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Chapter 13-ACapital Budgeting

M11-Chp-13-1A-Capital-Budget-2011-0525Edited May 25, 2011.

Copyright © 2011, Dr. Howard Godfrey

This file contains illustrative problems that will be used in the lecture to illustrate important concepts

and procedures.See separate PowerPoint file with review material on

interest.

Chapter Learning ObjectivesLO1: Net present valueLO2: Internal rate of returnLO3: Uncertain cash flowsLO4: Preference rankingLO5: PaybackLO6: Simple rate of returnLO7: Present value conceptsLO8: Income tax

Introductory Exercise

Joe’s Package Delivery Service.Joe had started a package delivery service in Charlotte. He bought a truck at a cost of $20,000. The truck will have a 5-year life, and will have no salvage value after 5 years. Joe receives a salary of $30,000 and has other expenses of $10,000 for insurance, oil, gas, etc. Please fill in the blanks on next slide.

Cost of Truck (5 year life) $20,000Revenue per year $50,000Salary - Joe 30,000 Insurance, Gas, etc. 10,000 Cash Expenses 40,000 Net Cash Inflow 10,000 DepreciationNet IncomeWhat is Payback Period?(Ignore Income Taxes)

Joe's Package Delivery Service

Cost of Truck (5 year life) $20,000Revenue per year $50,000Salary - Joe 30,000 Insurance, Gas, etc. 10,000 Cash Expenses 40,000 Net Cash Inflow 10,000 Depreciation (4,000)Net Income $6,000What is Payback Period? 2 years(Ignore Income Taxes)Remember, depreciation is not a cash expense.

Joe's Package Delivery Service

Review the problem on the preceding slides.Suppose revenue is only $44,000 per year.What is payback period?Would you recommend the project?

Cost of Truck (5 year life) $20,000Revenue per year $44,000Salary - Joe 30,000 Insurance, Gas, etc. 10,000 Cash ExpensesNet Cash InflowDepreciationNet IncomeWhat is Payback Period?(Ignore Income Taxes)

Joe's Package Delivery Service

Cost of Truck (5 year life) $20,000Revenue per year $44,000Salary - Joe 30,000Insurance, Gas, etc. 10,000Cash Expenses 40,000 Net Cash Inflow 4,000 Depreciation (4,000)Net Income $0What is Payback Period? 5 years(Ignore Income Taxes)

Joe's Package Delivery Service

1: Net present value

Present Value Problem - Bonkins

On Jan 1, Bonkins Inc., bought for $520,000 a new machine with a useful life of 8 years & no salvage value. Machine will be depreciated using the straight-line method. It will produce annual cash flow from operations, net of income taxes, of $132,500. PV of an ordinary annuity of $1 for eight periods at 14% is 4.639. PV of $1 for eight periods at 14% is 0.351. Assume a time adjusted rate of return of 14%, what is the NPV?a. $ 36,680 b. $ 94,668 c. $154,440 d. $255,145

Present Value Problem - Bonkins

Compute NPV for a new machineCost of Machine 520,000$ Annual after-tax cash flow 132,500 Annuity factor for PV at 14%Present valueCost of Machine (520,000) Net present Value

Present Value Problem - Bonkins

Compute NPV for a new machineCost of Machine 520,000$ Annual after-tax cash flow 132,500 Annuity factor for PV at 14% 4.6390 Present value 614,668 Cost of Machine (520,000) Net present Value 94,668$

HillsdaleHillsdale Company purchased a machine for $480,000. The machine has a useful life of six years and no salvage value. Straight-line depreciation is to be used. Machine will generate cash flow each year, net of taxes, of $140,000 for 6 years. Hillsdale's desired rate of return is 14%. Period P. V. of $1 At 14% P. V. of Annuity of $1 At 14%

1 0.877 0.8772 0.769 1.6473 0.675 2.3224 0.592 2.9145 0.519 3.4336 0.456 3.889

What would be the net present value?a. $63,840 b. $64,460 c. $218,880 d. $233,340

PV Problem-WillsdaleWillsdale purchased a machine for $480,000. The machine has a useful life of six years and no salvage value. Straight-line depreciation is used. The machine will generate cash flow from operations, net of income taxes, of $180,000 in each of the six years. Willsdale's desired rate of return is 14%. Information on present value factors is as follows: Period P. V. of $1 AT 14% 1 .877 2 .769 3 .675 4 .592 5 .519 6 .456What would be the net present value?a. $63,840 b. $64,460 c. $219,840 d. $233,340

GarwoodGarwood bought a machine which will be depreciated on the straight-line basis over an estimated useful life of 7 years and no salvage value. Machine will generate cash flow from operations, net of income taxes, of $80,000 in each of the 7 years Garwood's expected rate of return is 12%. Information on present value is: P.V. of $1 at 12% for 7 periods 0.452 P.V. of annuity of $1 at 12% for 7 periods 4.564Assuming a positive net present value of $12,720, what was the machine's cost?a. $240,400 b. $253,120 c. $352,400 d. $377,840

2: Internal rate of return

Scott will invest $110,000 in ten year project. Annual cash in flow, net of income taxes: $20,000. Scott's desired rate of return is 10%. Present value factors: At 10% At 12% P V of $1 for ten periods 0.368 0.322 P V of annuity of $1 for ten periods 6.145 5.65Expected rate of return on this investment: a. Less than 10%, but more than 0% b. 10%. c. Less than 12%, but more than 10%. d. 12%. e. More than 12%

Internal Rate of Return

RottRott is considering investing $130,000 in 10-year project. Rott estimates that the annual cash in flow, net of income taxes, from this project will be $20,000. Rott's desired rate of return on investment of this type is 10%. Information on present value factors is as follows: At 10% At 12% P V of $1 for ten periods 0.368 0.322 P V of annuity of $1 for ten periods 6.145 5.650

Rott's excepted rate of return on this investment is:a. Less than 10%, but more than 0% b. 10%.c. Less than 12%, but more than 10%. d. 12%.

Compute internal rate of returnAmount to be invested 130,000Life of project 10Annual cash flow (after taxes) $20,000P.V. annuity factor for 10% 6.1450 P.V. of cash flows $122,900Cost of investment 130,000 Net P.V. - negative (7,100)$ Rate of return must be less than 10%.How would you estimate rate of return?

Rott, Inc.

3: Uncertain cash flows

4: Preference ranking

5: Payback

Payback ModelPayback time, or payback period, is the time it will take to recoup, in the form of cash inflows from operations, the initial dollars invested in a project.

P= I ÷ O[P= I ÷ Cash flow]

Payback Model ExampleAssume that $12,000 is spent for a machine

with an estimated useful life of 8 years.Annual savings of $4,000 in cash outflows

are expected from operations.

What is the payback period?P = I ÷ O = $12,000 ÷ $4,000 = 3 years

Payback ProblemWhich of these is necessary to calculate the pay-back period for a project?a. Useful life. b. Minimum desired rate of return. c. Net present value. d. Annual cash flow

Note. In the following question, you are given the net amount of cash from the project, after subtracting expenses and income taxes.In later problems, you must compute taxable income, so you will know how much cash is spent for income taxes.Of course, tax payments are cash outflows.

Payback Problem-WomarkWomark Co. bought a new machine on January 1, for $90,000 with an estimated useful life of five years and a salvage value of $0. The machine will be depreciated using the straight-line method. The machine is expected to produce cash flow from operations, net of income taxes, of $22,500 a year in each of the next five years. The payback period will be:a. 2.2 years. b. 2.5 years. c. 4.0 years. d. 4.5 years.

Payback Problem-Womark

Payback. After tax cash flows given

Cost of investment $90,000

After tax cash flow per year

Payback period

Payback Problem-Womark

Payback. After tax cash flows given

Cost of investment $90,000

After tax cash flow per year $22,500

Payback period 4

In the next few problems, you must

compute taxable income, so you will know

how much cash is spent for income taxes.

Of course, tax payments are cash

outflows.

Payback-Monroe Monroe is planning to purchase a new machine for $500,000. The new machine is expected to produce cash flow from operations, before income taxes, of $155,000 a year in each of the next five years. Depreciation of $100,000 year will be charged to income for each of the next five years. The income tax rate is 40%. The payback period is approximatelya. 2.2 years b. 3.4 years c. 3.7 years d. 4.1 years

Cash Flow from Operations 155,000 Depreciation Expense

Taxable IncomeTax Rate

Income TaxNet Income After Taxes

Add: Depreciation ExpenseEquals net after-tax cash flow

Cost of ProjectAnnual Cash flow-after taxesPayback Period

Payback-Monroe

Cash Flow from Operations 155,000 Depreciation Expense 100,000

Taxable Income 55,000 Tax Rate 40%

Income Tax 22,000 Net Income After Taxes 33,000

Add: Depreciation Expense 100,000 Equals net after-tax cash flow 133,000

Cost of Project 500,000 Annual Cash flow-after taxes 133,000 Payback Period 3.759398

Payback-Monroe

Payback Problem-GravinaGravina plans to spend $6,000 for machine which it will depreciate on a straight-line basis over a ten-year period. The machine will generate additional cash revenues of $2,400 a year. Gravina will incur no additional costs except for depreciation and income tax. The income tax rate is 50%. What is the pay-back period?a. 3.3 years b. 4.0 years c. 5.0 years d. 6.7 years

Payback Problem-GravinaCash Flow from Operations 2,400

Depreciation Expense - 10 Yrs 600 Taxable Income 1,800

Tax Rate 50%Income Tax 900 Net Income After Taxes 900

Add: Depreciation Expense 600 Equals net after-tax cash flow

Cost of ProjectAnnual Cash flow-after taxesPayback Period

Payback Problem-GravinaCash Flow from Operations 2,400

Depreciation Expense - 10 Yrs 600 Taxable Income 1,800

Tax Rate 50%Income Tax 900 Net Income After Taxes 900

Add: Depreciation Expense 600 Equals net after-tax cash flow 1,500

Cost of Project 6,000 Annual Cash flow-after taxes 1,500 Payback Period 4

6: Simple rate of return

Accounting Rate-of-Return ModelThe accounting rate-of-return (ARR) model expresses a project’s return as the increase in expected average annual operating income divided by the required initial investment.

Increase in InitialARR = average annual ÷ required

income investment

Accounting Rate-of-Return Model Assume the following:Investment is $6,075.Useful life is four years.Estimated disposal value is zero.Expected annual cash inflowfrom operations is $2,000.What is the annual depreciation?Ignore Depreciation here.

Accounting Rate-of-Return $6,075 ÷ 4 = $1,518.75, (rounded to $1,519) (Deprec.)

What is the ARR? ARR = ($2,000 – $1,519) ÷ $6,075 = 7.9%

Acct Rate of Return - SaratogaSaratoga will purchase a new machine for $600,000. The new machine will be depreciated on the straight line basis over a 6 years, with no salvage, and a full year's depreciation is taken in the year of acquisition. The new machine will produce cash flow from operations, net of income taxes, of $200,000 a year in each of the next six years. The accounting (book value) rate of return on the initial investment will be a. 8.3% b. 12.0% c. 16.7% d. 25.0%

Saratoga - accounting rate of returnCost of new machine $600,000Life of machine 6 yearsDeprec. per year - S-L $100,000Cash flow after taxes $200,000 per yrDeprec. (not a cash flow ) ($100,000)Book income $100,000Acct rate of return (income/cost)

Acct Rate of Return - Saratoga

Saratoga - accounting rate of returnCost of new machine $600,000Life of machine 6 yearsDeprec. per year - S-L $100,000Cash flow after taxes $200,000 per yrDeprec. (not a cash flow ) ($100,000)Book income $100,000Acct rate of return (income/cost) 16.67%

Acct Rate of Return - Saratoga

ApexApex Company is evaluating a capital budgeting proposal. Relevant data follow: Year.............. 1 2 3 4 5 6 P. V. of Annuity of $1 at 15%.... $.870 1.626 2.284 2.856 3.353 3.785The initial investment would be $30,000. It would be depreciated on a straight- line basis over six years with no salvage value. The before tax annual cash flow due to this investment is $10,000, and the income tax rate is 40% paid in the same year as incurred. The desired rate of return is 15%. All cash flows occur at the end of the year. What is the net present value of this proposal?a. $(7,290) b. $280 c. $7,850 d. $11,860

Apex

Refer to the preceding slide.What is the after tax accounting rate of return?a. 10% b. 16-2/3% c. 26-2/3% d. 33-1/3%

8: Income tax

NPV after Tax- StudleyOn Jan. 1, Studley bought a new machine for $100,000 with an estimated useful life of five years and no salvage. For book and tax purposes, the machine will be depreciated using the straight line method and it is expected to produce annual cash flow from operations, before income taxes, of $40,000. Studley uses a time adjusted rate of 12% and its income tax rate will be 40% for all years. The present value of $1 at 12% for five periods is 0.57, and the present value of an ordinary annuity of $1 at 12% for five periods is 3.61. The NPV of the machine should bea. $15,520 positive b. $15,520 negative c. $14,000 positive d. $13,680 negative

Cost of Project 100,000$ Cash Flow from Operations

Depreciation Expense Taxable Income

Tax RateIncome TaxNet Income After Taxes

Add: Depreciation ExpenseEquals net after-tax cash flowAnnuity factorGross Present ValueNet Present Value

NPV after Tax- Studley

Cost of Project 100,000$ Cash Flow from Operations 40,000

Depreciation Expense 20,000 Taxable Income 20,000

Tax Rate 40%Income Tax 8,000 Net Income After Taxes 12,000

Add: Depreciation Expense 20,000 Equals net after-tax cash flow 32,000 Annuity factorGross Present ValueNet Present Value

NPV after Tax- Studley

Cost of Project 100,000$ Cash Flow from Operations 40,000

Depreciation Expense 20,000 Taxable Income 20,000

Tax Rate 40%Income Tax 8,000 Net Income After Taxes 12,000

Add: Depreciation Expense 20,000 Equals net after-tax cash flow 32,000 Annuity factor 3.61 Gross Present Value 115,520 Net Present Value 15,520$

NPV after Tax- Studley

Form for Capital Budgeting-1This format (following slides) can be used for revenue and expenses for a proposed project. If the same depreciation method is used on both the books and the return, you only need to complete the first column.(Many capital budgeting problems allow you to assume that the same depreciation methods is used for both purposes.)

Form for Capital Budgeting-2Books Tax Return

1. Revenue 2. Cost of Sales 3. Gross Margin 4. Operating Expenses Requiring Cash 5. Cash Flow from Operations 6. Depreciation Expense (Books) 7. Depreciation Expense (Tax Return) 8. Book Income 9. Taxable Income10. Income Tax Expense11. Tax Paid12. Net Income After Taxes

Form for Capital Budgeting-3Now Compute Net Cash Flow After Income Taxes: Cash Flow from Operation of asset (5) Less: Taxes on income from asset (11) Net after-tax cash flow from the assetIf Depreciation is Same on Tax Return & Books: Net Income after taxes (12) Add: Depreciation (6) Equals Net after-tax cash flow

Gains or Losses on Disposal -1Suppose a piece equipment purchased for $125,000 is sold at the end of year 3 after taking three years of straight-line depreciation.What is the book value?

$125,000 – (3 × $25,000) = $50,000

Gains or Losses on Disposal - 2Assume that it is sold for $70,000Assume that it is sold for $70,000and the tax rate is 40%.and the tax rate is 40%. What is the cash inflow? What is the cash inflow? ($70,000 – $50,000) × 40% = $8,000($70,000 – $50,000) × 40% = $8,000 $70,000 – $8,000 = $62,000$70,000 – $8,000 = $62,000

Gains or Losses on Disposal• If it is sold for book value, there is no

gain or loss and so there is no tax effect.

• If it is sold for more than $50,000, there is a gain and an additional tax payment.

• If it is sold for less than $50,000, there is a loss and a tax savings.

Combination of Problems-1Items 1 through 4 are based on the following:Ram Co. is negotiating for the purchase of equipment that would cost $100,000. Ram expects that $25,000 per year could be saved in after tax ‑cash costs if the equipment were acquired. The equipment's estimated useful life is 10 years, with no residual value, and would be depreciated by the straight-line method. Ram's minimum desired rate of return is 12%. PV of an annuity of 1 at 12% for 10 periods: 5.65 PV of 1 due in 10 periods at 12%: .322

Combination of Problems-2Continue from preceding slide.1. The net present value is a. $ 41,250 b. $ 6,440 c. $12,200 d. $13,000

2. The payback period is a. 4.0 years. b. 4.4 years. c. 4.5 years. d. 5.0 years.

Combination of Problems-3Continue from preceding slide.

3. The accrual accounting rate of return based on initial investment is a. 20% b. 15% c. 12% d. 10%

4. In estimating the internal rate of return, the factors in the table of present values of an annuity should be taken from the columns closest to the following multiple. a.0.65 b. 4.00 c. 5.00 d. 5.65

Combination of Problems

Information for Questions 1-4Cost of Machine 100,000$ Annual after-tax cash flow 25,000 Useful Life in years 10 Desired rate of return 12%P.V. of annuity of 1 at 12%-10 periods 5.65P.V of 1 due in 10 periods at 12% 0.322

Combination of Problems

1 A Compute Present valueAnnuity factor - P.V - 12% 5.65Annual Cash Flow 25,000 Present value 141,250 Cost of Machine (100,000) Net present Value 41,250$

Combination of Problems

2 A Payback periodCost of investment 100,000$ After tax cash flow per yr 25,000 Payback period 4

Combination of Problems

3 B Accounting Rate of ReturnCost of new machine 100,000$ Life of machine 10 Deprec. per year - S-L method $10,000Cash flow after taxes 25,000 Deprec. (not a cash flow item) ($10,000)Book income $15,000Accounting rate of return 15.00%

Combination of Problems

4 B Approx. Internal Rate of ReturnCost of equipment 100,000$ Annual after tax cash flow 25,000$ Multiple 4

HilltopHilltop Company invested $100,000 in a two-year project. Hilltop's expected rate of return was 12%. The cash flow, net of income taxes, was $40,000 for the first year. Present value and future value factors are as follows:Period Present value Future value

of $1 at 12% of $1 at 12% 1 .8929 1.1200 2 .7972 1.2544Assuming that the rate of return was exactly 12%, what was the cash flow, net of income taxes, for the second year of the project?a. $51,247 b. $60,000 c. $64,284 d. $80,638

HilltopPresent value problem-different unknown amountAmount to be invested 100,000$ Desired return 12%P.V. of cash flows must equal 100,000$ P.V. of first year cash flow 40,000$ P.V. factor-Year 1 0.8929

35,716$ P.V. of second year cash flow 64,284$ (Note this is the discounted P.V.)Present value factor-Year 2 0.7972 2nd year cash flow-Undiscounted 80,637.23$

The End

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