1. Capital Budgeting MF 807 Corporate Finance Professor Thomas Chemmanur

2. 2 2 Computing Cash Flows in Capital Budgeting Cash flows are the difference between the dollars received and the dollars paid at the point in time when the actual transaction takes place.  E.g. if a bulldozer is bought at the start of a project, the negative cash flow of, say, $100,000 would be recorded at t = 0 The accounting approach involves depreciating the cost over the useful life of the asset  E.g. straight-line depreciation expense of $20,000 over 5 years These different approaches would yield a different NPV. Thus, accounting figures, if used, are only a starting point for the cash flow analysis. Keep in mind that we estimate cash flows on an incremental, after-tax basis. Incremental cash flows are the inflows and outflows that occur if and only if the project is undertaken.

3. 3 3 Computing Cash Flows in Capital Budgeting Principles to keep in mind when computing cash flows:  1. Do not confuse incremental cash flows with average cash flows. E.g. if you hire an employee because of a project, his salary and any additional salary paid to existing employees because of this project become a part of the project. You would not use the average labor cost for all of the firm’s projects.  2. Include all incidental effects. E.g. if taking on a project requires the installation of a new sewage disposal system, its cost should be included in the cash flows of the project.  3. Remember additional working capital requirements due to the project. Net working capital (sometimes just ‘working capital’) is the difference between current assets and current liabilities.

4. 4 4 Computing Cash Flows in Capital Budgeting  4. Forget sunk costs. Any costs that have already been incurred are excluded. E.g. the cost of a marketing study to estimate the market size for a new product is left out of the decision to introduce the new product.  5. Include opportunity costs. These are the foregone cash flows that could have been generated from existing assets if they had not been allocated to the project.  6. Beware of allocated overheads. E.g. the salary of the company Chairman should not be apportioned to the project, if he would have been paid the same salary without the project. This point is related to point 1: only include incremental cash flows.

5. 5 5 Calculating Depreciation Depreciation is relevant to cash flow estimation because it impacts the incremental cash flows of the project by affecting the firm’s tax bill. When a portion of an investment can be expensed every year as depreciation, this means the taxable income of the firm is reduced by the same amount. The benefit to the firm is called the depreciation tax shield. (Again remember we only consider the incremental depreciation.)  Incremental depreciation tax shield in year t = T c * D t, where D t is the incremental depreciation due to the project in year t, and T c is the firm’s marginal corporate tax rate (i.e. tax on the ‘next’ dollar earned).

6. 6 6 Calculating Depreciation 1. Straight Line Depreciation:  where N is the number of years over which the capital equipment involved can be depreciated under the tax code 2. Accelerated Depreciation:  D t = Investment * ACRS factor for year t, corresponding to the ACRS depreciation class of the equipment, per the tax code.  Note: The ACRS factor is available in Table 6-5, page 102, Brealy and Myers. On an exam, I will specify these factors in any problems I give. Accelerated depreciation results in larger present values for projects than straight line depreciation, because the present value of tax shields is higher.

7. 7 7 Calculating Depreciation Accelerated depreciation results in larger present values for projects than straight line depreciation, because the present value of tax shields is higher. That is, the sooner we can capture the tax shield from depreciation the better. 3. Different kinds of project cash flows

8. 8 8 Different kinds of project cash flows Sometimes it is useful to categorize project cash flows into three groups:  1. Initial Cash Flows. These are cash flows which occur at the beginning of the project. E.g. initial investment, additional working capital requirements  2. Operating Cash Flows. These occur during the regular operation of the project. R t = Incremental Revenues due to the project in year t C t = Incremental Costs due to the project in year t. D t = Incremental Depreciation available in year t. Note: T c  D t is the tax shield in year t due to the project.

9. 9 9 Different kinds of project cash flows  3. Terminal Cash Flows. These are cash flows that occur while the project is being wound up. Examples are salvage value, return of additional working capital, etc. Note: Any amount of the salvage value in excess of the book value is subject to some taxation. (The book value of any capital equipment is the original cost of the equipment minus the sum of the various amounts written off as depreciation D t over the life of the project.)  If the tax rate applicable to any salvage value in excess of book value is t, then the cash flow related to the salvage is: Book value + (1 – t)(Salvage value – Book value)  In problems, I will specify if you need to take into account the taxation of salvage value, and what tax rate to use.

10. 10 Example 1 Initial Cash Flows: Price(100,000) Modification(20,000) Net Working Capital(5,000) Total- 125,000 Operating Cash Flows: Year 1 Year 2 Year 3 After tax savings25,600 25,600 25,600 Depreciation39,996 53,340 17,772 T  D t 14,398.56 19,202.40 6,397.92 Total39,998.56 44,802.4 31,997.2

11. 11 Example 1 Terminal Cash Flows: Salvage Value50,000 Return of NWC 5,000 Total55,000 NPV = -125,000 + 39,998.56 (PVIF 10%, 1 yrs) + 44,802.4 (PVIF 10%, 2 yrs) + 31,997.2 (PVIF 10%, 3yrs) + 55,000 (PVIF 10%, 3yrs) = -125,000 + 138, 748.38 = 13,748.38 > 0, So Accept.

12. 12 How Should We Handle Inflation? There is a positive rate of inflation in most real world economies. We can define the inflation rate, denoted by p, as: The inflation rate is already built into the nominal (or “money”) discounting rate, which is what we observe. The relationship between the nominal (or money) rate of return r, the inflation rate p, and the real rate of return r c is given by: (1 + r) = (1 + r c )(1 + p) If we use the nominal rate of return to discount a given cash flow stream, we should also adjust the cash flows we use in our investment analysis for inflation.

13. 13 How Should We Handle Inflation? This adjustment is particularly important in the case of projects lasting for longer periods, where this can make a significant difference in our accept / reject decision. Denote by CF t the cash flow at date t in current prices (I.e., cash flows which are not adjusted for inflation) Then the cash flows adjusted for inflation for date t, denoted by ACF t, is given by: ACF t = CF t (1 + p) t The NPV of the project is:

14. 14 How Should We Handle Inflation? Sometimes, it is convenient to adjust the interest rate at which the cash flows are discounted, keeping the cash flows at current prices. To see how to do this, replace the nominal discount rate in the previous expression for NPV by the real discount rate. Thus, another way to handle inflation is to discount cash flows at current prices at the real discount rate (i.e., use unadjusted cash flows, but adjust the discount rate).

15. 15 Example 2 Sales = 1000(138) 138,000 Cost = 1000(105) 105,000 Net before tax33,000 Net income after tax33,000 ( 1 – 0.36) 21,120 Cost of capital = 15% in nominal terms Inflation rate = 6% (1 + i) = (1 + i r )(1 + p) i r = 1.15/1.06 - 1 = 0.0849  8.5% As a perpetuity, PV of benefit = 21,120 / 0.0849 = 248,763.25 NPV = 248,763.25 – 150,000 = 98,763.25 Note: this project will have negative NPV if we ignore inflation

16. 16 Project Interactions So far, we have assumed that the investment opportunities available to the company are ‘cleanly’ separable, and that we can analyze each project separately. This is a simplification. Furthermore, a decision involving a project may not be one of accept / reject but accept / reject / delay. Cases of project interaction:  Optional timing of an investment:  Choosing between projects with unequal lives.  When to replace a machine.

17. 17 Project Interactions Optimal timing examples:  E.g. a drilling project might not be currently profitable because of low oil prices, but the NPV could turn positive at higher prices in the future. The right choice may be to buy an option on the land (and thus the NPV of buying the land and potentially drilling in the future is positive, given the probability distribution of future oil prices).  E.g. the problem of when to harvest a crop of timber, given that trees are growing and there will be more over time. (Assume for simplicity that timber prices are constant). The answer here is not to wait forever, since there is a time value for money, but to harvest the timber at a certain optimal point in time.

18. 18 Project Interactions An example of two mutually exclusive projects with unequal lives:  Consider a company having to decide between two machines, one having a life of five years and the other seven years. Assume further that the NPV of buying the machine with a shorter life is larger. The solution here is not necessarily to buy the first machine, if it also means the company has to buy a new machine sooner (after 5 years).  The concept of equivalent annual cost is useful in solving this problem. The EAC is the annual amount of an annuity with the same present value as that of the project under consideration. The firm should buy the machine with the lower equivalent annual cost.

19. 19 Example 3 PV of A = - 40,000 + {-10,000(PVIFA 6%, 3 yrs)} = - 40,000 + -10,000(2.6730) = - 66,730 Equivalent Annual Cost (EAC) EAC A  [PVIFA 6%, 3 yrs] = -66,730 EAC A = 66,730/2.6730 = -24,964 PV of B = -50,000 + {-8,000(PVIFA 6%, 4 yrs)} EAC B  [PVIFA 6%, 4 yrs] = -77,720 EAC B = -77,720 / [PVIFA 6%, 4 yrs] = -22,430 Buy machine B, since the EAC is lower.