# Chapter 5 Capital Budgeting

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1 Chapter 5 Capital Budgeting Road Map Part A Introduction to finance. Part B Valuation of assets, given discount rates. Fixed-Income securities. Common stocks. Real assets (capital budgeting). Part C Determination of risk-adjusted discount rates. Part D Introduction to derivatives. Main Issues NPV Rule Cash Flow Calculations Alternatives to NPV Rule

2 Chapter 5 Capital Budgeting NPV Rule A firm s business involves capital investments (capital budgeting), e.g., the acquisition of real assets. The objective is to increase the firm s current market value. Decision reduces to valuing real assets, i.e., their cash flows. Let the cash flow of an investment (a project) be {CF 0,CF 1,,CF t }. Its current market value is NPV = CF 0 + CF 1 1+r CF t (1+r t ) t. This is the increase in firm s market value by the project. Investment Criteria: 1. For a single project, take it if and only if its NPV is positive. 2. For many independent projects, take all those with positive NPV. 3. For mutually exclusive projects, take the one with positive and highest NPV. Fall 2006 c J. Wang Lecture Notes

3 5-2 Capital Budgeting Chapter 5 In order to compute the NPV of a project, we need to analyze 1. Cash flows 2. Discount rates 3. Strategic options. We focus on cash flow here and return to discount rate (Part C) and strategic options (Part D) later Lecture Notes c J. Wang Fall 2006

4 Chapter 5 Capital Budgeting Cash Flow Calculations Main Points: 1. Use cash flows, not accounting earnings. 2. Use after-tax cash flows. 3. Use cash flows attributable to the project (compare firm value with and without the project): Use incremental cash flows. Forget sunk costs: bygones are bygones. Include investment in working capital as capital expenditure. Include opportunity costs of using existing facilities. Fall 2006 c J. Wang Lecture Notes

5 5-4 Capital Budgeting Chapter 5 In what follows, all cash flows are attributable to the project. CF = [Project Cash Inflows] [Project Cash Outflows] = [Operating Revenues] [Operating Expenses without depreciation] [Capital Expenditures] [Taxes]. Defining operating profit by Operating Profit = Operating Revenues Operating Expenses w/o Depreciation Let τ denote the effective tax rate. The income taxes are [Taxes] =(τ)[operating Profit] (τ) [Depreciation]. Accounting depreciation affects cash flows because it reduces the company s tax bill. Then CF = (1 τ)[operating Profits] [Capital Expenditures] +(τ)[depreciation] Lecture Notes c J. Wang Fall 2006

6 Chapter 5 Capital Budgeting Use Cash Flows, Not Accounting Earnings Example. Accounting Earnings vs. Cash Flows. A machine purchased for \$1,000,000 with a life of 10 years generates annual revenues of \$300,000 and operating expenses of \$100,000. Assume that machine will be depreciated over 10 years using straight-line depreciation. The corporate tax rate is 40%. Date Accounting Earnings Accounting Earnings Cash Flow After-tax Before Tax After Tax ,000, , , ,000 = (1-0.4)(100,000) = (1-0.4) (300, ,00) + 100,000 60,000 40,000 = 160, ,000 60, , ,000 60, , ,000 60, , ,000 60, , ,000 60, , ,000 60, , ,000 60, , ,000 60, , ,000 60, ,000 The accounting earnings do not accurately reflect the actual timing of cash flows. Fall 2006 c J. Wang Lecture Notes

7 5-6 Capital Budgeting Chapter Use After-tax Cash Flows Example. Consider the following project (the cash flow is in thousands of dollars and tax rate is 50%): Year Invest 500 Operating CF Depreciation Income Tax After-tax CF PV at 10% NPV = Lecture Notes c J. Wang Fall 2006

8 Chapter 5 Capital Budgeting Investment In WC Is A Capital Expenditure Typically, there are timing differences between the accounting measure of earnings (Sales - Cost of Goods Sold) and cash flows. Working Capital (WC) = Inventory + A/R A/P. Changes in Working Capital Inventory: Cost of goods sold includes only the cost of items sold. When inventory is rising, the cost of goods sold understates cash outflows. When inventory is falling, cost of goods sold overstates cash outflows. Accounts Receivable (A/R): Accounting sales may reflect sales that have not been paid for. Accounting sales understate cash inflows if the company is receiving payment for sales in past periods. Accounts Payable (A/P) conceptually the reverse of A/R. Fall 2006 c J. Wang Lecture Notes

9 5-8 Capital Budgeting Chapter 5 Example. You run a chain of stores that sell sweaters. This quarter, you buy 1,000,000 sweaters at a price of \$30.00 each. For the next two quarters, you sell 500,000 sweaters each quarter for \$60.00 each. The corporate tax rate is 40%. In million dollars, your cash flows are Date After Tax Profit Inventory Cash Flow 0 0 (1)(30) = (0.5)(60-30)(1-0.4) = 9 (0.5)(30) = 15 (0.5)(60) - (0.5)(60-30)(0.4) = 24 2 (0.5)(60-30)(1-0.4) = 9 0 (0.5)(60) - (0.5)(60-30)(0.4) = 24 Note: Cash flow = Profit (after tax) Change in Inventory Lecture Notes c J. Wang Fall 2006

10 Chapter 5 Capital Budgeting Use Market Valuation Example. Reopen King Solomon s mine: Initial investment \$39.2 M Capacity 0.1 million oz for a life of 1year Production cost \$200 per oz Current gold price P 0 = \$400 per oz Forecasted gold price growth 5% by bearish manager Discount rate 10%. NPV using the forecast: NPV = (0.1)(420) 1.10 = \$1million. However, gold pays no dividend. Thus, P 0 = PV (P 1 ) and NPV = Investment + PV (Payoff)) = 39.2+PV (0.1 P 1 ) = = +\$0.8million. Use today s gold price. Fall 2006 c J. Wang Lecture Notes

11 5-10 Capital Budgeting Chapter 5 Example (Gromb). MSW Inc. is considering the introduction of a new product: Turbo-Widgets (TW). TW were developed at an R&D cost of \$1M over past 3 years New machine to produce TW would cost \$2M New machine lasts for 15 years, with salvage value of \$50,000 New machine can be depreciated linearly to \$0 over 10 years TW need to be painted; this can be done using excess capacity of the painting machine, which currently runs at a cost of \$30,000 (regardless of how much it is used) Operating cost: \$40,000 per year Sales: \$400,000, but cannibalization would lead existing sales of regular widgets to decrease by \$20,000 Working Capital (WC): \$250,000 needed over the life of the project Tax rate: 34% Opportunity cost of capital: 10%. Question: What is the project s NPV (i.e., should MSW go ahead with the production of TW)? Lecture Notes c J. Wang Fall 2006

12 Chapter 5 Capital Budgeting Initial investment includes capital expenditure and WC 2. R&D expense is a sunk cost 3. Depreciation is \$2M/10 = \$0.2M for first 10 years 4. Project should not be charged for painting-machine time 5. Project should be charged for cannibalization of regular widget sales 6. Salvage value is fully taxable since the book value at the end of year 10 is \$0 (the machine cost has been fully depreciated). The cash flows (in thousand dollars) are Year Cash Flow 0 - ( ) = ( )(1-0.34) + (200)(0.34) = ( )(1-0.34) = (50)(1-0.34) = NPV = \$57, 617. Fall 2006 c J. Wang Lecture Notes

13 5-12 Capital Budgeting Chapter 5 3 Project Interaction Often we have to decide on more than one project. For mutually independent projects, we just apply the NPV rule to each one of them. For projects dependent of each other (e.g., mutually exclusive accepting one rules out the others), we have to compare their NPVs. Example. Potential demand for your product is projected to increase over time. If you start the project early, your competitors will catch up with you faster, by copying your idea. Your opportunity cost of capital is 10%. Denoting by FPV the project s NPV at the time of introduction, we have: Year to Start FPV % Change in FPV NPV Before year 4, the return to waiting is larger that the opportunity cost of capital, 10%. As long as the growth rate of FPV remains below 10% after year 4, it is best to wait and introduce at the end of year Lecture Notes c J. Wang Fall 2006

14 Chapter 5 Capital Budgeting Alternatives to NPV In practice, investment rules other than NPV are also used: Payback Period Profitability Index (PI) Internal Rate of Return (IRR) Firms use these rules because they were used historically and they may have worked (in combination with common sense) in the particular cases encountered by these firms. These rules sometimes give the same answer as NPV, but in general they do not. We should be aware of their shortcomings and use NPV whenever possible. The bottom line is: The NPV rule dominates these alternative rules. Fall 2006 c J. Wang Lecture Notes

15 5-14 Capital Budgeting Chapter Payback Period Definition: Payback period is the minimum s so that CF 1 + CF CF s CF 0 = I 0 In words, s is the minimum length of time such that the sum of cash flows from a project is positive. Decision Criterion Using Payback Period For independent projects: Accept if s is less than or equal to some fixed threshold t. For mutually exclusive projects: Among all the projects having s t, accept the one that has the minimum payback period. Example. Let t =3. Consider the two independent projects with the following cash flows (in thousands): CF 0 CF 1 CF 2 CF 3 CF 4 CF 5 CF 6 t Project Project Decision: Accept Project Lecture Notes c J. Wang Fall 2006

16 Chapter 5 Capital Budgeting 5-15 Problems with Payback Period It ignores cash flows after the payback period. It ignores discounting. Example. (Continued.) Suppose that the appropriate discount rate is a constant 10% per period. Then NPV 1 =39, 315 and NPV 2 = 7, 270. But we accepted project 2 and not project 1! Discounted Payback Period Taking into account appropriate discounting, we have the discounted payback period: Definition: Discounted payback period is the minimum t so that CF 1 1+r + CF 2 CF t + + (1 + r) 2 (1 + r) CF t 0 where r is the discount rate. Problem: It still ignores the cash flows after the discounted payback period. Fall 2006 c J. Wang Lecture Notes

17 5-16 Capital Budgeting Chapter Internal Rate of Return (IRR) IRR is the number that satisfies 0=CF 0 + CF 1 (1 + IRR) + CF 2 (1 + IRR) 2 + CF t (1 + IRR) t. Decision Criterion Using IRR For independent projects: Accept a project if its IRR is greater than some fixed IRR, the threshold rate. For mutually exclusive projects: Among the projects having IRR s greater than IRR, accept one with the highest IRR. Example Consider the following mutually exclusive projects: CF 0 CF 1 CF 2 CF 3 CF 4 CF 5 CF 6 Project Project Then, IRR 1 = 21% and IRR 2 =7%. IRR rule leads to the same decisions as NPV if 1. Cash outflow occurs only at time 0 2. Only one project is under consideration 3. Opportunity cost of capital is the same for all periods 4. Threshold rate is set equal to opportunity cost of capital Lecture Notes c J. Wang Fall 2006

18 Chapter 5 Capital Budgeting 5-17 Problems with IRR 1. Non-existence of IRR CF 0 CF 1 CF 2 Project Project No IRR exists for these two projects. 2. Multiple IRR s CF 0 CF 1 CF 2 CF 3 Project 1-500,000 1,575,000-1,653, ,815 Project 2-500,000 1,605,000-1,716, ,040 IRR 1 =7% and IRR 2 = 4% 7% 10% 40 NPV of Project 1 NPV of Project NPV Discount rate Fall 2006 c J. Wang Lecture Notes

19 5-18 Capital Budgeting Chapter 5 3. Project ranking using IRR for mutually exclusive projects: (a) Projects of different scales: CF 0 CF 1 IRR NPV at 10% Project 1-10,000 20, % 8, Project 2-20,000 36,000 80% 12, A way around this problem is to use incremental CF: See if lower investment (project 1) is a good idea See if incremental investment (project 2) is a good idea. CF 0 CF 1 IRR NPV at 10% Project 1-10,000 20, % 8, Project 2-20,000 36,000 80% 12, Project ,000 16,000 60% 4, (b) Projects with different time patterns of cash flows: CF t ETC IRR NPV at 10% Project % Project % Project % Lecture Notes c J. Wang Fall 2006

20 Chapter 5 Capital Budgeting Profitability Index Definition: Profitability Index (PI) is the ratio of the present value of future cash flows and the initial cost of a project: PI = PV = PV. CF 0 I 0 Decision Criterion Using PI For independent projects: Accept all projects with PI greater than one (this is identical to the NPV rule) For mutually exclusive projects: Among the projects with PI greater than one, accept the one with the highest PI. Problems with PI PI gives the same answer as NPV when (1) There is only one cash outflow, which is at time 0 (2) Only one project is under consideration. PI scales projects by their initial investments. The scaling can lead to wrong answers in comparing mutually exclusive projects. CF 0 CF 1 IRR NPV at 10% PI at 10% Project 1-1,000 2, % Project 2-2,000 3,600 80% 1, Project ,000 1,600 60% Fall 2006 c J. Wang Lecture Notes

21 5-20 Capital Budgeting Chapter The Practice of Capital Budgeting Comparison of Methods Used by Large U.S. and Multinational Firms Large U.S. Firms Percentage Using Each Method Use as Primary Method Multinationals Use as Secondary Method Payback Period 80.3% 5.0% 37.6% IRR NPV Other Historical Comparison of Primary use of Various Capital Budgeting Techniques Payback Period 34% 24% 12% 15% 9% 10% 5.0% IRR NPV IRR or NPV Source: S. Ross, R. Westerfield, and B. Jordon, Essentials of Corporate Finance, Irwin, 1996.) Lecture Notes c J. Wang Fall 2006

22 Chapter 5 Capital Budgeting Other Issues in Capital Budgeting 1. Competitive Response: CF forecasts should consider responses of competitors. 2. Capital Rationing. 3. Sources of Positive-NPV Projects: Short-run competitive advantage (right place at right time) Long-run competitive advantage - patent - technology - economies of scale, etc. Noise. Fall 2006 c J. Wang Lecture Notes

23 5-22 Capital Budgeting Chapter 5 6 Homework Readings: BMA Chapters 5, 6, 10, 11. Assignment: Case write-up on capital budgeting: Acid Rain Lecture Notes c J. Wang Fall 2006

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