# Chapter 13 Income Taxes

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1 Chapter 13 Income Taxes 13-1 A tool costing \$300 has no salvage value and will be depreciated over 3 years according to the sum-of-the-years-digits method. The cash flows before tax due to the tool are shown below. The tax rate is 35%. SOYD Taxable BTCF Depreciation Income Taxes ATCF 0 -\$ a) Fill in the table. b) What is the internal rate of return after tax? a) BTCF SOYD Depreciation Taxable Income Taxes ATCF 0 -\$ b) NPW = (P/A, i%, 3) + 15(P/G, i%, 3) = 0 By trial and error. Try i = 12% NPW = \$15.55 Try i = 15% NPW = -\$ 0.68 IRR = i 15% (By interpolation i = 14.87%)

2 182 Chapter 13 Income Taxes A company, whose earnings put them in the 35% marginal tax bracket, is considering the purchase of a new piece of equipment for \$25,000. The equipment will be depreciated using the straight line method over a 4-year depreciable life to a salvage value of \$5,000. It is estimated that the equipment will increase the company s earnings by \$8,000 for each of the 4 years it is used. Should the equipment be purchased? Use an interest rate of 10%. BTCF Depreciation T.I Taxes ATCF 0-25,000-25, ,000 5,000 3,000 1,050 6, ,000 5,000 3,000 1,050 6, ,000 5,000 3,000 1,050 6, ,000 5,000 3,000 1,050 6,950 5,000 5,000 SL Depreciation = ¼(25,000-5,000) = \$5,000 Find net present worth: if NPV > 0 purchase equipment. NPV = -25, ,950(P/A, 10%, 4) + 5,000(P/F, 10%, 4) = \$ Purchase equipment 13-3 By purchasing a truck for \$30,000, a large profitable company in the 34% income tax bracket was able to save \$8,000 during year 1, with the savings decreasing by \$1,000 each year thereafter. The company depreciated the truck using the sum-of-years-digits depreciation method over its four year depreciable life, while assuming a zero salvage value for depreciation purpose. The company wants to sell the truck at the end of year 5. What resale value will yield a 12% after-tax rate of return for the company? SOYD = = 10 Depreciation 1 4/10(30,000-0) = 12, /10(30,000-0) = 9, /10(30,000-0) = 6, /10(30,000-0) = 3,000 ATCF Calculations: BTCF Depreciation T.I. Taxes ATCF 0-30, ,000

3 Chapter 13 Income Taxes ,000 12,000-4,000-1,360 9, ,000 9,000-2, , ,000 6,000-0, , ,000 3,000 2, , ,000-4,000 +1,360 2,640 Resale - Resale.34Resale.66Resale Solve for Resale (R): 30,000 = 9,360(P/A, 12%, 5) - 1,680(P/G, 12%, 5) +.66R(P/F, 12%, 5) 30,000 = 22, R R = \$18, A company has purchased a major piece of equipment that has a useful life of 20 years. An analyst is trying to decide on a maintenance program and has narrowed the choice to two alternatives. Alternative A is to perform \$1,000 of major maintenance every year. Alternative B is to perform \$,5000 of major maintenance only every fourth year. In either case, maintenance will be performed during the last year so that the equipment can be sold for \$10,000. If the MARR is 18%, which maintenance plan should be chosen? Is it possible the decision would change if income taxes were considered? Why or Why not? Equivalent Annual Cost A = \$1,000 Equivalent Annual Cost B = \$5,000(A/F, 18%, 4) = \$ Therefore choose Alternative B. The decision would not change it taxes were considered. The cash flows for both alternatives, would be reduced by the same percentage due to taxes so EAC A > EAC B would still be true. If we assume a 45% tax rate, for example, the computations as follows: Alternative A BTCF T.I. Taxes ATCF ,000-1, EAC A = \$550 Alternative B BTCF T.I. Taxes ATCF ,000-5,000-2,250-2,750 EAC B = 2,750(A/F, 18%, 4) = \$ A large company must build a bridge to have access to land for expansion of its manufacturing plant. The bridge could be fabricated of normal steel for an initial cost of \$30,000 and should last 15 years. Maintenance will cost \$1,000/year. If more corrosion resistant steel were used, the annual maintenance cost would be only \$100/year, although the life would be the same. In 15 years there will be no salvage value for either bridge. The company pays a combined state and federal income tax rate of 48% and uses straight-line depreciation. If the minimum attractive after

4 184 Chapter 13 Income Taxes tax rate of return is 12%, what is the maximum amount that should be spent on the corrosion resistant bridge? Steel BTCF Depreciation T.I. Taxes ATCF 0-30,000-30, ,000 2,000-3,000-1, Corrosion Resistant Steel BTCF Depreciation T.I. Taxes ATCF 0 -P -P P/ P/15 ( P) P NPW A = NPW B for breakeven 440(P/A, 12%, 15) - 30,000 = ( P)(P/A, 12%, 15) - P -27,003 = P - P P = \$34, Gillespie Gold Products Inc. is considering the purchase of new smelting equipment. The new equipment is expected to increase production and decrease costs with a resulting increase in profits. The equipment under consideration is summarized below. Determine the after-tax cash flow using a tax rate of 42% and sum-of-the-years-digits depreciation. Cost \$50,000 Net Savings/year 15,000 the first year decreasing by \$1,000 each year thereafter Depreciable Life 4 yrs Actual Useful Life 6 yrs Salvage Value 4,000 BTCF Depreciation TI Taxes ATCF 0-50, , ,000 18,400-3,400-1,428 16, ,000 13, , ,000 9,200 3,800 1,596 11, ,000 4,600 7,400 3,108 8, ,000-11,000 4,620 6,380

5 Chapter 13 Income Taxes ,000-10,000 4,200 9,800 \$4,000 capital recovery in year 6 is not taxable An asset with five year MACRS* life will be purchased for \$10,000. It will produce net annual benefits of \$2,000 per year for six years, after which it will have a net salvage value of zero and will be retired. The company s incremental tax is 34%. Calculate the after tax cash flows. *The MACRS annual percentages are 20, 32, 19.20, 11.52, 11.52, and 5.76 for years 1 through 6. BTCF Depreciation T.I. Taxes ATCF 0-10,000-10, ,000 2, , ,000 3,200-1, , ,000 1, , ,000 1, , ,000 1, , , , , A state tax of 10% is deductible from the income taxed by the federal government. The federal tax is 34%. The combined effective tax rate is a. 24.0% b. 35.0% c. 40.6% d. 45.0% Effective rate = S + (1 - S)F =.1 + (1 -.1).34 =.1 + (.9).34 = =.406 = 40.6% The answer is c For engineering economic analysis a corporation uses an incremental state income tax rate of 7.4% and an incremental federal rate of 34%. Calculate the effective tax rate.

6 186 Chapter 13 Income Taxes Effective rate = S + (1 - S)F = ( )(.34) = (.926).34 = =.3888 = 38.88% A one-year savings certificate that pays 15% is purchased for \$10,000. If the purchaser pays taxes at the 27% incremental income tax rate, the after tax rate of return on this investment is a. 4.05% b % c % d % After tax ROR = (1 - tax rate)(before tax IRR) = (1 -.27)(.15) = 10.95% The answer is b A corporation s tax rate is 34%. An outlay of \$35,000 is being considered for a new asset. Estimated annual receipts are \$20,000 and annual disbursements \$10,000. The useful life of the asset is 5 years and it has no salvage value. a) What is the prospective rate of return before income tax? b) What is the prospective rate of return after taxes, assuming straight-line depreciation? StL Depreciation = (P S) = = \$7,000/year. BTCF Depreciation T.I. Taxes ATCF 0-35, , ,000 7,000 3,000 1,020 8, ,000 7,000 3,000 1,020 8, ,000 7,000 3,000 1,020 8, ,000 7,000 3,000 1,020 8, ,000 7,000 3,000 1,020 8,980 a) ROR BEFORE TAX PW B = PW C 10,000(P/A, i%, 5) = 35,000 At 12% P/A = 3.605

7 (P/A, i%, 5) = = At i% P/A = At 15% P/A = By interpolation: ROR = 13.25% b) ROR AFTER TAX PW B = PW C 8,980(P/A, i%, n) = 35,000 At 8% P/A = (P/A, i%, 5) = = At i% P/A = At 9% P/A = By interpolation: ROR = 8.92% Chapter 13 Income Taxes A large and profitable company, in the 34% income tax bracket, is considering the purchase of a new piece of machinery that will yield benefits of \$10,000 for year 1, \$15,000 for year 2, \$20,000 for year 3, \$20,000 for year 4, and \$20,000 for year 5. The machinery is to be depreciated using the modified accelerated cost recovery system (MACRS) with a three-year recovery period. The MACRS percentages are 33.33, 44.45, 14.81, 8.41, respectively, for years 1, 2, 3, and 4. The company believes the machinery can be sold at the end of five years of use for 25% of the original purchase price. What is the maximum purchase cost the company can pay if it requires a 12% after-tax rate of return? BTCF Depreciation T.I. Taxes ATCF 0 -P P 1 10, P 10, P 3, P 6, P 2 15, P 15, P 5, P 9, P 3 20, P 20, P 6, P 13, P 4 20, P 20, P 6, P 13, P 5 20,000-20,000 6,800 13,200.25P -.25P.085P.165P P = 6,600(P/A 12%, 3) + 3,300(P/G, 12%, 3) + 13,200(P/A, 12%, 2)(P/F, 12%, 3) P(P/F, 12%, 1) P(P/F, 12%, 2) P(P/F, 12%, 3) P(P/F, 12%, 4) +.165P(P/F, 12%, 5) P = \$61, A company bought an asset at the beginning of 2007 for \$100,000. The company now has an offer to sell the asset for \$60,000 at the end of For each of the depreciation methods shown below determine the capital loss or recaptured depreciation that would be realized for Depreciation Depreciable Salvage Recaptured Capital

8 188 Chapter 13 Income Taxes Method Life Value* Depreciation Loss SL 10 years \$ 1,000 SOYD 5 25,000 DDB %DB 15 0 *This was assumed for depreciation purposes Depreciation Depreciable Salvage Recaptured Capital Method Life Value* Depreciation Loss SL 10 years \$ 1,000 \$20,200 SOYD 5 25,000 \$ 5,000 DDB , %DB ,000 SL Depreciation = (100,000-1,000) = 9,900 Book Value = 100,000-2(9,900) = 80,200 Capital Loss = 80,200-60,000 = \$20,200 SOYD Depreciation ( 1 + 2) = (100,000-25,000) = 45,000 Book Value = 100,000-45,000 = 55,000 Recaptured Depreciation = 60,000-55,000 = \$5,000 DDB Depreciation 1 = (100,000) = 50,000 Depreciation 2 = (100,000-50,000) = 25,000 Book Value = 100,000-75,000 = 25,000 Recaptured Depreciation = 60,000-25,000 = \$35, %DB Depreciation 1 = (100,000) = 10,000 Depreciation 2 = (100,000-10,000) = 9,000 Book Value = 100,000-19,000 = 81,000 Capital Loss = 81,000-60,000 = \$35,000

9 Chapter 13 Income Taxes A corporation expects to receive \$32,000 each year for 15 years if a particular project is undertaken. There will be an initial investment of \$150,000. The expenses associated with the project are expected to be \$7,530 per year. Assume straight-line depreciation, a 15-year useful life and no salvage value. Use a combined state and federal 48% income tax rate and determine the project s after-tax rate of return. BTCF Depreciation T.I. Taxes ATCF 0-150, , ,470 10,000 14,470 6,946 17,524 Take the ATCF and compute the interest rate where the PW BENEFITS equals PW COSTS. 17,524(P/A, i%, 15) = 150,000 (P/A, i%, 15) = = From interest tables, i = 8% A manufacturing firm purchases a machine in January for \$100,000. The machine has an estimated useful life of 5 years, with an estimated salvage value of \$20,000. The use of the machine should generate \$40,000 before-tax profit each year over its 5-year useful life. The firm pays combined taxes at the 40% and uses sum-of-the-years-digits depreciation. PART 1 Complete the following table. BTCF Depreciation T.I. Taxes ATCF PART 2 Does the sum-of-years-digits depreciation represent a cash flow? PART 3. Calculate the before-tax rate of return and the after-tax rate of return. PART 1: Sum-of-years-digits Depreciation -- 1 = (100,000-20,000) = \$26,667 2 = (80,000) = \$21,333

10 190 Chapter 13 Income Taxes 3 = (80,000) = \$16,000 4 = (80,000) = \$10,667 5 = (80,000) = \$ 5,333 BTCF Depreciation T.I. Taxes ATCF 0-100, , ,000 26,667 13,333-5,333 34, ,000 21,333 18,667-7,467 32, ,000 16,000 24,000-9,600 30, ,000 10,667 29,333-11,733 28, ,000 5,333 34,667-13,867 26, , ,000 PART 2: The sum-of-years-digits depreciation is a bookkeeping allocation of capital expense for purposes of computing taxable income. Therefore it does not represent an actual cash flow (exchange of money). PART 3: Before tax ROR NPW = 0 at IRR 0 = -100, ,000(P/A, i%, 5) + 20,000(P/F, i%, 5) Try 30% * NPW = +2,826 Try 35% NPW = -6,740 By interpolation: IRR = 31.5% After tax ROR NPW = 0 at IRR 0 = -100, ,667(P/A, i%, n) - 2,133(P/G, i%, n) + 20,000(P/F, i%, n) Try 20% * NPW = +1,263 Try 25% NPW = -9,193 By interpolation: IRR = 20.60% *Caution should be exercised when interpolating to find an interest rate. Linear interpolation is being imposed on a non-linear function. Therefore the solution is approximate. A maximum range over which to interpolate and achieve generally good results is usually

11 Chapter 13 Income Taxes 191 considered to be three percentage points. Often times the interest tables you have at your disposal will force you to use a larger range. This is the case in this problem PARC, a large profitable firm, has an opportunity to expand one of its production facilities at a cost of \$375,000. The equipment is expected to have an economic life of 10 years and to have a resale value of \$25,000 after 10 years of use. If the expansion is undertaken, PARC expects that their income will increase by \$60,000 for year 1, and then increase by \$5000 each year through year 10. The annual operating cost is expected to be \$5000 for the first year and to increase by \$250 per year thereafter. If the equipment is purchased, PARC will depreciate it using straightline to a zero salvage value at the end of year 8 for tax purposes. Since PARC is a large and profitable firm their tax rate is 34%. If PARC s minimum attractive rate of return (MARR) is 15%, should they undertake this expansion? Income Costs BTCF 1 60,000 5,000 55, ,000 5,250 59, ,000 5,500 64, ,000 5,750 69, ,000 6,000 74, ,000 6,250 78, ,000 6,500 83, ,000 6,750 88, ,000 7,000 93, ,000 7,250 97,750 BTCF Depreciation T.I. Taxes ATCF 0-375, , ,000 46,875 8,125 2, , ,750 46,875 12,875 4, , ,500 46,875 17,625 5, , ,250 46,875 22,375 7, , ,000 46,875 27,125 9, , ,750 46,875 31,875 10, , ,500 46,875 36,625 12, , ,250 46,875 41,375 14, , ,000-93,000 31, , ,750-97,750 31, , ,000-25,000 8, , NPW = -375,000 + [52,237.50(P/A, 15%, 8) + 3,135(P/G, 15%, 8)] + 61,380(P/F, 15%, 9) + 77,880(P/F, 15%, 10)

12 192 Chapter 13 Income Taxes NPW = -\$64, PARC should not undertake the expansion A project under consideration by PHI Inc. is summarized in the table below. The company uses straight-line depreciation, pays income taxes at the 30% marginal rate and requires an after-tax MARR of return of 12%. First Cost \$75,000 Annual Revenues 26,000 Annual Costs 13,500 Salvage Value 15,000 Useful Life 30 years a) Using net present worth, determine whether the project should be undertaken. b) If the company used sum-of-the-years-digits depreciation, is it possible the decision would change? (No computations needed.) a) BTCF Depreciation T.I. Taxes ATCF 0-75, , ,500 2,000 10,500 3,150 9, , ,000 NPW = -75, ,350(P/A, 12%, 30) + 15,000(P/F, 12%, 30) = \$815 Yes, take project since NPW > 0 b) No. Although total depreciation is the same, SOYD is larger in the early years when it is worth more. Therefore the NPW would increase with SOYD making the project even more desirable A heat exchanger purchased by Hot Spot Manufacturing cost \$24,000. The exchanger will save \$4,500 in each of the next 10 years. Hot Spot will use SOYD depreciation over a six-year depreciable life. The declared salvage value is \$3,000. It is expected the exchanger will be sold for the declared value. Hot Spot pays taxes at a combined rate of 42% and has a MARR of 8%. Was the purchased justified?

13 Chapter 13 Income Taxes First Cost -24, Annual Savings 4,500(P/A, 8%, 10)(.58) 17, Depr. [6,000(P/A, 8%, 6) - 1,000(P/G, 8%, 6)](.42) 7, Capital Recovery 3,000(P/F, 8%, 10) 1,390 NPW \$2,133 Yes the purchase was justified The Red Ranger Company recorded revenues of \$45,000 and recaptured depreciation of \$1,200 for the year just ended. During the year they incurred cash expenses of \$23,500 and depreciation expenses of \$11,575. Red Ranger s taxable income is a. \$9,925 b. \$11,125 c. \$21,500 d. \$34,275 TI = revenues - expenses - depreciation + recaptured depreciation = 45,000-23,500-11, ,200 = \$11,125 The answer is b A project will require the investment of \$108,000 in capital equipment (SOYD with a depreciable life of eight years and zero salvage value) and \$25,000 in other non-depreciable materials that will be purchased during the first year. The annual net income realized from the is projected to be \$28,000. At the end of the eight years, the project will be discontinued and the equipment sold for \$24,000. Assuming a tax rate of 28% and a MARR of 10%, should the project be undertaken? Cash expenses are multiplied by (1 - tax rate) Incomes are multiplied by (1 - tax rate) Depreciation is multiplied by tax rate Recaptured depreciation is multiplied by (1 - tax rate) 0 First Cost -108,000 1 Other Costs 25,000(P/F, 10%, 1)(.72) -16, Depr. [24,000(P/A, 10%, 8) - 3,000(P/G, 10%, 8)](.28) 22, Income 28,000(P/A, 10%, 8) 107,554 8 Recaptured Depr. 24,000(P/F, 10%, 8)(.72) 8,061 NPW \$13,638 Project should be undertaken.

14 194 Chapter 13 Income Taxes The Salsaz-Hot manufacturing company must replace a machine used to crush tomatoes for its salsa. The industrial engineer favors a machine called the Crusher. Information concerning the machine is presented below. First Cost \$95,000 Annual Operating Costs 6,000 Annual Insurance Cost* 1,750 Annual Productivity Savings 19,000 *Payable at the beginning of each year Depreciable Salvage Value \$10,000 Actual Salvage Value 14,000 Depreciable Life 6 yrs Actual Useful Life 10 yrs Depreciation Method SL Property taxes equal to 5% of the first cost are payable at the end of each year. Relevant financial information for Salsaz-Hot: Marginal Tax Rate 34% MARR 10% Determine net present worth. Cash expenses are multiplied by (1 - tax rate) Incomes are multiplied by (1 - tax rate) Depreciation is multiplied by tax rate Capital recovery is not taxable therefore multiplied by 1 Recaptured depreciation is multiplied by (1 - tax rate) 0 First Cost -95, Net Savings 13,000(P/A, 10%, 10)(.66) 52, Property Taxes.05(95,000)(P/A, 10%, 10)(.66) -19, Insurance [1, ,750(P/A, 10%, 9)](.66) -7, Depr. 14,167(P/A, 10%, 6)(.34) 20, Capital Recovery 10,000(P/F, 10%, 10) 3, Recaptured Depr. 4,000(P/F, 10%, 10)(.66) 1,018 NPW -\$43,498

15 Chapter 13 Income Taxes Momma Mia s Pizza must replace its current pizza baking oven. The two best alternatives are presented below. Crispy Cruster Easy Baker Initial Cost \$24,000 \$33,000 Annual Costs 9,000 6,000 Depreciable Salvage Value 6,000 5,000 Actual Salvage Value 6,000 8,000 Depreciable Life 3 yrs 4 yrs Actual Useful Life 5 yrs 5 yrs Depreciation Method SL SOYD Assume Momma pays taxes at the 34% rate and has a MARR of 8%. Which oven should be chosen? CC EB 0 First Cost -24, Annual Costs 9,000(P/A, 8%, 5)(.66) -23, Depr. 6,000(P/A, 8%, 3)(.34) 5,257 5 Capital Recovery 6,000(P/F, 8%, 5) 4,084 NPW -\$38,377 0 First Cost -33, Annual Costs 6,000(P/A, 8%, 5)(.66) -15, Depr. [11,200(P/A, 8%, 4) - 2,800(P/G, 8%, 4)](.34) 8,185 5 Capital Recovery 5,000(P/F, 8%, 5) 3,403 5 Recaptured Depreciation 3,000(P/F, 8%, 5)(.66) 1,348 NPW -\$35,877 Choose the Easy Baker oven

16 196 Chapter 13 Income Taxes Pinion Potato Chip Inc., must purchase new potato peeling equipment for its Union City, Tennessee plant. The plant engineer, Abby Wheeler, has determined that there are three possible set-ups that could be purchased. Relevant data are presented below. Naked Peel Skinner Peel-O-Matic First Cost \$45,000 \$52,000 \$76,000 Annual Costs 6,000 5,000 5,000 Declared Salvage Value 12% of FC 5,500 10,000 Useful Life 6 years 6 years 6 years Actual Salvage Value 6,500 5,500 12,000 Part A Part B All assets are depreciated using the SL method. Determine which set-up should be chosen if P 2 C Inc. has a MARR of 10% and pays taxes at the 34% marginal rate. Due to economic considerations P 2 C Inc. must eliminate from consideration the Peel-O- Matic set-up and because of a change in the tax laws they must use MACRS depreciation. If all other information concerning the other two alternatives remains the same, which should be chosen? Part A NP S 0 First Cost -45, Annual Costs 6,000(P/A, 10%, 6)(.66) -17, Depr. 6,600(P/A, 10%, 6)(.34) 9,773 6 Capital Recovery 5,400(P/F, 10%, 6) 3,048 6 Recaptured Depr. 1,100(P/F, 10%, 6)(.66) 410 NPW -\$49,015 0 First Cost -52, Annual Costs 5,000(P/A, 10%, 6)(.66) -14, Depr. 7,750(P/A, 10%, 6)(.34) 11,475 6 Capital Recovery 5,500(P/F, 10%, 6) 3,105 NPW -\$51,792 POM 0 First Cost -76,000

17 Chapter 13 Income Taxes Annual Costs 5,000(P/A, 10%, 6)(.66) -52, Depr. 11,000(P/A, 10%, 6)(.34) 16,288 6 Capital Recovery 10,000(P/F, 10%, 6) 5,645 6 Recaptured Depr. 2,000(P/F, 10%, 6)(.66) 745 NPW -\$67,694 Choose Naked Peel. Part B NP S 0 First Cost -45, Annual Costs 6,000(P/A, 10%, 6)(.66) -17,246 1 Depr. (.3333)(45,000)(P/F, 10%, 1)(.34) 4,636 2 Depr. (.4445)(45,000)(P/F, 10%, 2)(.34) 5,620 3 Depr. (.1481)(45,000)(P/F, 10%, 3)(.34) 1,702 4 Depr. (.0741)(45,000)(P/F, 10%, 4)(.34) Recaptured Depr. 6,500(P/F, 10%, 6)(.66) 2,422 NPW -\$47,092 0 First Cost -52, Annual Costs 5,000(P/A, 10%, 6)(.66) -14,372 1 Depr. (.3333)(52,000)(P/F, 10%, 1)(.34) 5,357 2 Depr. (.4445)(52,000)(P/F, 10%, 2)(.34) 6,494 3 Depr. (.1481)(52,000)(P/F, 10%, 3)(.34) 1,967 4 Depr. (.0741)(52,000)(P/F, 10%, 4)(.34) Recaptured Depr. 5,500(P/F, 10%, 6)(.66) 2,049 NPW -\$49,610 Choose Naked Peel.

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