FIN 40153: Advanced Corporate Finance

1. FIN 40153: Advanced Corporate Finance • EVALUATING AN INVESTMENT OPPORTUNITY • (BASED ON RWJ CHAPTER 5)

2. Capital Budgeting: Deciding what investments the company should make. • Some Criteria that a good procedure for evaluating proposed investments should meet. • (1) Base the analysis on incremental costs and benefits, and don’t arbitrarily exclude any costs or benefits from the analysis. • (2) Allow for time value of money and for the risk involved. • (3) If forced to choose among proposals, select the one that does shareholders the most good.

3. NPV Analysis • Our recommended approach to evaluating proposed investments is Net Present Value (NPV) analysis. NPV = Present Value of the Incremental Benefits - Present Value of Incremental Costs. • NPV-based decision rules: • When evaluating independent projects, take those with positive NPVs, reject those with negative NPVs. • When evaluating interdependent projects, take the combination with the highest combined NPV.

4. What About Approaches Other Than NPV? • Other techniques are prevalent (or somewhat prevalent) in practice • Internal rate of return • Payback • Equivalent Annual Costs • According to Graham and Harvey (2001), only the first two are used much in practice (see Table 6.5)

5. Mechanics of Each Technique • Payback period • Payback period is number of years before cumulative cash flows equal the initial investment outlay • Internal Rate of Return (IRR) is the discount rate that sets a project's NPV equal to zero • NPV = Present Value of the Benefits - Present Value of the Costs • EAA converts cash flows from projects into a similar annuity

6. The Internal Rate of Return (IRR) Method • IRR is a useful complement to NPV. • The IRR is defined as the discount rate that causes the project’s computed NPV to equal zero. • Note that the IRR computation starts with the same set of cash flow projections as the NPV analysis. • The only way to compute an IRR is by trial and error.

7. The IRR Intuition • The IRR can be interpreted as the answer to the following questions: • If the capital were placed in a bank account instead of the proposed project, what interest rate would that account have to pay, in order to generate the same future cash flows as this project? • Or, what rate of return can our shareholders expect to earn on the capital invested in this project?

8. 0 1 2 3 400 400 400 -1,000 Internal Rate of Return (IRR) Example • Consider the following stream of cash flows: Calculate the NPV at different discount rates until you find the discount rate where NPV equals zero.

9. Internal Rate of Return (IRR) Example

10. Two Mutually Exclusive Projects: EAA • Ignoring the difference in lives, project L should be accepted. But what if we can replicate project S?

11. Equivalent Annual Annuity Approach • The EAA is the value of the level annuity payment that would be equivalent in present value terms to the projects original NPV. • For Project S: EAAS = 4,132/1.7355 = $2,381 • For Project L: EAAL = 6,190/3.1699 = $1,953 • The EAA method says accept project S. • Be careful if you are working with costs rather than revenues.

12. Profitability Index Ratio of the total PV of future cash flows to the value of the initial costs Example: Two investment opportunities Project Cash FlowPV of C1 and C2PIPV@12% C0 C1 C2 1 -20 70 10 $70.5 $3.53 $50.5 2 -10 15 40 $45.3 $4.53 $35.3 Project 2 has the highest profitability index but Project 1 has the highest NPV. What should you do?

13. Use of PI: Capital Rationing Example: Suppose that you face a capital constraint of $20. Consider the previous example with an additional project. ProjectCash FlowPV of C1 and C2PINPV@12% C0 C1 C2 1 -20 70 10 $70.5 3.53 $50.5 2 -10 15 40 $45.3 4.53 $35.3 3 -10 -5 60 $43.4 4.34 $33.4

14. Some Issues with IRR • Multiple IRRs • Scale effects • Timing effects • Mutually exclusive projects

15. 0 1 2 Multiple IRRs • There can be as many solutions to the IRR definition as there are changes of sign in the time-ordered cash flow series. • Consider the stream: • Can (and does) have two IRR’s. -100 -132 230

16. Calculate NPV at different rates: The project is desirable if the discount rate is between 10.00% and 20.00%. But you don't know this until you calculate NPVs. This curve could be inverted!

17. Another IRR pitfall: Mutually Exclusive Projects: • IRR can lead to incorrect conclusions about different projects' relative worth. • Ralph owns a warehouse he wants to fix up and use for one of two purposes. • A: Store toxic waste containers • B: Store electronic equipment. • Let's look at the cash flows, IRR’s and NPV’s:

18. There are also limitations in using IRR to choose between Projects. Example:

19. At low discount rates, B is better. At high discount rates, A is better. • But A always has the higher IRR. An easy mistake would be to choose A regardless of discount rate.

20. Additional Cautions about IRR • The IRR is stated as a percent per period (like an interest rate), so it is insensitive to the size of the project and to how many periods the project lasts. • Would you rather earn, over the next 24 hours, a 200% return on a $1 investment, or a 100% return on a $1000 investment? • Would you rather earn 25% for one year (with no unusual opportunities to follow) or 24% per year until you retire? • Is NPV sensitive to these considerations? • Simply choosing the project with the larger IRR would be justified only if cash flows could always be reinvested at the IRR instead of the actual capital market rate, r.