Chapter 8 - Cash Flows and Other Topics in Capital Budgeting

Capital Budgeting: The process of planning for purchases of long-term assets. For example: Our firm must decide whether to purchase a new plastic molding machine for $127,000. How do we decide? Will the machine be profitable? Will our firm earn a high rate of return on the investment? The relevant project information follows:

The cost of the new machine is $127,000. Installation will cost $20,000. $4,000 in net working capital will be needed at the time of installation. The project will increase revenues by $85,000 per year, but operating costs will increase by 35% of the revenue increase. Simplified straight line depreciation is used. Class life is 5 years, and the firm is planning to keep the project for 5 years. Salvage value at the end of year 5 will be $50,000. 14% cost of capital; 34% marginal tax rate.

Capital Budgeting Steps 1) Evaluate Cash Flows Look at all incremental cash flows occurring as a result of the project. Initial outlay Differential Cash Flows over the life of the project (also referred to as annual cash flows). Terminal Cash Flows

Capital Budgeting Steps 1) Evaluate Cash Flows 1 2 3 4 5 n 6 . . .

Capital Budgeting Steps 1) Evaluate Cash Flows Initial outlay 1 2 3 4 5 n 6 . . .

Capital Budgeting Steps 1) Evaluate Cash Flows Initial outlay 1 2 3 4 5 n 6 . . . Annual Cash Flows

Capital Budgeting Steps 1) Evaluate Cash Flows Terminal Cash flow Initial outlay 1 2 3 4 5 n 6 . . . Annual Cash Flows

Capital Budgeting Steps 2) Evaluate the Risk of the Project We’ll get to this in the next chapter. For now, we’ll assume that the risk of the project is the same as the risk of the overall firm. If we do this, we can use the firm’s cost of capital as the discount rate for capital investment projects.

Capital Budgeting Steps 3) Accept or Reject the Project

Step 1: Evaluate Cash Flows a) Initial Outlay: What is the cash flow at “time 0?” (Purchase price of the asset) + (shipping and installation costs) (Depreciable asset) + (Investment in working capital) + After-tax proceeds from sale of old asset Net Initial Outlay

Step 1: Evaluate Cash Flows a) Initial Outlay: What is the cash flow at “time 0?” (127,000) + (shipping and installation costs) (Depreciable asset) + (Investment in working capital) + After-tax proceeds from sale of old asset Net Initial Outlay

Step 1: Evaluate Cash Flows a) Initial Outlay: What is the cash flow at “time 0?” (127,000) + ( 20,000) (Depreciable asset) + (Investment in working capital) + After-tax proceeds from sale of old asset Net Initial Outlay

Step 1: Evaluate Cash Flows a) Initial Outlay: What is the cash flow at “time 0?” (127,000) + ( 20,000) (147,000) + (Investment in working capital) + After-tax proceeds from sale of old asset Net Initial Outlay

Step 1: Evaluate Cash Flows a) Initial Outlay: What is the cash flow at “time 0?” (127,000) + (20,000) (147,000) + (4,000) + After-tax proceeds from sale of old asset Net Initial Outlay

Step 1: Evaluate Cash Flows a) Initial Outlay: What is the cash flow at “time 0?” (127,000) + (20,000) (147,000) + (4,000) + 0 Net Initial Outlay

Step 1: Evaluate Cash Flows a) Initial Outlay: What is the cash flow at “time 0?” (127,000) Purchase price of asset + (20,000) Shipping and installation (147,000) Depreciable asset + (4,000) Net working capital + 0 Proceeds from sale of old asset ($151,000) Net initial outlay

Step 1: Evaluate Cash Flows a) Initial Outlay: What is the cash flow at “time 0?” (127,000) Purchase price of asset + (20,000) Shipping and installation (147,000) Depreciable asset + (4,000) Net working capital + 0 Proceeds from sale of old asset ($151,000) Net initial outlay

Step 1: Evaluate Cash Flows b) Annual Cash Flows: What incremental cash flows occur over the life of the project?

For Each Year, Calculate: Incremental revenue - Incremental costs - Depreciation on project Incremental earnings before taxes - Tax on incremental EBT Incremental earnings after taxes + Depreciation reversal Annual Cash Flow

For Years 1 - 5: Incremental revenue - Incremental costs - Depreciation on project Incremental earnings before taxes - Tax on incremental EBT Incremental earnings after taxes + Depreciation reversal Annual Cash Flow

For Years 1 - 5: 85,000 - Incremental costs - Depreciation on project Incremental earnings before taxes - Tax on incremental EBT Incremental earnings after taxes + Depreciation reversal Annual Cash Flow

For Years 1 - 5: 85,000 (29,750) - Depreciation on project Incremental earnings before taxes - Tax on incremental EBT Incremental earnings after taxes + Depreciation reversal Annual Cash Flow

For Years 1 - 5: 85,000 (29,750) (29,400) Incremental earnings before taxes - Tax on incremental EBT Incremental earnings after taxes + Depreciation reversal Annual Cash Flow

For Years 1 - 5: 85,000 (29,750) (29,400) 25,850 - Tax on incremental EBT Incremental earnings after taxes + Depreciation reversal Annual Cash Flow

For Years 1 - 5: 85,000 (29,750) (29,400) 25,850 (8,789) Incremental earnings after taxes + Depreciation reversal Annual Cash Flow

For Years 1 - 5: 85,000 (29,750) (29,400) 25,850 (8,789) 17,061 + Depreciation reversal Annual Cash Flow

For Years 1 - 5: 85,000 (29,750) (29,400) 25,850 (8,789) 17,061 29,400 Annual Cash Flow

For Years 1 - 5: 85,000 Revenue (29,750) Costs (29,400) Depreciation 25,850 EBT (8,789) Taxes 17,061 EAT 29,400 Depreciation reversal 46,461 = Annual Cash Flow

Step 1: Evaluate Cash Flows c) Terminal Cash Flow: What is the cash flow at the end of the project’s life? Salvage value +/- Tax effects of capital gain/loss + Recapture of net working capital Terminal Cash Flow

Step 1: Evaluate Cash Flows c) Terminal Cash Flow: What is the cash flow at the end of the project’s life? 50,000 Salvage value +/- Tax effects of capital gain/loss + Recapture of net working capital Terminal Cash Flow

Tax Effects of Sale of Asset: Salvage value = $50,000. Book value = depreciable asset - total amount depreciated. Book value = $147,000 - $147,000 = $0. Capital gain = SV - BV = 50,000 - 0 = $50,000. Tax payment = 50,000 x .34 = ($17,000).

Step 1: Evaluate Cash Flows c) Terminal Cash Flow: What is the cash flow at the end of the project’s life? 50,000 Salvage value (17,000) Tax on capital gain Recapture of NWC Terminal Cash Flow

Step 1: Evaluate Cash Flows c) Terminal Cash Flow: What is the cash flow at the end of the project’s life? 50,000 Salvage value (17,000) Tax on capital gain 4,000 Recapture of NWC Terminal Cash Flow

Step 1: Evaluate Cash Flows c) Terminal Cash Flow: What is the cash flow at the end of the project’s life? 50,000 Salvage value (17,000) Tax on capital gain 4,000 Recapture of NWC 37,000 Terminal Cash Flow

Project NPV: CF(0) = -151,000. CF(1 - 4) = 46,461. Discount rate = 14%. NPV = $27,721. We would accept the project.

Capital Rationing Suppose that you have evaluated five capital investment projects for your company. Suppose that the VP of Finance has given you a limited capital budget. How do you decide which projects to select?

Capital Rationing You could rank the projects by IRR:

Capital Rationing You could rank the projects by IRR: IRR 25% 20% 15% 10% 15% 20% 25% $ 1

Capital Rationing You could rank the projects by IRR: IRR 5% 10% 15% 20% 25% $ 1 2

Capital Rationing You could rank the projects by IRR: IRR 5% 10% 15% 20% 25% $ 1 2 3

Capital Rationing You could rank the projects by IRR: IRR 5% 10% 15% 20% 25% $ 1 2 3 4

Capital Rationing You could rank the projects by IRR: IRR 5% 10% 15% 20% 25% $ 5 1 2 3 4

Capital Rationing You could rank the projects by IRR: IRR 5% 10% 15% 20% 25% $ Our budget is limited so we accept only projects 1, 2, and 3. 1 2 3 4 5 $X

Capital Rationing You could rank the projects by IRR: IRR 5% 10% 15% 20% 25% $ Our budget is limited so we accept only projects 1, 2, and 3. 1 2 3 $X

Capital Rationing Ranking projects by IRR is not always the best way to deal with a limited capital budget. It’s better to pick the largest NPVs. Let’s try ranking projects by NPV.

Problems with Project Ranking 1) Mutually exclusive projects of unequal size (the size disparity problem) The NPV decision may not agree with IRR or PI. Solution: select the project with the largest NPV.

Size Disparity Example Project A year cash flow 0 (135,000) 1 60,000 2 60,000 3 60,000 required return = 12% IRR = 15.89% NPV = $9,110 PI = 1.07

Size Disparity Example Project A year cash flow 0 (135,000) 1 60,000 2 60,000 3 60,000 required return = 12% IRR = 15.89% NPV = $9,110 PI = 1.07 Project B year cash flow 0 (30,000) 1 15,000 2 15,000 3 15,000 required return = 12% IRR = 23.38% NPV = $6,027 PI = 1.20

Size Disparity Example Project A year cash flow 0 (135,000) 1 60,000 2 60,000 3 60,000 required return = 12% IRR = 15.89% NPV = $9,110 PI = 1.07 Project B year cash flow 0 (30,000) 1 15,000 2 15,000 3 15,000 required return = 12% IRR = 23.38% NPV = $6,027 PI = 1.20

Problems with Project Ranking 2) The time disparity problem with mutually exclusive projects. NPV and PI assume cash flows are reinvested at the required rate of return for the project. IRR assumes cash flows are reinvested at the IRR. The NPV or PI decision may not agree with the IRR. Solution: select the largest NPV.

Time Disparity Example Project A year cash flow 0 (48,000) 1 1,200 2 2,400 3 39,000 4 42,000 required return = 12% IRR = 18.10% NPV = $9,436 PI = 1.20

Time Disparity Example Project A year cash flow 0 (48,000) 1 1,200 2 2,400 3 39,000 4 42,000 required return = 12% IRR = 18.10% NPV = $9,436 PI = 1.20 Project B year cash flow 0 (46,500) 1 36,500 2 24,000 3 2,400 4 2,400 required return = 12% IRR = 25.51% NPV = $8,455 PI = 1.18

Time Disparity Example Project A year cash flow 0 (48,000) 1 1,200 2 2,400 3 39,000 4 42,000 required return = 12% IRR = 18.10% NPV = $9,436 PI = 1.20 Project B year cash flow 0 (46,500) 1 36,500 2 24,000 3 2,400 4 2,400 required return = 12% IRR = 25.51% NPV = $8,455 PI = 1.18

Mutually Exclusive Investments with Unequal Lives Suppose our firm is planning to expand and we have to select one of two machines. They differ in terms of economic life and capacity. How do we decide which machine to select?

The after-tax cash flows are: Year Machine 1 Machine 2 0 (45,000) (45,000) 1 20,000 12,000 2 20,000 12,000 3 20,000 12,000 4 12,000 5 12,000 6 12,000 Assume a required return of 14%.

Step 1: Calculate NPV NPV1 = $1,433 NPV2 = $1,664 So, does this mean #2 is better? No! The two NPVs can’t be compared!

Step 2: Equivalent Annual Annuity (EAA) method If we assume that each project will be replaced an infinite number of times in the future, we can convert each NPV to an annuity. The projects’ EAAs can be compared to determine which is the best project! EAA: Simply annuitize the NPV over the project’s life.

EAA with your calculator: Simply “spread the NPV over the life of the project” Machine 1: PV = 1433, N = 3, I = 14, solve: PMT = -617.24. Machine 2: PV = 1664, N = 6, I = 14, solve: PMT = -427.91.

EAA1 = $617 EAA2 = $428 This tells us that: NPV1 = annuity of $617 per year. NPV2 = annuity of $428 per year. So, we’ve reduced a problem with different time horizons to a couple of annuities. Decision Rule: Select the highest EAA. We would choose machine #1.

Step 3: Convert back to NPV ¥

Step 3: Convert back to NPV ¥ Assuming infinite replacement, the EAAs are actually perpetuities. Get the PV by dividing the EAA by the required rate of return.

Step 3: Convert back to NPV ¥ Assuming infinite replacement, the EAAs are actually perpetuities. Get the PV by dividing the EAA by the required rate of return. NPV 1 = 617/.14 = $4,407 ¥

Step 3: Convert back to NPV ¥ Assuming infinite replacement, the EAAs are actually perpetuities. Get the PV by dividing the EAA by the required rate of return. NPV 1 = 617/.14 = $4,407 NPV 2 = 428/.14 = $3,057 ¥

Step 3: Convert back to NPV ¥ Assuming infinite replacement, the EAAs are actually perpetuities. Get the PV by dividing the EAA by the required rate of return. NPV 1 = 617/.14 = $4,407 NPV 2 = 428/.14 = $3,057 This doesn’t change the answer, of course; it just converts EAA to an NPV that can be compared. ¥

Practice Problems: Cash Flows & Other Topics in Capital Budgeting

Problem 1a Project Information: Cost of equipment = $400,000. Shipping & installation will be $20,000. $25,000 in net working capital required at setup. 3-year project life, 5-year class life. Simplified straight line depreciation. Revenues will increase by $220,000 per year. Defects costs will fall by $10,000 per year. Operating costs will rise by $30,000 per year. Salvage value after year 3 is $200,000. Cost of capital = 12%, marginal tax rate = 34%. Problem 1a

Problem 1a Initial Outlay: (400,000) Cost of asset + ( 20,000) Shipping & installation (420,000) Depreciable asset + ( 25,000) Investment in NWC ($445,000) Net Initial Outlay

For Years 1 - 3: Problem 1a 220,000 Increased revenue 10,000 Decreased defects (30,000) Increased operating costs (84,000) Increased depreciation 116,000 EBT (39,440) Taxes (34%) 76,560 EAT 84,000 Depreciation reversal 160,560 = Annual Cash Flow

Problem 1a Terminal Cash Flow: Salvage value +/- Tax effects of capital gain/loss + Recapture of net working capital Terminal Cash Flow

Problem 1a Terminal Cash Flow: Salvage value = $200,000. Book value = depreciable asset - total amount depreciated. Book value = $168,000. Capital gain = SV - BV = $32,000. Tax payment = 32,000 x .34 = ($10,880).

Problem 1a Terminal Cash Flow: 200,000 Salvage value (10,880) Tax on capital gain 25,000 Recapture of NWC 214,120 Terminal Cash Flow

Problem 1a Solution NPV and IRR: CF(0) = -445,000 CF(1 ), (2), = 160,560 CF(3 ) = 160,560 + 214,120 = 374,680 Discount rate = 12% IRR = 22.1% NPV = $93,044. Accept the project!

Problem 1b Project Information: For the same project, suppose we can only get $100,000 for the old equipment after year 3, due to rapidly changing technology. Calculate the IRR and NPV for the project. Is it still acceptable?

Problem 1b Terminal Cash Flow: Salvage value +/- Tax effects of capital gain/loss + Recapture of net working capital Terminal Cash Flow

Problem 1b Terminal Cash Flow: Salvage value = $100,000. Book value = depreciable asset - total amount depreciated. Book value = $168,000. Capital loss = SV - BV = ($68,000). Tax refund = 68,000 x .34 = $23,120.

Problem 1b Terminal Cash Flow: 100,000 Salvage value 23,120 Tax on capital gain 25,000 Recapture of NWC 148,120 Terminal Cash Flow

Problem 1b Solution NPV and IRR: CF(0) = -445,000. CF(1), (2) = 160,560. CF(3) = 160,560 + 148,120 = 308,680. Discount rate = 12%. IRR = 17.3%. NPV = $46,067. Accept the project!

Problem 2 Automation Project: Cost of equipment = $550,000. Shipping & installation will be $25,000. $15,000 in net working capital required at setup. 8-year project life, 5-year class life. Simplified straight line depreciation. Current operating expenses are $640,000 per yr. New operating expenses will be $400,000 per yr. Already paid consultant $25,000 for analysis. Salvage value after year 8 is $40,000. Cost of capital = 14%, marginal tax rate = 34%. Problem 2

Problem 2 Initial Outlay: (550,000) Cost of new machine + (25,000) Shipping & installation (575,000) Depreciable asset + (15,000) NWC investment (590,000) Net Initial Outlay

Problem 2 For Years 1 - 5: 240,000 Cost decrease (115,000) Depreciation increase 125,000 EBIT (42,500) Taxes (34%) 82,500 EAT 115,000 Depreciation reversal 197,500 = Annual Cash Flow

Problem 2 For Years 6 - 8: 240,000 Cost decrease ( 0) Depreciation increase 240,000 EBIT (81,600) Taxes (34%) 158,400 EAT 0 Depreciation reversal 158,400 = Annual Cash Flow

Problem 2 Terminal Cash Flow: 40,000 Salvage value (13,600) Tax on capital gain 15,000 Recapture of NWC 41,400 Terminal Cash Flow

Problem 2 Solution NPV and IRR: CF(0) = -590,000. CF(1 - 5) = 197,500. CF(6 - 7) = 158,400. CF(10) = 158,400 + 41,400 = 199,800. Discount rate = 14%. IRR = 28.13% NPV = $293,543. We would accept the project!

Problem 3 Replacement Project: Old Asset (5 years old): Cost of equipment = $1,125,000. 10-year project life, 10-year class life. Simplified straight line depreciation. Current salvage value is $400,000. Cost of capital = 14%, marginal tax rate = 35%.

Problem 3 Replacement Project: New Asset: Cost of equipment = $1,750,000. Shipping & installation will be $56,000. $68,000 investment in net working capital. 5-year project life, 5-year class life. Simplified straight line depreciation. Will increase sales by $285,000 per year. Operating expenses will fall by $100,000 per year. Already paid $15,000 for training program. Salvage value after year 5 is $500,000. Cost of capital = 14%, marginal tax rate = 34%. Problem 3

Problem 3: Sell the Old Asset Salvage value = $400,000. Book value = depreciable asset - total amount depreciated. Book value = $1,125,000 - $562,500 = $562,500. Capital gain = SV - BV = 400,000 - 562,500 = ($162,500). Tax refund = 162,500 x .35 = $56,875.

Problem 3 Initial Outlay: (1,750,000) Cost of new machine + ( 56,000) Shipping & installation (1,806,000) Depreciable asset + ( 68,000) NWC investment + 456,875 After-tax proceeds (sold old machine) (1,417,125) Net Initial Outlay

Problem 3 For Years 1 - 5: 385,000 Increased sales & cost savings (248,700) Extra depreciation 136,300 EBT (47,705) Taxes (35%) 88,595 EAT 248,700 Depreciation reversal 337,295 = Differential Cash Flow

Problem 3 Terminal Cash Flow: 500,000 Salvage value (175,000) Tax on capital gain 68,000 Recapture of NWC 393,000 Terminal Cash Flow

Problem 3 Solution NPV and IRR: CF(0) = -1,417,125. CF(1 - 4) = 337,295. CF(5) = 337,295 + 393,000 = 730,295. Discount rate = 14%. NPV = (55,052.07). IRR = 12.55%. We would not accept the project!