# Capital Budgeting Cash Flows

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1 Learning Objectives 1-1 Capital Budgeting Cash Flows 1 Corporate Financial Management 3e Emery Finnerty Stowe 1-2 Calculate incremental after-tax cash flows for a capital budgeting project. Explain the importance and difficulty of incorporating the effects of erosion and enhancement on the firm s existing operations. Incorporate the effects of inflation into an NPV calculation. Explain the importance of using current tax laws. Calculate equivalent annual annuities and determine optimal asset life and replacement cycles. Chapter Outline Focus on Principles An Overview of Estimating Cash Flows 1.2 Calculating Incremental Cash Flows 1.3 An Example of Incremental Cash Flow Analysis 1.4 Inflation 1.5 A Little More About Taxes 1.6 Evaluating Replacement Cycles 1-4 Incremental Benefits Identify and estimate the incremental expected after-tax future cash flows for a project. Time-Value-Of-Money Measure the value of the project: its NPV. Risk-Return Trade-Off Incorporate the risk of a project into its cost of capital. 1-5 Focus on Principles Valuable Ideas Look for new ideas to use as a basis for capital budgeting projects that will create value. Comparative Advantage Look for projects that exploit the firm s comparative advantage. Options Recognize the options embedded in a capital budgeting project. 1-6 Focus on Principles Two-Sided Transactions Consider why the party on the other side of the transaction is willing to participate. Signaling Consider the actions and products of competitors. 1

2 1.1 An Overview of Estimating Cash Flows Tax Considerations 1-7 Costs and benefits are measured in terms of cash flow not income. Cash flows are incremental (marginal). The cash flows with the project minus the cash flows without the project. Cash flows are after tax. Cash flow timing affects the project s value. Financing costs are included in the cost of capital. 1-8 Taxes and the timing of tax payments significantly affect the incremental cash flows. The relevant tax rate is the firm s marginal tax rate, T. Revenues, represented by R, increase tax liability by TR. When the revenue and the tax treatment occur simultaneously, the after-tax cash flow is the revenue minus the tax liability: after-tax revenue cash flow = R Τ R = (1 Τ) R Tax Considerations Tax Considerations 1-9 Less obvious is that expenses, represented by E, reduce tax liability. When the revenue and the tax treatment occur When the expense and the tax treatment occur simultaneously, the algebraic signs carry through and the aftertax cash flow is minus the expense plus the reduced tax liability: after-tax expense cash flow = E + Τ E = (1 Τ) E In some cases the cash flow and tax treatment are separated. This complicates the analysis. The most common situation where they are separated is when an asset is capitalized (depreciated). Let I be a net expenditure to be capitalized, and D t be its depreciation expense to be claimed in year t. The separated incremental after-tax cash flow for each depreciation expense is +T D t. (This is just like the +T Efor an expense.) 1-1 Tax Considerations Tax Considerations 1-11 With depreciation, the stream of after-tax incremental cash flows for the expenditure, I, are then: t CF -I TD 1 TD 2 TD 3... The sum of the D t sequals I. So the total amount of tax reduction is T(I ) whether you depreciate or expense the item. Suppose you pay \$1, for an asset. If capitalized, depreciation would be straightline to zero over 4 years, 25 per yr. With a tax rate of 4%, that s 1 per yr. after-tax. Time Depr. Exp ATCF -1, If expensed: -6 Which set of cash flows is preferred?

3 Tax Considerations The difference between expensing and depreciating and between alternative tax treatments in most cases, then, is because of the time value of money. If you have a choice, expense rather than capitalize because of the time value of money. Unfortunately, you rarely have a choice! 1.2 Calculating Incremental Cash Flows Net initial investment outlay. Future net operating cash flows. Non-operating cash flows required to support the initial investment outlay. E.g., cash flows associated with a major overhaul. Net salvage value received upon termination of the project Net Initial Investment Outlay Cash expenditure. Changes in net working capital. Net cash flow from sale of old asset (if any). Investment tax credits. Cash Expenditure Let I be the net expenditure to be capitalized, E be the net expenditure to be expensed immediately, and T be the firm s marginal tax rate. Cash expenditure = I E + Τ E = I (1 Τ) E Changes in Net Working Capital At the start of a project, an investment of net working capital may be required. Operating cash Inventory Accounts receivable But, an increase in accounts payable offsets some of the net working capital needs. A project could also reduce the net working capital requirements. Asset replacement Net Cash Flow from Sale of Old Asset If an existing asset is being replaced by a new one, the sale of the old asset may generate a cash flow. If the selling price is greater than the net book value of the old asset, taxes will have to be paid on this sale. If the selling price is less than the net book value of the old asset, a tax credit is generated

4 Net Cash Flow from Sale of Old Asset Let S be the selling price of the old asset, and B be its net book value. Taxes on the sale will be Τ (S B ). So the net cash flow from sale of old asset is: Net Initial Outlay Let C be the net initial outlay. Let ΔW be the change in the net working capital. Let I c be the investment tax credit. Then, S - Τ (S B ) C = I ΔW (1 T) E + S T(S B ) + I c Net Operating Cash Flow Let ΔR be the change in periodic revenue and ΔE be the change in periodic expenses associated with the project. Let ΔD be the change in the periodic depreciation expense. The Net Operating Cash Flow After Tax (CFAT) is given by Net Operating Cash Flow CFAT = ΔR - ΔE - Tax liability = ΔR - ΔE - T(ΔR - ΔE - ΔD) CFAT = (1 - T)(ΔR - ΔE) + TΔD CFAT = after-tax operating income + tax credit on depreciation Net Operating Cash Flow Alternatively, by rearranging the terms, we can rewrite CFAT as: CFAT = (1 - T)(ΔR - ΔE - ΔD) + ΔD = after-tax net income + depreciation Note that there is no interest expense, and this after-tax net income is not from an accounting income statement Non-Operating Cash Flows These are treated in the same way as the initial cash expenditure. The expensed non-operating cash flows are multiplied by (1 - T) to adjust for taxes, because the cash flow and tax treatment occur simultaneously. Capitalized non-operating cash flows create a cash outflow when they occur, but only in subsequent years does the tax treatment create the depreciation tax shields. 4

5 Net Salvage Value Let S be the selling price of the asset and B its book value. Let REX be the cleanup and removal expenses (to be expensed) and ΔW the net working capital recovered upon termination of the project. 1.3 An Example of Incremental Cash Flow Analysis See handout on Perma-Filter Co., attached as speaker notes. Net salvage value = = S -T(S -B) -(1 -T)REX + ΔW Perma-Filter: By-Item Cash Flows Perma-Filter: By-Item Cash Flows Net expenditure to be capitalized is I = 5,1, + 4, = \$5,5, after-tax CF = -\$5,5, Installation cost to be expensed immediately is E = \$2,, after-tax CF = -\$12, The replacement requires an investment in net working capital: Inventory increase - Accounts Payable increase = 4, - 25, = \$15, after-tax CF = -\$15, Annual depreciation on the old machine is (3,, - )/1 = \$3,/yr Therefore, the current net book value is 3,, - 5(3,) = \$1,5, = B Selling price of old machine is \$1,75, = S Taxes on the difference are \$1,, so the after-tax CF for the old machine is \$1,65, There is no investment tax credit, I c = Perma-Filter: By-Item Cash Flows Annual depreciation expense on the new machine is (5,5, - 35,)/1 = \$515,/yr after-tax CF is \$26,/yr, years 1-1 In the first five years after the replacement, the firm loses the depreciation expense on the old machine, after that, depreciation on the old machine (if kept) would be \$. Perma-Filter: By-Item Cash Flows Recall that annual depreciation on the old machine is \$3,/yr. Therefore, there will be lost after-tax CF = -\$12,/yr, years 1-5 Sales do not increase, and ΔR =. Cash expenses decline, so ΔE = -\$1,2,/yr, giving after-tax CF savings = \$72,/yr, years

6 Perma-Filter: By-Item Cash Flows Net Present Value The new machine is expected to be sold for S = \$3, But will have a net book value at that time of B = \$35, The difference creates a tax credit, so the after-tax CF = \$32, Removal expenses will be REX = -\$15,, and after-tax CF = -\$9, Net working capital (recovered) will be an after-tax CF = \$15, See handout on NPV calculation, attached as speaker notes Adding Value per Share The replacement project will create value because the NPV is positive. How much value would the project add to each share? With 5, shares outstanding, making the replacement will add about \$1.79 to each share s value: 893,417 / 5, = \$1.79 per share The Internal Rate of Return (IRR) The IRR is the discount rate that makes the NPV equal to zero. For Perma-Filter s replacement project, IRR = 16.95% NOTE: It is very important to understand that this does not mean the stock price will increase by this amount when the project is undertaken. Stock prices are based on expectations. The stock price could increase by less because the project was partially anticipated. It could also not change because the project was fully anticipated, or even fall because the project produces less value than had been expected NPV (\$ thousands) NPV Profile - Perma-Filter Co. \$6, \$5, \$4, \$3, \$2, \$1, \$- \$(1,) \$(2,) % 5% 1% 15% 2% 25% Discount Rate IRR 16.95% 1-36 New Project Side Effects Innovation can result in the erosion of one or more existing products. Sales reduction Decline in market value of existing facilities. Innovation can also lead to enhancement of existing and future products and services. Expanding one product line can stimulate sales of another. (service contracts). Both erosion and enhancement must be incorporated into a capital budgeting analysis. 6

7 1.4 Inflation Inflation affects the project s expected cash flows. Effect on revenues Effect on expenses Inflation also affects the cost of capital. The higher the expected inflation, the higher the return required by investors. So the effects of inflation must be properly incorporated in the NPV analysis. Effect of Inflation on the Cost of Capital Notation: r r = cost of capital in real terms r n = cost of capital in nominal terms i = expected annual inflation rate (1 + r n ) = (1 + r r ) (1 + i) r n = r r + i + ir r Effect of Inflation on the Cost of Capital Inflation increases the nominal amounts of both revenues and expenses, even though their real values may stay the same. However, depreciation expense is fixed. It is based on historical cost. Therefore, inflation decreases the real value of depreciation tax credits. Effect of Inflation on the Cost of Capital If expected future cash flows are given in nominal terms, then we must use the nominal cost of capital to calculate their present value. If expected future cash flows are given in real terms, we must use the real cost of capital to calculate their present value Inflation and NPV Wildcat Washer Works (WWW) is evaluating a new project that costs \$12,. It has a life of 3 years and no salvage value. Annual revenues, less operating expenses (excluding depreciation) are \$65, per year in real dollars. WWW will use straight line depreciation to a zero book value over 3 years. Its marginal tax rate is 4%. The real cost of capital is 1% and inflation is expected to be 8% per year. Compute the NPV of the project in real and in nominal dollars NPV in Real Dollars Annual after-tax revenues (less expenses), in real dollars are 65,(1-.4) = \$39, per year. Annual depreciation expense (in nominal dollars) is (12, - )/3 = \$4, per year. Annual depreciation tax credit (in nominal dollars) is 4,(.4) = \$16, per year. 7

8 NPV in Real Dollars NPV in Real Dollars 1-43 In real dollars, the first year s depreciation tax credit is worth 16,/(1.8) = \$14,815. In real dollars, the second year s depreciation tax credit is worth 16,/(1.8) 2 = \$13,717. In real dollars, the third year s depreciation tax credit is worth 16,/(1.8) 3 = \$12,71. The annual after-tax cash flow is the after tax revenues (less expenses) plus the depreciation tax credit Time Item BTCF ATCF Initial inv. Net rev. Depr. Depr. Depr. 65/yr 39/yr NPV= NPV in Nominal Dollars Annual depreciation expense (in nominal dollars) is (12, - )/3 = \$4, per year. Annual depreciation tax credit (in nominal dollars) is 4,(.4) = \$16, per year. NPV in Nominal Dollars In nominal dollars, revenues net of expenses in year 1 are 65,(1.8) = \$7,2. After-tax net revenues = 7,2(1-.4) = \$42,12. In nominal dollars, revenues net of expenses in year 2 are 65,(1.8) 2 = \$75,816 After-tax net revenues = 75,816(1-.4) = \$45,49. After-tax net revenues in year 3 are \$49, NPV in Nominal Dollars The nominal cost of capital is: r n = r r + i + (i)r r = (.8)(.1) =.188 r n = 18.8% NPV in Nominal Dollars Time Item BTCF ATCF Initial inv. Depr. Net rev. Net rev. Net rev. /yr /yr NPV= NOTE: = And =

9 NPV Inflation and NPV Analysis Time Item BTCF ATCF PV Initial inv. Net rev. Depr. 65/yr 39/yr 16/yr 1% 18.8% NPV= The NPV of the project is unchanged as long as the cash flows and the cost of capital are expressed in consistent terms. If inflation is expected to affect revenues and expenses differently, these differences must be incorporated in the analysis Inflation and NPV Analysis 1.5 A Little More About Taxes 1-51 See handout on Jip-Sum Corp., attached as speaker notes. Tax laws frequently change: Marginal tax rates. Provisions for allowable depreciation of capital assets. Investment tax credit. Therefore, it is critical to use the current tax laws to determine after-tax cash flows for a capital budgeting decision. The marginal tax rate may be higher than the marginal federal income tax rate due to other taxes, such as state, excise, and local A Note on Depreciation 1.6 Evaluating Replacement Cycles 1-53 The total amount of depreciation tax credits over the life of the project is independent of the depreciation method used. The present value of these tax credits are dependent on the depreciation method. Accelerated versus straight line methods. A firm should use the depreciation method that results in the largest present value of depreciation tax credits. Certain assets need to be replaced after the original is worn out. Example: delivery vehicles The initial choice may involve alternative models that essentially do the same job but differ in their costs and usable life. The choice can be made in two ways: Equivalent Annual Cost method Common Horizon method

10 Unequal Life Projects The Mid-Town Transit Co. is considering the purchase of a special purpose delivery vehicle. Two models are available: Model A Model B Cost Useful life After-tax annual operating expenses \$4, 5 years \$12, \$6, 9 years \$1,5 If the cost of capital is 15%, which one should it choose? 1-55 Unequal Life Projects First, compute the total present value of the costs (TC) over the life of the project. Next, determine the annual cash flow that, if it occurred every year, would have a present value = TC. This annual cash flow is called the Equivalent Annual Cost (EAC). Now choose the project that has the lowest EAC. If both projects have the same EAC, choose the one with the shorter life Computing the EAC TC = C + n t = 1 C t ( 1+ r ) t EAC for Mid-Town Transit Co. s Projects Cost Useful life After-tax annual operating expenses Model A \$4, 5 years \$12, Model B \$6, 9 years \$1,5 EAC = TC n r( 1+ r ) n ( 1+ r ) 1 Total Present Value Equivalent Annual Cost -\$8,226 -\$23,933 -\$11,12 -\$23, N=n i=r PV=TC FV= PMT= EAC N=5 i=15 PV=8,226 FV= PMT= -23,933 (Note operating leverage difference, and at 17% for B, EAC 1-58 = \$23,981) Optimal Replacement Frequency Optimal Replacement Frequency Fisher Plastics uses an extruding machine in its manufacturing process. The machine costs \$5,, and annual after-tax operating expenses are \$12, per year. If used for 4 years, it can be sold for an aftertax salvage value of \$15,. If used for 6 years, the after-tax salvage value would be zero. If the cost of capital is 15%, should Fisher use this machine for 4 or 6 years? By replacing the machine every 4 (6) years, the firm incurs the cost of the new machine more (less) often. However, it receives a higher (lower) salvage value. The optimal replacement frequency takes into account these opposing effects

11 1-61 Optimal Replacement Frequency Replacement Frequency: 4 Years 6 years Cost Annual operating expenses Salvage Value \$5, \$12, \$15, \$5, \$12, \$ Total Present Value Cost Equivalent Annual Cost -\$75,683 -\$26,59 -\$95,414 -\$25,212 N=4 i=15 PMT=-12, FV=+15, PV= 25,683 25, , = 75,683 N=4 i=15 PV=75,683 FV= PMT= -26, Equivalent Annual Annuity The EAC annualizes the cost of the project over its life. This concept can be applied to annualize any amount: A project s NPV A project s total revenues The general term is called the Equivalent Annual Annuity (EAA) Equivalent Annual Annuity The EAA can be used to choose among mutually exclusive projects with unequal lives. Choose the project with the highest EAA. If two projects have the same EAA, choose the project with the shorter life. Equivalent Annual Annuity Fisher Plastics is considering a new 6 year project that has an NPV of \$2,65 at a cost of capital of 15%. What is the project s Equivalent Annual Annuity (EAA)? N=6 i=15 PV=2,65 FV= PMT= Summary This chapter describes the critical problem of estimating a capital budgeting project s incremental cash flows. We want to leave you with one final observation: The accuracy of the estimates used in capital budgeting is critically important

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