Making Capital Investment Decisions Chapter 6 Making Capital Investment Decisions

Questions How can we determine the relevant cash flows for various types of capital investments? How do we compute operating cash flow in various methods? How can we incorporate the inflation into the capital budgeting decision? What is so called the Equivalent Annual Cost approach(約當年度化成本)?

6.1 Incremental Cash Flows Cash flows matter—not accounting earnings. Sunk costs (沉默成本) do not matter. Incremental cash flows matter. Opportunity costs (機會成本) matter. Side effects like cannibalism and erosion matter. Taxes matter: we want incremental after-tax cash flows. Inflation matters.

Cash Flows—Not Accounting Income Consider depreciation expense. You never write a check made out to “depreciation.” Much of the work in evaluating a project lies in taking accounting numbers and generating cash flows.

Incremental Cash Flows Sunk costs are not relevant Just because “we have come this far” does not mean that we should continue to throw good money after bad. Opportunity costs do matter. Just because a project has a positive NPV, that does not mean that it should also have automatic acceptance. Specifically, if another project with a higher NPV would have to be passed up, then we should not proceed. I heard a story about an undergrad at the University of Missouri-Rolla. A student named Louis abandoned college three credit hours shy of graduation. Really. Entreaties from his friends and parents regarding how far he had come and how hard he had worked could not change Louis’ mind. That was all a sunk cost to Louis. He already had a job and didn’t value the degree as much as the incremental work of an easy three-hour required class called ET-10 Engineering Drafting. Fifteen years later, he still has a good job, a great wife and two charming daughters. Louis taught me a lot about sunk costs.

Incremental Cash Flows Side effects matter. Erosion is a “bad” thing. If our new product causes existing customers to demand less of our current products, we need to recognize that. If, however, synergies result that create increased demand of existing products, we also need to recognize that.

Estimating Cash Flows Cash Flow from Operations Net Capital Spending Recall that: OCF = EBIT – Taxes + Depreciation Net Capital Spending Do not forget salvage value(殘值) (after tax, of course). Changes in Net Working Capital (淨營運資金) Recall that when the project winds down, we enjoy a return of net working capital. Of course, amortization could be included as well; however, the formula as presented is the typical statement.

Interest Expense Later chapters will deal with the impact that the amount of debt that a firm has in its capital structure has on firm value. For now, it is enough to assume that the firm’s level of debt (and, hence, interest expense) is independent of the project at hand. It may be beneficial to note the separation theorem, i.e., financing and investment decisions are separate activities.

6.2 The Baldwin Company Costs of test marketing (already spent): $250,000 Current market value of proposed factory site (which we own): $150,000 Cost of bowling ball machine: $100,000 (depreciated according to MACRS 5-year) Increase in net working capital: $10,000 Production (in units) by year during 5-year life of the machine: 5,000, 8,000, 12,000, 10,000, 6,000 See the text for the details of the case.

The Baldwin Company Price during first year is $20; price increases 2% per year thereafter. Production costs during first year are $10 per unit and increase 10% per year thereafter. Annual inflation rate: 5% Working Capital: initial $10,000 changes with sales

The Baldwin Company Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 ($ thousands) (All cash flows occur at the end of the year.) Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Investments: (1) Bowling ball machine –100.00 21.77* (2) Accumulated 20.00 52.00 71.20 82.70 94.20 depreciation (3) Adjusted basis of 80.00 48.00 28.80 17.30 5.80 machine after depreciation (end of year) (4) Opportunity cost –150.00 150.00 (warehouse) (5) Net working capital 10.00 10.00 16.32 24.97 21.22 0 (end of year) (6) Change in net –10.00 –6.32 –8.65 3.75 21.22 working capital (7) Total cash flow of –260.00 –6.32 –8.65 3.75 193.00 investment [(1) + (4) + (6)] It is assumed that the ending market value of the capital investment at year 5 is $30,000. Capital gain is the difference between ending market value and adjusted basis of the machine. The adjusted basis is the original purchase price of the machine less depreciation. Year0 Year 1 Year 2 Year 3 Year 4 Year 5 (1) Bowling ball machine –100.00 (2) Accumulated depreciation 20.00 52.00 71.20 82.70 94.20 (3) Adjusted basis of machine after depreciation (end of year) 80.00 48.00 28.80 17.30 5.80 The capital gain is $24,240 (= $30,000 – $5,800). We will assume the incremental corporate tax for Baldwin on this project is 34 percent. Capital gains tax due is $8,230 [0.34* ($30,000 – $5,800)]. The after-tax salvage value is $30,000 – [0.34 * ($30,000 – $5,800)] = 21,770. * We assume that the ending market value of the capital investment at year 5 is $30,000. Capital gain is the difference between ending market value and adjusted basis of the machine. The adjusted basis is the original purchase price of the machine less depreciation. The capital gain is $24,200 (= $30,000 – $5,800). We will assume the incremental corporate tax for Baldwin on this project is 34 percent. Capital gains are now taxed at the ordinary income rate, so the capital gains tax due is $8,228 = [0.34 * ($30,000 – $5,800)]. The after-tax salvage value is $30,000 – 8,228 = $21,772.

The Baldwin Company Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Investments: (1) Bowling ball machine –100.00 21.77 (2) Accumulated 20.00 52.00 71.20 82.70 94.20 depreciation (3) Adjusted basis of 80.00 48.00 28.80 17.30 5.80 machine after depreciation (end of year) (4) Opportunity cost –150.00 150.00 (warehouse) (5) Net working capital 10.00 10.00 16.32 24.97 21.22 0 (end of year) (6) Change in net –10.00 –6.32 –8.65 3.75 21.22 working capital (7) Total cash flow of –260.00 –6.32 –8.65 3.75 193.00 investment [(1) + (4) + (6)] In practice, we would want to forecast the market value of the warehouse at the time the project ends. In this case, the implicit assumption is that there is no price inflation or deflation over the period. At the end of the project, the warehouse is unencumbered, so we can sell it if we want to.

The Baldwin Company Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Income: (8) Sales Revenues 100.00 163.20 249.70 212.24 129.89 Recall that production (in units) by year during the 5-year life of the machine is given by: (5,000, 8,000, 12,000, 10,000, 6,000). Price during the first year is $20 and increases 2% per year thereafter. Sales revenue in year 2 = 8,000×[$20×(1.02)1] = 8,000×$20.40 = $163,200.

The Baldwin Company Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Income: (8) Sales Revenues 100.00 163.20 249.70 212.24 129.89 (9) Operating costs 50.00 88.00 145.20 133.10 87.85 Again, production (in units) by year during 5-year life of the machine is given by: (5,000, 8,000, 12,000, 10,000, 6,000). Production costs during the first year (per unit) are $10, and they increase 10% per year thereafter. Production costs in year 2 = 8,000×[$10×(1.10)1] = $88,000

The Baldwin Company Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Income: (8) Sales Revenues 100.00 163.20 249.70 212.24 129.89 (9) Operating costs 50.00 88.00 145.20 133.10 87.85 (10) Depreciation 20.00 32.00 19.20 11.50 11.50 Year ACRS % 1 20.0% 2 32.0% 3 19.2% 4 11.5% 5 11.5% 6 5.8% Total 100.00% Depreciation is calculated using the Modified Accelerated Cost Recovery System (shown at right). Our cost basis is $100,000. Depreciation charge in year 4 = $100,000×(.115) = $11,500.

The Baldwin Company Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Income: (8) Sales Revenues 100.00 163.20 249.70 212.24 129.89 (9) Operating costs 50.00 88.00 145.20 133.10 87.85 (10) Depreciation 20.00 32.00 19.20 11.50 11.50 (11) Income before taxes 30.00 43.20 85.30 67.64 30.55 [(8) – (9) - (10)] (12) Tax at 34 percent 10.20 14.69 29.00 23.00 10.39 (13) Net Income 19.80 28.51 56.30 44.64 20.16

Incremental After Tax Cash Flows Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 (1) Sales Revenues   $100.00 $163.20 $249.70 $212.24 $129.89   (2) Operating costs -50.00 -88.00 -145.20 133.10 -87.85   (3) Taxes -10.20 -14.69 -29.00 -23.00 -10.39   (4) OCF (1) – (2) – (3) 39.80 60.51 75.50 56.14 31.66   (5) Total CF of Investment –260. –6.32 –8.65 3.75 193.00   (6) IATCF [(4) + (5)] –260. 39.80 54.19 66.85 59.89 224.66

7.3 Inflation and Capital Budgeting Inflation is an important fact of economic life and must be considered in capital budgeting. Consider the relationship between interest rates and inflation, often referred to as the Fisher equation(費雪方程式): (1 + Nominal Rate) = (1 + Real Rate) × (1 + Inflation Rate) 名目利率 實質利率 通貨膨脹率

Inflation and Capital Budgeting For low rates of inflation, this is often approximated: Real Rate  Nominal Rate – Inflation Rate While the nominal rate in the U.S. has fluctuated with inflation, the real rate has generally exhibited far less variance than the nominal rate. In capital budgeting, one must compare real cash flows discounted at real rates or nominal cash flows discounted at nominal rates.

6.4 Other Methods for Computing OCF Bottom-Up Approach Works only when there is no interest expense OCF = NI + depreciation Top-Down Approach OCF = Sales – Costs – Taxes Do not subtract non-cash deductions Tax Shield (稅盾)Approach OCF = (Sales – Costs)(1 – T) + Depreciation*T

6.5 Investments of Unequal Lives There are times when application of the NPV rule can lead to the wrong decision. Consider a factory that must have an air cleaner that is mandated by law. There are two choices: The “Cadillac cleaner” costs $4,000 today, has annual operating costs of $100, and lasts 10 years. The “Cheapskate cleaner” costs $1,000 today, has annual operating costs of $500, and lasts 5 years. Assuming a 10% discount rate, which one should we choose?

Investments of Unequal Lives Cadillac Air Cleaner Cheapskate Air Cleaner CF1 N CF0 I NPV – 4,000 CF1 N CF0 I NPV –1,000 –100 –500 10 5 10% 10% –4,614.46 –2,895.39 At first glance, the Cheapskate cleaner has a higher NPV.

Investments of Unequal Lives This overlooks the fact that the Cadillac cleaner lasts twice as long. When we incorporate the difference in lives, the Cadillac cleaner is actually cheaper (i.e., has a higher NPV).

Equivalent Annual Cost (EAC) The EAC is the value of the level payment annuity that has the same PV as our original set of cash flows. For example, the EAC for the Cadillac air cleaner is $750.98. The EAC for the Cheapskate air cleaner is $763.80, thus we should reject it.

Cadillac EAC with a Calculator CF1 N CF0 I NPV –4,000 PMT I/Y FV PV N 10 –100 10% –4,614.46 10 10% 750.98 –4,614.46

Cheapskate EAC with a Calculator CF1 N CF0 I NPV –1,000 PMT I/Y FV PV N 5 –500 10% -2,895.39 5 10% 763.80 –2,895.39

Exercise 1 Your firm purchased a warehouse for $335,000 six years ago. Four years ago, repairs were made to the building which cost $60,000. The annual taxes on the property are $20,000. The warehouse has a current book value of $268,000 and a market value of $295,000. The warehouse is totally paid for and solely owned by your firm. If the company decides to assign this warehouse to a new project, what value, if any, should be included in the initial cash flow of the project for this building?  Opportunity cost = $295,000

Exercise 2 Ernie's Electrical is evaluating a project which will increase sales by $50,000 and costs by $30,000. The project will cost $150,000 and will be depreciated straight-line to a zero book value over the 10 year life of the project. The applicable tax rate is 34%. What is the operating cash flow for this project? Tax = .34  [$50,000 - 30,000 - ($150,000  10)] = $1,700; OCF = $50,000 - $30,000 - $1,700 = $18,300  

Exercise 3 A project will produce operating cash flows of $45,000 a year for four years. During the life of the project, inventory will be lowered by $30,000 and accounts receivable will increase by $15,000. Accounts payable will decrease by $10,000. The project requires the purchase of equipment at an initial cost of $120,000. The equipment will be depreciated straight-line to a zero book value over the life of the project. The equipment will be salvaged at the end of the project creating a $25,000 after-tax cash flow. At the end of the project, net working capital will return to its normal level. What is the net present value of this project given a required return of 14%?  CF0 = $30,000 - $15,000 - $10,000 - $120,000 = -$115,000 C04 = $45,000 -$30,000 + $15,000 + $10,000 + $25,000 = $65,000