate NPV ($) IRR = 14.3% (occurs where NPV = 0)

24. 2-24 Copyright © 2006 McGraw Hill Ryerson Limited Other Investment Criteria Multi-period IRR  You can purchase a building for $350,000. The investment will generate $16,000 in cash flows (i.e. rent) during the first three years. At the end of three years you will sell the building for $450,000. What is the IRR on this investment?

25. 2-25 Copyright © 2006 McGraw Hill Ryerson Limited Other Investment Criteria Multi-period IRR 0 1 $16,000-$350,000 2 $16,000 3 $466,000 IRR = 12.96% By trial and error; or using a financial calculator,

26. 2-26 Copyright © 2006 McGraw Hill Ryerson Limited Project Interactions Pitfalls with IRR – Lending vs Borrowing  Project J involves lending $100 at 50% interest.  Project K involves borrowing $100 at 50% interest.  W hich option should you choose?.

27. 2-27 Copyright © 2006 McGraw Hill Ryerson Limited Project Interactions Pitfalls with IRR – Lending vs Borrowing  According to the IRR rule, both projects have a 50% rate of return and are thus equally desirable.  However, you lend in Project J, and earn 50%; you borrow in Project K, and pay 50%.  Pick the project where you earn more than the opportunity cost of capital..

28. 2-28 Copyright © 2006 McGraw Hill Ryerson Limited Project Interactions Pitfalls with IRR – Multiple Rates of Return  Certain cash flows can generate NPV=0 at more than one discount rate.  The IRR rule would not work in this case; NPV works!.

29. 2-29 Copyright © 2006 McGraw Hill Ryerson Limited Project Interactions Pitfalls with IRR – Mutually Exclusive Projects  Two or more projects that cannot be pursued simultaneously are called mutually exclusive.  When choosing amongst mutually exclusive projects, choose the one with the highest NPV..

30. 2-30 Copyright © 2006 McGraw Hill Ryerson Limited Project Interactions Pitfalls with IRR – Mutually Exclusive Projects  Calculate the IRR and NPV for the following projects: Cash Flows in Dollars Project:C 0 C 1 C 2 C 3 IRR NPV @ 6% H-350400 - - I-350 1616466.

31. 2-31 Copyright © 2006 McGraw Hill Ryerson Limited Project Interactions Pitfalls with IRR – Mutually Exclusive Projects  Calculate the IRR and NPV for the following projects: Cash Flows in Dollars Project:C 0 C 1 C 2 C 3 IRR NPV @ 6% H-350400 - - I-350 1616466. Choose Project I since it makes a greater contribution to the value of the firm! 14.29% $24,000 12.96% $59,000

32. 2-32 Copyright © 2006 McGraw Hill Ryerson Limited Project Interactions Pitfalls with IRR  Higher IRR for a project does not necessarily mean a higher NPV.  You goal should be to maximize the value of the firm.  NPV is the most reliable criterion for project evaluation..

33. 2-33 Copyright © 2006 McGraw Hill Ryerson Limited Project Interactions The Investment Timing Decision  Sometimes you have the ability to defer an investment and select a time that is more ideal at which to make the investment decision.  The decision rule is to choose the investment date that results in the highest NPV today.

34. 2-34 Copyright © 2006 McGraw Hill Ryerson Limited Project Interactions The Investment Timing Decision  You can buy a computer system today for $50,000. Based on the savings it provides to you, the NPV of this investment ~ $20,000.  However, you know that these systems are dropping in price every year.  When should you purchase the computer?

35. 2-35 Copyright © 2006 McGraw Hill Ryerson Limited Project Interactions Decision rule for investment timing: Choose the investment date which results in the highest NPV today.

36. 2-36 Copyright © 2006 McGraw Hill Ryerson Limited Project Interactions Long- vs Short-Lived Equipment  Suppose you must choose between buying two machines with different lives.  Machines D and E are designed differently, but have identical capacity and do the same job.  Machine D costs $15,000 and lasts 3 years. It costs $4,000 per year to operate.  Machine E costs $10,000 and lasts 2 years. It costs $6,000 per year to operate.  Which machine should the firm acquire?

37. 2-37 Copyright © 2006 McGraw Hill Ryerson Limited Project Interactions Long- vs Short-Lived Equipment a Cash Costs [outflows] in Dollars Project:C 0 C 1 C 2 C 3 PV @ 6% Machine D15444$25.69 Machine E1066-$21.00 We cannot compare the PV of costs of assets with different lives..

38. 2-38 Copyright © 2006 McGraw Hill Ryerson Limited Project Interactions Long- vs Short-Lived Equipment  For comparing assets with different lives, we need to compare their Equivalent Annual Costs.  The Equivalent Annual Cost is the cost per period with the same PV as the cost of the machine. a.

39. 2-39 Copyright © 2006 McGraw Hill Ryerson Limited Project Interactions Calculating Equivalent Annual Cost: Cash Flows in Dollars Project:C 0 C 1 C 2 C 3 PV @ 6% Machine D15444$25.69 Equivalent Annual cost:???$25.69  The equivalent annual cost is calculated as follows:. Equivalent Annual Cost= PV of Costs / Annuity Factor = $25.69 / 3 Year Annuity Factor = $25.69 / 2.673 = $9.61 per year 9.61 9.61 9.61

40. 2-40 Copyright © 2006 McGraw Hill Ryerson Limited Project Interactions Long- vs Short-Lived Equipment  If mutually exclusive projects have unequal lives, then you should calculate the equivalent annual cost of the projects.  Picking the lowest EAC allows you to select the project which will maximize the value of the firm. Cash Flows in Dollars Project:PV @ 6% Equivalent Annual Cost D $25.69$9.61 E $21.00$11.45

41. 2-41 Copyright © 2006 McGraw Hill Ryerson Limited Capital Rationing  Limit is set on the amount of funds available to a firm for investment. Soft Rationing  Limits imposed by senior management. Hard Rationing  Limits imposed by the unavailability of funds in the capital markets.

42. 2-42 Copyright © 2006 McGraw Hill Ryerson Limited Capital Rationing Rules for Project Selection  A firm maximizes its value by accepting all positive NPV projects.  With capital rationing, you need to select a group of projects which  is within the company’s resources and  gives the highest NPV.

43. 2-43 Copyright © 2006 McGraw Hill Ryerson Limited Capital Rationing Profitability Index (PI)  The solution is to pick the projects that give the highest NPV per dollar of investment.  We do this by calculating the Profitability Index: PI = NPV / Initial Investment (C 0 )

44. 2-44 Copyright © 2006 McGraw Hill Ryerson Limited Capital Rationing Profitability Index (PI)  Suppose your firm had the following projects and only $20 million to spend: Which Projects should your firm select?

45. 2-45 Copyright © 2006 McGraw Hill Ryerson Limited Capital Rationing Profitability Index ACCEPT

46. 2-46 Copyright © 2006 McGraw Hill Ryerson Limited Summary of Chapter 7  NPV is the only measure which always gives the correct decision when evaluating projects.  The other measures can mislead you into making poor decisions if used alone.  The other measures are:  IRR  Payback  Discounted Payback  Book Rate of Return  Profitability Index (PI)

47. 2-47 Copyright © 2006 McGraw Hill Ryerson Limited Summary of Chapter 7              