cash flows and other topics in capital budgeting chap 10

Cash Flows and Other Topics in Capital Budgeting Cash Flow estimation Problems in Capital Budgeting Capital Rationing Problems with Project Ranking Size disparity problem Time disparity problem Mutually exclusive investment with unequal lives

Capital Budgeting Example Capital Budgeting: the process of planning for

purchases of long-term assets. 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:

Capital Budgeting Example (Continued) 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 (Continued) 2) Evaluate the risk of the project

For now, we’ll assume that the risk of the project is the same as the risk of the overall firm if not we would require a greater return

If we do this, we can use the firm’s cost of capital as the discount rate for capital investment projects. We’ll cover cost of capital in Chapter 12

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 (Continued) a) Initial Outlay: What is the cash flow at “time

0?” Note amounts in parentheses are negative

–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 (Continued) b) Annual Cash Flows: What incremental cash

flows occur over the life of the project?Incremental revenue

– Incremental costs– Depreciation on project= Incremental earnings before taxes– Tax on incremental EBT (Based on marginal tax rate)

= Incremental earnings after taxes+ Depreciation reversal (Because it is not an actual cash flow)

= Annual Cash Flow

Step 1: Evaluate Cash Flows (Continued)

85,000 Revenue

–29,750 Costs (35% of revenues)–29,400 Depreciation (Straight-line over 5 years, 147K/5)

25,850 EBT

–8,789 Taxes (34 marginal tax rate)

17,061 EAT

29,400 Depreciation reversal

46,461 Annual Cash Flow

Step 1: Evaluate Cash Flows (Continued) 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 Salvage value (SV) = $50,000 Book value (BV) = 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 0.34 = $17,000

Step 1: Evaluate Cash Flows (Continued) 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 CF(5) = 46,461 + 37,000 = 83,461 Discount rate = 14% NPV = $27,721 We would accept the project

Problems in Capital Budgeting:Capital Rationing

Suppose that you have evaluated 5 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? 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

Project B year cash flow 0 (30,000) 1 15,000 2 15,000 3 15,000required return = 12%IRR = 23.38%NPV = 6,027PI = 1.20

Project A year cash flow 0 (135,000) 1 60,000 2 60,000 3 60,000required return = 12%IRR = 15.89%NPV = 9,1100PI = 1.07

Size Disparity – Example

Problems with Project Ranking (Continued) 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 42,000required return = 12%

IRR = 18.10%NPV = $9,436PI = 1.20

Project B year cash flow 0 (46,500) 1 36,500 2 24,000 3 2,400 4 2,400required return = 12%

IRR = 25.51%

NPV = $8,455

PI = 1.18

Problems with Project Ranking (Continued) 3) Mutually exclusive investments with unequal

lives Suppose our firm is planning to expand and we have to

select 1 of 2 machines They differ in terms of economic life and capacity How do we decide which machine to select?

Mutually Exclusive Investments with Unequal Lives 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 annualize the NPV over the project’s life

EAA with your Calculator Simply “spread the NPV over the life of the

project” Machine 1: PV = –1,433, N = 3, I = 14, Solve: PMT = 617.24

Machine 2: PV = –1,664, N = 6, I = 14, Solve: PMT = 427.91

EAA Decision Rule 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

EAA Decision Rule Assuming infinite replacement, the EAAs are

actually perpetuities. Get the PV by dividing the EAA by the required rate of return

NPV∞,1 = 617 / 0.14 = $4,407

NPV∞,2 = 428 / 0.14 = $3,057 This doesn’t change the answer, of course; it just

converts EAA to a NPV that can be compared

cash flows and other topics in capital budgeting chap 10

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