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Capital Expenditure Decisions

16 Chapter Sixteen

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Discounted-Cash-Flow Analysis

Cost reduction

Plant expansion

Equipment selection

Lease or buy

Equipment replacement

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Net-Present-Value Method

Prepare a table showing cash flows for each year,Calculate the present value of each cash flow using a discount rate,Compute net present value,If the net present value (NPV) is positive, accept the investment proposal. Otherwise, reject it.

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Net-Present-Value MethodMattson Co. has been offered a five year contract to

provide component parts for a large manufacturer.

Cost and revenue informationCost of special equipment $160,000 Working capital required 100,000 Relining equipment in 3 years 30,000 Salvage value of equipment in 5 years 5,000 Annual cash revenue and costs: Sales revenue from parts 750,000 Cost of parts sold 400,000 Salaries, shipping, etc. 270,000

Cost and revenue informationCost of special equipment $160,000 Working capital required 100,000 Relining equipment in 3 years 30,000 Salvage value of equipment in 5 years 5,000 Annual cash revenue and costs: Sales revenue from parts 750,000 Cost of parts sold 400,000 Salaries, shipping, etc. 270,000

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Net-Present-Value Method

☯At the end of five years the working capital will be released and may be used elsewhere by Mattson.

☯Mattson uses a discount rate of 10%.

Should the contract be accepted?

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Net-Present-Value Method

Annual net cash inflows from operations

Sales revenue 750,000$ Cost of parts sold 400,000 Gross margin 350,000 Less out-of-pocket costs 270,000 Annual net cash inflows 80,000$

Sales revenue 750,000$ Cost of parts sold 400,000 Gross margin 350,000 Less out-of-pocket costs 270,000 Annual net cash inflows 80,000$

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Net-Present-Value MethodYears

Cash Flows

10% Factor

Present Value

Investment in equipment Now $(160,000) 1.000 (160,000)$Working capital needed Now (100,000) 1.000 (100,000)

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Years Cash Flows

10% Factor

Present Value

Investment in equipment Now $(160,000) 1.000 (160,000)$Working capital needed Now (100,000) 1.000 (100,000) Annual net cash inflows 1-5 80,000 3.791 303,280

Net-Present-Value Method

Present value of an annuity of $1 factor for 5 years at 10%.

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Years Cash Flows

10% Factor

Present Value

Investment in equipment Now $(160,000) 1.000 (160,000)$Working capital needed Now (100,000) 1.000 (100,000) Annual net cash inflows 1-5 80,000 3.791 303,280 Relining of equipment 3 (30,000) 0.751 (22,530)

Net-Present-Value Method

Present value of $1 factor for 3 years at 10%.

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Years Cash Flows

10% Factor

Present Value

Investment in equipment Now $(160,000) 1.000 (160,000)$Working capital needed Now (100,000) 1.000 (100,000) Annual net cash inflows 1-5 80,000 3.791 303,280 Relining of equipment 3 (30,000) 0.751 (22,530) Salvage value of equip. 5 5,000 0.621 3,105

Net-Present-Value Method

Present value of $1 factor for 5 years at 10%.

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Net-Present-Value MethodYears

Cash Flows

10% Factor

Present Value

Investment in equipment Now $(160,000) 1.000 (160,000)$Working capital needed Now (100,000) 1.000 (100,000) Annual net cash inflows 1-5 80,000 3.791 303,280 Relining of equipment 3 (30,000) 0.751 (22,530) Salvage value of equip. 5 5,000 0.621 3,105 Working capital released 5 100,000 0.621 62,100 Net present value 85,955$

Mattson should accept the contract because the present value of the cash inflows exceeds the present

value of the cash outflows by $85,955. The project has a positive net present value.

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Internal-Rate-of-Return Method

☯The internal rate of return is the true economic return earned by the asset over its life.

☯The internal rate of return is computed by finding the discount rate that will cause the net present value of a project to be zero.

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Internal-Rate-of-Return Method

☯Black Co. can purchase a new machine at a cost of $104,320 that will save $20,000 per year in cash operating costs.

☯The machine has a 10-year life.

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Internal-Rate-of-Return Method

Future cash flows are the same every year in this example, so we can calculate the

internal rate of return as follows:

Investment required Net annual cash flows = Present value factor

$104, 320 $20,000 = 5.216

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Internal-Rate-of-Return Method

$104, 320 $20,000 = 5.216

The present value factor (5.216) is located on the Table IV in the Appendix. Scan the 10-

period row and locate the value 5.216. Look at the top of the column and you find a rate of

14% which is the internal rate of return.

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Internal-Rate-of-Return Method

Here’s the proof . . .

Year Amount14%

FactorPresent Value

Investment required Now (104,320)$ 1.000 (104,320) Annual cost savings 1-10 20,000 5.216 104,320Net present value -$

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Comparing the NPV and IRR Methods

Net Present ValueThe cost of capital is used as the actual discount rate.

Any project with a negative net present value is rejected.

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Comparing the NPV and IRR Methods

Internal Rate of ReturnThe cost of capital is compared to the internal rate of return on a project.

To be acceptable, a project’s rate of return must be greater than the cost of capital.

Net Present ValueThe cost of capital is used as the actual discount rate.

Any project with a negative net present value is rejected.

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Comparing the NPV and IRR Methods

The net present value method has the following advantages over the internal rate of return

method . . .Easier to use.Easier to adjust for risk.Provides more usable information.

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Assumptions Underlying Discounted-Cash-Flow Analysis

All cash flows aretreated as though

they occur at year end.

Cash flows are treated as if

they are knownwith certainty.

Cash inflows areimmediatelyreinvested atthe required

rate of return.

Assumes aperfectcapitalmarket.

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Choosing the Hurdle Rate

☯The discount rate generally is associated with the company’s cost of capital.

☯The cost of capital involves a blending of the costs of all sources of investment funds, both debt and equity.

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Depreciable Assets

Both the NPV and IRR methods focus on cash flows, and periodic depreciation

charges are not cash flows . . .

Tax ReturnForm 1120 Depreciation

is taxdeductibleand . . .

Reducescashoutflows fortaxes.

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Comparing Two Investment Projects

To compare competing investment projects we can use the following net present value

approaches:Total-Cost Approach.Incremental-Cost Approach.

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Total-Cost Approach

☯Black Co. is trying to decide whether to remodel an old car wash or remove it entirely and install a new one.

☯The company uses a discount rate of 10%.

New Car Wash

Old Car Wash

Annual revenues 90,000$ 70,000$ Annual cash operating costs 30,000 25,000 Net annual cash inflows 60,000$ 45,000$

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Total-Cost Approach☯The new washer costs $300,000 and will produce

revenues for 10 years.☯The brushes have to be replaced at the end of 6 years at

a cost of $50,000.☯The old washer has a current salvage value of $40,000.☯The estimated salvage value of the new washer will be

$7,000 at the end of 10 years.☯Remodeling the old washer costs $175,000 and the

brushes must be replaced at the end of 6 years at a cost of $80,000 .

Should Black replace the washer?

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Total-Cost ApproachInstall the New Washer

Year Cash Flows10%

FactorPresent

ValueInitial investment Now (300,000)$ 1.000 (300,000)$ Replace brushes 6 (50,000) 0.564 (28,200) Net annual cash inflows 1-10 60,000 6.145 368,700 Salvage old equipment Now 40,000 1.000 40,000 Salvage new equipment 10 7,000 0.386 2,702 Net present value 83,202$

Install the New Washer

Year Cash Flows10%

FactorPresent

ValueInitial investment Now (300,000)$ 1.000 (300,000)$ Replace brushes 6 (50,000) 0.564 (28,200) Net annual cash inflows 1-10 60,000 6.145 368,700 Salvage old equipment Now 40,000 1.000 40,000 Salvage new equipment 10 7,000 0.386 2,702 Net present value 83,202$

If Black Co. installs the new washer,the investment will yield a

positive net present value of $83,202.

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Total-Cost ApproachRemodel the Old Washer

YearCash Flows

10% Factor

Present Value

Initial investment Now (175,000)$ 1.000 (175,000)$ Replace brushes 6 (80,000) 0.564 (45,120) Net annual cash inflows 1-10 45,000 6.145 276,525 Net present value 56,405$

Remodel the Old Washer

YearCash Flows

10% Factor

Present Value

Initial investment Now (175,000)$ 1.000 (175,000)$ Replace brushes 6 (80,000) 0.564 (45,120) Net annual cash inflows 1-10 45,000 6.145 276,525 Net present value 56,405$

If Black Co. remodels the existingwasher, it will produce a

positive net present value of $56,405.

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Total-Cost ApproachBoth projects yield a positive net present value.

NPVInvest in new washer 83,202$ Remodel existing washer 56,405 In favor of new washer 26,797$

However, investing in the new washer will produce a higher net present value than

remodeling the old washer.

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Incremental-Cost Approach

Under the incremental-cost approach, only those cash flows that differ between the

two alternatives are considered.

Let’s look at an analysis of the Black Co. decision using

the incremental-cost approach.

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Year Cash Flows10%

FactorPresent

ValueIncremental investment Now $ (125,000) 1.000 $ (125,000)

Incremental-Cost Approach

$300,000 new - $175,000 remodel = $125,000

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Year Cash Flows10%

FactorPresent

ValueIncremental investment Now $ (125,000) 1.000 $ (125,000)Incre. cost of brushes 6 30,000$ 0.564 16,920

Incremental-Cost Approach

$80,000 remodel - $50,000 new = $30,000

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Year Cash Flows10%

FactorPresent

ValueIncremental investment Now $ (125,000) 1.000 $ (125,000)Incre. cost of brushes 6 30,000$ 0.564 16,920 Increased net cash inflows 1-10 15,000 6.145 92,175

Incremental-Cost Approach

$60,000 new - $45,000 remodel = $15,000

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Incremental-Cost Approach

Year Cash Flows10%

FactorPresent

ValueIncremental investment Now $ (125,000) 1.000 $ (125,000)Incre. cost of brushes 6 30,000$ 0.564 16,920 Increased net cash inflows 1-10 15,000 6.145 92,175 Salvage old equipment Now 40,000 1.000 40,000 Salvage new equipment 10 7,000 0.386 2,702 Net present value $ 26,797

We get the same answer under either thetotal-cost and incremental-cost approach.

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Managerial Accountant’s Role

Managerial accountants are often asked to predict cash flows related to operating cost savings, additional working capital requirements, and

incremental costs and revenues.When cash flow projections are very uncertain, the

accountant may . . .increase the hurdle rate,use sensitivity analysis.

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Postaudit of Investment Projects

A postaudit is a follow-up after the project has been approved to see whether or not

expected results are actually realized.

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Income Taxes and Capital Budgeting

Cash flows from an investment proposal affect the company’s profit and its income

tax liability.

Income = Revenue - Expenses + Gains - Losses

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After-Tax Cash Flows High Country Department Stores

For the Year Ended June 30, 2001Revenue 1,000,000$ Expenses (475,000) Income before taxes 525,000 Income taxes (147,000) Net income 378,000$

Income Statement

The tax rate is 28%, so income taxes are$525,000 × 28% = $147,000

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Cash Revenues

High Country’s management is considering the purchase of a new truck that will increase cash

revenues by $110,000 and increase cash cost of goods sold by $60,000. The company is subject

to a tax rate of 28%.

Let’s calculate the company’s after-tax cash flows.

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Cash Revenues

Cash revenues 110,000$ Cash cost of goods sold (60,000) Increase in income 50,000 Income taxes (14,000) After-tax cash flows 36,000$

High Country Department StoresAfter-Tax Cash Flows

$50,000 × 28% = $14,000

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Cash revenues 110,000$ Cash cost of goods sold (60,000) Increase in income 50,000 Income taxes (14,000) After-tax cash flows 36,000$

High Country Department StoresAfter-Tax Cash Flows

Cash Revenues

A short cut works like this:Increase in income × ( 1 - tax rate)$50,000 × ( 1 - .28) = $36,000

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Noncash Expenses

Not all expenses require cash outflows. The most common example is depreciation.

Recall that High Country’s proposal involved the purchase of a truck. The truck cost $40,000 and will be depreciated over four years using straight-line depreciation. The truck is to be purchased

on June 30, 2001. One-half year depreciation is taken in 2001.

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Noncash Expenses

Here is a complete depreciation schedule for High Country.

YearDepreciation

Expense Tax RateReduced Tax

Payment1 5,000$ 28% 1,400$ 2 10,000 28% 2,800 3 10,000 28% 2,800 4 10,000 28% 2,800 5 5,000 28% 1,400

40,000$ 11,200$

DepreciationTax

Shield

16-8

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Net Present Value Analysis

Calculation of the present value of proposal cash flows.

Time 0 Time 1 Time 2 Time 3 Time 4 Time 5Acquisition cost (40,000)$ Cash flows from proposal 18,000$ 36,000$ 36,000$ 36,000$ 18,000$ Depreciation tax shield 1,400 2,800 2,800 2,800 1,400 Total cash flows (40,000) 19,400 38,800 38,800 38,800 19,400 Discount factor (12%) 1.000 0.893 0.797 0.712 0.636 0.567 Present value (40,000)$ 17,324$ 30,924$ 27,626$ 24,677$ 11,000$

The sum of the present values from thisproposal is a positive $71,550

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Modified Accelerated Cost Recovery System (MACRS)

Tax depreciation is usually computed using MACRS. Here are the depreciation rate for 3,

5, and 7-year class life assets.

Year 3-year 5-year 7-year1 33.33% 20.00% 14.29%2 44.45% 32.00% 24.49%3 14.81% 19.20% 17.49%4 7.41% 11.52% 12.49%5 11.52% 8.93%6 5.76% 8.92%7 8.93%8 4.46%

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Modified Accelerated Cost Recovery System (MACRS)

A company is considering the purchase of a machine that will increase after-tax cash

flows by $20,000 over the next five years. The machine is depreciated using MACRS

and the company uses a 10% discount rate to compute all present values. The machine will cost $100,000 and the company is subject to

a 28% tax rate.

Let’s calculate the net present value of the proposal.

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Modified Accelerated Cost Recovery System (MACRS)

Calculation of the present value of the depreciation tax shield.

YearTax

Depreciation Tax ShieldPV of Tax

Shield1 20,000$ 5,600$ 5,090$ 2 32,000 8,960 7,401 3 19,200 5,376 4,037 4 11,520 3,226 2,203 5 11,520 3,226 2,003 6 5,760 1,613 910

100,000$ 21,644$

$5,600 × (1.10)^-1

$20,000 × 28%

$100,000 × 20%

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Modified Accelerated Cost Recovery System (MACRS)

Calculation of the present value proposal cash flows.

YearCash Flows

PV of Cash Flows

1 20,000$ 18,180$ 2 20,000 16,520 3 20,000 15,020 4 20,000 13,660 5 20,000 12,420 6 - -

100,000$ 75,800$

$20,000 × (1.10)^-1

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Modified Accelerated Cost Recovery System (MACRS)

Net present value of the proposal.

YearPV of Cash

FlowsPV of Tax

ShieldPresent Value

1 18,180$ 5,090$ 23,270$ 2 16,520 7,401 23,921 3 15,020 4,037 19,057 4 13,660 2,203 15,863 5 12,420 2,003 14,423 6 - 910 910

75,800$ 21,644$ 97,444$

The presentvalue of the

proposal is lessthan the cost

of the equipment($100,000). Theproposal has a

negative netpresent value.

16-9

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Investment in Working Capital

Some investment proposals require additional outlays for working capital such as increases in cash, accounts receivable,

and inventory.

Current assets 100,000$ Less: current liabilities (65,000) Working capital 35,000$

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Extended Illustration

Let take a close look at a present value analysis for an investment decision facing

James Company.

JamesCompany

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Extended IllustrationJames Company has been offered a five-year contract

to provide component parts for a large manufacturer.

Cost and revenue informationCost of special equipment $160,000 Working capital required 100,000 Relining equipment in 3 years 30,000 Salvage value of equipment in 5 years 5,000 Annual cash revenue and costs: Sales revenue from parts 750,000 Cost of parts sold 400,000 Salaries, advertising and others 200,000

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Extended Illustration

☯At the end of five years the working capital will be released and may be used elsewhere by James.

☯James Company uses a discount rate of 10%.

☯James uses straight-line depreciation.☯All items are taxed at 30%.

Should the contract be accepted?

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Extended Illustration

Annual accounting income from operations

Sales revenue 750,000$ Cost of parts sold 450,000 Gross margin 300,000 Salaries and other 200,000 Depreciation expense 31,000 Income before taxes 69,000 Income taxes 20,700 Net income 48,300$

Rememberdepreciation isa non-cashexpense thatprovides atax shield.

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Extended Illustration

Annual cash inflows from operations

Sales revenue 750,000$ Cost of parts sold 450,000 Gross margin 300,000 Salaries and other 200,000 Depreciation expense - Income before taxes 100,000 Income taxes 20,700 Net cash flows 79,300$

Rememberdepreciation isa non-cashexpense thatprovides atax shield.

16-10

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Extended Illustration

The relining is considered normal maintenance and will reduce income in year 3. Because the cost is tax deductible, income will be lower by

$21,000 ($30,000 × 1- tax rate).

Years Cash Flows

Investment in equipment Now $(160,000)Working capital needed Now (100,000) Annual net cash inflows 1-5 79,300 Relining of equipment 3 (21,000) Salvage value of equipment 5 5,000 Working capital released 5 100,000 Net present value

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Extended Illustration

Years Cash Flows

Investment in equipment Now $(160,000)Working capital needed Now (100,000) Annual net cash inflows 1-5 79,300 Relining of equipment 3 (21,000) Salvage value of equipment 5 5,000 Working capital released 5 100,000 Net present value

Because the salvage value of the equipment will equal the book value (cost less accumulated depreciation),

there will be no taxable gain or loss.

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Years Cash Flows

10% Factor

Present Value

Investment in equipment Now $(160,000) 1.000 (160,000)$Working capital needed Now (100,000) 1.000 (100,000) Annual net cash inflows 1-5 79,300 303,402

Extended Illustration

YearNet Cash

Inflow PV FactorPV of Cash

Inflow1 79,300$ 0.909 72,084$ 2 79,300 0.862 68,357 3 79,300 0.751 59,554 4 79,300 0.683 54,162 5 79,300 0.621 49,245

396,500$ 303,402$

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Years Cash Flows

10% Factor

Present Value

Investment in equipment Now $(160,000) 1.000 (160,000)$Working capital needed Now (100,000) 1.000 (100,000) Annual net cash inflows 1-5 79,300 303,402 Relining of equipment 3 (21,000) 0.751 (15,771)

Extended Illustration

Present value of $1 factor for 3 years at 10%.

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Years Cash Flows

10% Factor

Present Value

Investment in equipment Now $(160,000) 1.000 (160,000)$Working capital needed Now (100,000) 1.000 (100,000) Annual net cash inflows 1-5 79,300 303,402 Relining of equipment 3 (21,000) 0.751 (15,771) Salvage value of equipment 5 5,000 0.621 3,105

Extended Illustration

Present value of $1 factor for 5 years at 10%.

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Extended Illustration

Years Cash Flows

10% Factor

Present Value

Investment in equipment Now $(160,000) 1.000 (160,000)$Working capital needed Now (100,000) 1.000 (100,000) Annual net cash inflows 1-5 79,300 303,402 Relining of equipment 3 (21,000) 0.751 (15,771) Salvage value of equipment 5 5,000 0.621 3,105 Working capital released 5 100,000 0.621 62,100 Net present value 92,836$

We should accept the contract because the presentvalue of the cash inflows exceeds the present valueof the cash outflows by $92,836. The project has a

positive net present value.

16-11

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Extended IllustrationGeneral decision rule . . .

If the Net Present Value is . . . Then the Project is . . .

Positive . . . Acceptable, since it promises a return greater than the required

rate of return.

Zero . . . Acceptable, since it promises a return equal to the required rate

of return.

Negative . . .Not acceptable, since it promises a return less than the required

rate of return.

If the Net Present Value is . . . Then the Project is . . .

Positive . . . Acceptable, since it promises a return greater than the required

rate of return.

Zero . . . Acceptable, since it promises a return equal to the required rate

of return.

Negative . . .Not acceptable, since it promises a return less than the required

rate of return.

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Ranking Investment ProjectsWe can invest in either of these projects. Use a 10% discount rate to determine the

net present value of the cash flows.

Project A Project BImmediate cash outlay 100,000$ 100,000$ Cash inflows: Year 1 50,000$ 30,000$ Year 2 40,000 40,000 Year 3 30,000 50,000 Total inflows 120,000$ 120,000$

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Project A Project BImmediate cash outlay 100,000$ 100,000$ Cash inflows: Year 1 50,000$ 30,000$ Year 2 40,000 40,000 Year 3 30,000 50,000 Total inflows 120,000$ 120,000$

We can invest in either of these projects. Use a 10% discount rate to determine the

net present value of the cash flows.

Ranking Investment Projects

The total cash flows are the same,but the pattern of the flows is

different.

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Project A PV Factor PVImmediate cash outlay (100,000)$ 1.000 (100,000)$ Cash inflows: Year 1 50,000$ 0.909 45,450 Year 2 40,000 Year 3 30,000 Net present value

Ranking Investment Projects

Let’s calculate the present value of the cash flows associated with Project A.

(1.10)-1 = 0.909 rounded

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Project A PV Factor PVImmediate cash outlay (100,000)$ 1.000 (100,000)$ Cash inflows: Year 1 50,000$ 0.909 45,450 Year 2 40,000 0.826 33,040 Year 3Net present value

Ranking Investment Projects

Let’s calculate the present value of the cash flows associated with Project A.

(1.10)-2 = 0.826 rounded

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Ranking Investment Projects

Let’s calculate the present value of the cash flows associated with Project A.

This project has a positive net present value which means the project’s return is greater than the discount rate.

Project A PV Factor PVImmediate cash outlay (100,000)$ 1.000 (100,000)$ Cash inflows: Year 1 50,000$ 0.909 45,450 Year 2 40,000 0.826 33,040 Year 3 30,000 0.751 22,530 Net present value 1,020$

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Ranking Investment Projects

Here is the net present value of the cash flows associated with Project B.

Project B PV Factor PVImmediate cash outlay (100,000)$ 1.000 (100,000)$ Cash inflows: Year 1 30,000$ 0.909 27,270 Year 2 40,000 0.826 33,040 Year 3 50,000 0.751 37,550 Net present value (2,140)$

Project B has a negative net present value which means the project’s return is less than the discount rate.

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Internal Rate of Return (IRR)

The interest rate that equates the present value of inflows and outflows from an

investment project.

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Internal Rate of Return (IRR)

When the cash flows from a project are constant, the present value of an annuity

factor can be used to approximate the rate of return.

A project cost $90,119, and will yield net cash inflows of $25,000 at the end of each of the

next five years.

Let’s determine the IRR for this project!McGraw-Hill/Irwin

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Internal Rate of Return (IRR)

PV factor = Required InvestmentAnnual net cash flow

$90,119$25,000

3.605 rounded

The present value of an annuity factor of 3.605,is an internal rate of return of 12%.

PV factor =

PV factor =

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Alternative Methods for Making Investment Decisions

Payback Method

Paybackperiod

Initial investment Annual after-tax cash inflow

=

Paybackperiod = $20,000

$4,000 = 5 years

A company can purchase a machine for $20,000 thatwill provide annual cash inflows of $4,000 for 7 years.

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Payback: Pro and Con

Fails to consider the time value of money.Does not consider a project’s cash flows beyond the payback period.

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Payback: Pro and Con

Provides a tool for roughly screening investments.For some firms, it may be essential that an investment recoup its initial cash outflows as quickly as possible.

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Accounting-Rate-of-Return Method

Discounted-cash-flow method focuses on cash flows and the time value of money.

Accounting-rate-of-return method focuses on the incremental accounting income that

results from a project.

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Accounting-Rate-of-Return Method

The following formula is used to calculate the accounting rate of return:

Accountingrate ofreturn

=

Average Average incremental incremental expenses,

revenues including depreciation-

Initial investment

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Accounting-Rate-of-Return MethodMeyers Company wants to install an espresso bar in

its restaurant.The espresso bar:

Cost $140,000 and has a 10-year life.Will generate incremental revenues of $100,000 and incremental expenses of $80,000 including depreciation.

What is the accounting rate of return on the investment project?

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Accounting-Rate-of-Return Method

The accounting rate of return method is not recommendedfor a variety of reasons, the most important of which

is that it ignores the time value of money.

Accountingrate of return

$100,000 - $80,000 $140,000 = 14.3%=

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Capital Budgeting Practices

75

86

7175

20

69 68

5346

60

28

64

0102030405060708090

Payback IRR ARR NPV

KoreaJapanU.S.

Percent of managers who believe each technique is important.