1. 1 Relevant Cash Flows and Other Topics in Capital Budgeting Timothy R. Mayes, Ph.D. FIN 3300: Chapter 10

2. 2 Project Cash Flows v When deciding whether or not to make an investment, we must first estimate the cash flows that the investment will provide v Generally, these cash flows can be categorized as follows: The initial outlay (IO) The annual after-tax cash flows (ATCF) The terminal cash flow (TCF)

3. 3 Relevant Cash Flows v Determining the relevant cash flows can sometimes be difficult, here are some guidelines v Cash flows must be: Incremental (i.e., in addition to what you already have) After-tax v Ignore those cash flows that are: Sunk costs (monies already spent, and not recoverable) Additional financing costs (e.g., extra interest expense)

4. 4 The Initial Outlay v The initial outlay is the total up-front cost of the investment v The initial outlay can consist of many components, among these are: The cost of the investment Shipping and setup costs Training costs Any increase in net working capital v When we are making a replacement decision, we also need to subtract the after-tax salvage value of the old machine (or land, building, etc.)

5. 5 The Annual After-tax Cash Flows v The annual after-tax cash flows (ATCF) are the incremental after-tax cash flows that the investment will provide v Generally, these cash flows fall into four categories: Incremental savings (positive cash flow) or expenses (negative cash flow) Incremental income (positive cash flow) The tax savings due to depreciation Lost cash flows (negative cash flow) from the existing project. This is an opportunity cost.

6. 6 The Terminal Cash Flow v The terminal cash flow consists of those cash flows that are unique to the last year of the life of the project v There may be a number of components of the TCF, but three common categories are: Estimated salvage value Shut-down costs Recovery of the increase in net working capital

7. 7 Problems in Capital Budgeting v Thus far we have been analyzing relatively simple capital budgeting problems. The methodolgy that we have used is fairly robust, but there are some difficulties. In particular we will now look at problems with: Unequal lives Inflation Differential risk

8. 8 The Unequal Lives Problem v Any time that mutually exclusive projects are being examined, it is vital that we make “apples to apples” comparisons. A perfect example is two projects with unequal lives. v Suppose, for example, that we are trying to decide between projects A and B and that they are mutually exclusive. They have the following cash flows, and the cost of capital is 10%: 012345 3000 35004000-10,000 6000 Project A Project B

9. 9 The Unequal Lives Problem (cont.) v If we calculate the NPVs of both projects, we find: NPV A = $413.22 NPV B = $568.27 v From these calculations it appears that project B is the better project. However, we are making a potentially serious mistake. v Obviously, because we are willing to invest in B we have a 5-year investment horizon. So, we must ask if we accepted project A, what would we do with our money for the remaining 3 years? Only then can a valid comparison be made.

10. 10 The Unequal Lives Problem (cont.) v There are two ways to correctly deal with the unequal lives problem: The replacement chain approach The equivalent annual annuity approach

11. 11 The Replacement Chain Approach v The replacement chain approach assumes that a project will be repeated as many times as necessary to fit into the investment horizon. In this example, we need to repeat project A just once so that it has a 4-year life (the same a B). After replication, the cash flows for A are: 012345 -10,0006000 Project A -10,000 6000

12. 12 The Rep. Chain Approach (Cont.) v Note that the net cash flow in year 2 is now -$4,000 because we must pay for project A a second time. v Now, recalculating the NPV for project A reveals that the correct NPV for the entire 4-year horizon is actually $754.73 which exceeds the NPV of project B. v Therefore, when the problem is correctly analyzed, we find that it is actually project A which should be accepted, not B.

13. 13 The EAA Approach v The equivalent annual annuity approach is identical to the replacement chain approach in its results, but it is much simpler to perform v First, we calculate the NPVs for both projects assuming that they are NOT replicated. Then, we convert these NPVs into equivalent annuity payments that they could provide over the life of the project.

14. 14 The EAA Approach (Cont.) v Using the formula for the present value of an ordinary annuity, we simply solve for the annuity payment: v Solving for the payment for project A, we find that its EAA is $238.09. v Using the same methodology for project B we find that its EAA is $179.27. v Since the EAA for A is higher than the EAA for B, we should accept project A.

15. 15 Dealing with Inflation v Inflation must be accounted for in capital budgeting if we are to make correct decisions. v Generally, we should inflate the cash flow estimates by the expected rate of inflation since the discount rate that we are using already incorporates expected inflation. If we do not do this, then the estimated NPV will be lower than the correct NPV. This could cause us to reject a project that (because it appears to have a negative NPV) when, in fact, we should accept it.

16. 16 Incorporating Risk Estimates v Recall from our discussions in Chapters 1 and 5 that we assume that investors are risk averse. This means that they will require higher rates of return on higher risk investments. v This means that the WACC is not the appropriate discount rate for projects that are riskier or less risky than the average for the firm. Instead, we need to increase the discount rate for riskier projects and decrease it for less risky projects. This is known as the risk-adjusted discount rate (RADR).

17. 17 Incorporating Risk Estimates v There are, of course, several other techniques for incorporating risk into our decision making. However, they are beyond the scope of this course. v Just for completeness, here are a few: Certainty equivalents Scenario analysis Sensitivity analysis Monte-Carlo Simulation