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IEEN 5329 Homework 12 17

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IEEN 5329

Homework 12

17.7, 17.14, 17.20, 17.37

18.5, 18.26, 18.33

 

Basic Tax Computations

(1) Write the equation to calculate TL and NPAT for a corporation, using only the following terms: gross income, tax rate, business expenses, and depreciation.

17.2 Describe the basic difference between an income tax and a property tax for an individual.

17.3 From the following list. Select the tax-related term that is best described by each event below: depreciation, operating expense, taxable income, income tax, or net profit after taxes. |

(a) A corporation reports that it had a negative $200,000 net profit on its annual income statement.

(b) An asset with a current book value of $80,000 was utilized on a new processing line to increase sales by $200,000 this year.

(c) A machine has an annual, straight-line write-off equal to $21,000.

(d) The cost to maintain equipment during the past year was $3,680,200.

(e) A particular supermarket collected $23,550 in lottery ticket sales last year. Based on winnings paid to individuals holding these tickets, a rebate of $250 was sent to the store manager.

17.4 Two companies have the following values on their annual tax return

	Company 1	Company 2
Sales revenue, $	1,500,000	820,000
Interest revenue, $	31,000	25,000
Expense, $	-754,000	-591,000
Depreciation, $	148,000	18,000

 

(a) Calculate the federal income tax for the year.

(b) Determine the percent of sales revenue each company will pay in federal income taxes.

(c) Estimate the taxes using an effective rate of 34% of the entire TI. Determine the percentage error made relative to the exact taxes in part (a).

17.5 Last year, one separate division of Compete.com, a dot-com sports industry service firm that provides real-time analysis of mechanical stress due to athlete injury, had $300,000 in taxable income. This year, TI is estimated to be $500,000. Calculate the federal income taxes and answer the following.

(a) What was the average federal tax rate paid last year?

(b) What is the marginal federal tax rate on the additional TI?

(c} what will be the average federal tax rate this year?

(d) What will be the NPAT on just the additional $200,000 in taxable in-come?

17.6 Yamachi and Nadler of Hawaii have a gross income of $6.5 million for the year. Depreciation and expenses total $4.1 million. If the combined state and local tax rate is 7.6%, use an effective federal rate of 34% to estimate the income taxes, using the effective tax rate equation.

 

17.7 Rotana Construction, Inc., has operated for the last 21 years in a northern U.S. state where the state income tax on corporate revenue is 6% per year. Rotana pays an average federal tax of 23% undreports taxable income of $7 million. Because of pressing labor cost increases, liability insurance premium increases, and other cost increases, the president wants to move to another state to reduce the total tax burden. The new state may have to be willing to offer tax allowances or an interest-free grant for the first couple of years in order to attract the company. You are an engineer with the company and are asked to do the following.

(a) Determine the effective tax rate for Rotana.

(b) Estimate the state tax rate that would be necessary to reduce the overall effective tax rate by 10% per year.

(c) Determine what the new state would have to do financially for Rotana to move there and to reduce

Its effective tax rate to 22% per year.

17.8 Workman Tools reported a TI of $80,000 last year. If the state income tax rate is 6%, determine the (a) average federal tax rate, (b) overall effective tax rate, (c) total taxes to be paid based on the effective tax rate, and (a) total taxes paid to the state and paid to the federal government.

17.9 Donald is a civil engineer with an annual salary of $98,000. He has dividends and interest of $7500 for the year. Total ex-emptions and deductions are $10,500.

(a) Calculate federal income taxes as a person filing single.

(b) Determine what percentage of his annual salary goes toward federal income taxes.

(c) Calculate by how much the total of exemptions and deductions has to increase for Donald's income taxes to go down by 10%.

CFBT and CFAT

17.10 What is the basic difference between cash flow after taxes (CFAT) and net profit after taxes (NPAT)?

17.11 Derive a general relation for calculating CFAT under the situation that there is no annual depreciation to deduct and it is a year in which no investment P or salvage S occurs.

17.12 Where is depreciation considered in the CFBT and CFAT expressions used to analyze an engineering economy alternatives cash flow estimates’?

17.13 Four years ago ABB purchased an asset for $300,000 with an estimated salvage of $60,000. Depreciation was $60.000 per year. The following annual gross incomes and expenses were recorded. The asset was sold for $60,000 after 4 years.

(a) Tabulate the cash flows by hand after an effective 32% tax rate is applied. Use the format of Table 17-3.

 

(b) Continue the table above and calculate the net income (NI) estimates.

(c) Setup the spreadsheet and determine the annual CFAT and NI values. Additionally plot these values versus year of ownership.

Year of Ownership	1	2	3	4
Gross income, $	80,000	150,000	120,000	100,000
Expense, $	-20,000	-40,000	-30,000	-50,000

 

17.14 Four years ago Hartcourt-Banks purchased an asset for $200,000 with an estimated $ = $40,000. MACRS depreciation was charged over a 3-yeur recovery period. The following gross incomes and expenses were recorded, and an effective tax rate of 40% was applied. Tabulate CFAT under the assumption that the asset was (a) discarded for $0 after 4 years and (b) sold for $20,000 after 4 years. For this tabulation only, neglect any taxes that may be incurred on the sale of the asset.

Year of Ownership	1	2	3	4
Gross income, $	80,000	150,000	120,000	100,000
Expense, $	-20,000	-40,000	-30,000	-50,000

 

17.15 A petroleum engineer with Halstrom Exploration must estimate the minimum required cash flow before taxes if the CFAT is $2,000.000. The effective federal tax rate is 35%, and the state tax rate is 4.5%. A total of $1 million in tax-deductible depreciation will be charged this year. Estimate the required CFBT.

17.16 A division of Hanes has the following data at the end of a year.

Total revenue = $48 million

Depreciation = $8.2 million

Operating expenses = $28 million

For an effective federal tax rate of 35% and state tax rate of 6.5%, determine (a) CFAT, (2) percentage of total revenue expended on taxes. And (c) net income for the year.

17.17 Wal-Mart Distribution Centers has put into service forklifts and conveyors purchased for $250,000. Use a spreadsheet to tabulate the CFBT, CFAT, and NPAT for 6 years of ownership, using an effective tax rate of 40% and the estimated cash flow and depreciation amounts shown. Salvage is expected to be zero.

Income	Gross Income, $	Operating Expenses, $	MACRS Depreciation, $
1	90.000	-20.000	50.000
2	100.000	-20.000	80.000
3	60.000	-22.000	48.000
4	60.000	-24.000	28.800
5	60.000	-26.000	28.800
6	40.000	-28.000	14.400

 

 

17.18 A highway construction company purchased pipeline boring equipment for $80.000 and depreciated it using MACRS and a 5-year recovery period. It had no estimated salvage and produced annual GI - E amounts of $50,000, which were taxed at an effective 38%. The company decided to prematurely sell the equipment after 2 full years of use.

(a) Find the price if the company wants to sell it for exactly the amount reflected by the current book value.

(b) Determine the CFAT values if the equipment was actually sold after 2 years for the amount determined in part (a) and no replacement was acquired.

Depreciation Method Effects on Taxes

17.19) an overland freight company has purchased new trailers for $150,000 and expects to realize a net $80,000 in gross income over operating expenses for each of the next 3 years. The trailers have a recovery period of 3 years. Assume an effective tax rate of 35% and an interest rate of 15% per year.

(a) Show the advantage of accelerated depreciation by calculating the present worth of taxes for the MACRS method versus the classical SL method. Since MACRS takes an additional year to fully depreciate the basis, assume no CFBT beyond year 3, but include any negative tax as a tax saving.

(b) Show that the total taxes are the same for both methods.

17.20 Work Problem [7.19 using one spread-sheet.

17.21) perform an analysis using a spreadsheet between the following two depreciation options for a company operating in a South American country. Select the preferred method based on the better PW of tax value at i = 8% and Te = 40%.

	Option 1	Option 2
Initial investment, $	— 100,000	— 100,000
CFBT, $/year	40,000	40,000
Depreciation method	Straight Line	Double declining balance
Recovery period, years	5	8

 

17.22 Imperial Chem, Inc., an international chemical products company headquartered in the United Kingdom, purchased two identical systems used in the manufacture of synthetic fibers, one system is located in Pennsylvania in the United States, the other in Genoa, Italy. Each is estimated to generate additional annual CFBT of $65,000 USD for the next 6 years. The company’s division in Italy is incorporated there and may not use MACRS for depreciation. Assume the classical straight line method is the one approved for foreign corporations with incorporated units in Italy. The U.S. incorporated unit uses MACRS, the same as any U.S.-based corporation would. (a) What is the difference in the present worth of taxes and total taxes for the 6 years? Why are these two totals not equal? For this analysis, use the full 6 years as the evaluation period and an interest rate of 12% per year. Neglect any capital gains, losses, or depreciation recapture at sale time, and assume that any negative income tax is a tax savings.

	Asset Located in U.S.	Asset Located in Italy
First Cost, $	-250,000	-250,000
Salvage Value, $	25,000	25,000
Total annual CFBT, $/year	65,000	65,000
Tax rate, %	40	40
Depreciation method	MACRS	Classical SL(no half-year convention)
Recovery period, years	5	5

 

17.23 An asset with a first cost of $9000 is depreciated by MACRS over a 5-year recovery period. The CFBT is estimated at $10.000 the first 4 years and $5000 thereafter as long as the asset is retained. The effective tax rate is 40%, and money is worth [0% per year. In present worth dollars, how much of the cash flow generated by the asset over its recovery period is lost to taxes? Work using hand or spreadsheet calculations as directed by the instructor.

17.24 The effective tax savings in a year TS, due to depreciation is calculated as TS, = (depreciation (effective tax rate) (Di)(Te)

(a) Develop a relation for the present worth of tax savings PW_TS, and explain how it may be utilized rather than the PW_tax  criterion in evaluating the effect of depreciation on taxes.

(b) Calculate PW_ts . for an asset using MACRS with a first cost of $80,000, no salvage value, and a recovery period of 3 years. Use i = 10% per year and T, = 0.42.

17.25 An engineering graduate has taken over his father’s power tool manufacturing business, Hartley Tools. The company has purchased new equipment for $200,000 with an expected life of 10 years and no salvage value. For tax purposes, the depreciation choices are as follows:

* Alternative straight line depreciation with the half-year convention and a recovery period of 10 years

* MACRS depreciation with a recovery period of 5 years.

The anticipated CFBT is $60,000 per year for only 10 years. The effective tax rate for Hartley is 42% including all taxes. Use a spreadsheet to determine the following:

(a) Rate of return before taxes over the total of 11 years.

(b) Rate of return after taxes over the total of 11 years.

(c) The depreciation method that minimizes the time value of taxes. Use an interest rate of 1O% per year, and consider any negative tax as a tax savings in the year incurred.

Depreciation Recapture and Capital Gains (Losses)

17.26 Determine any depreciation recapture or capital gain or capital loss generated by each event described below. Use them to determine the amount of the income tax effect, if the effective tax rate is 30%. (a) A-strip of land zoned as “‘Commercial A’ purchased 8 years ago for $2.6 million was just sold at a 15% profit.

(b) Earthmoving equipment purchased for $155,000 was depreciated using MACRS over a 5-year recovery period. It was sold at the end of the fifth year of ownership for $10,000.

(c) A MACRS-depreciated asset with a 7-year recovery period has been sold after 8 years at an amount equal to 20% of its first cost. Which was $150,000.

17.27 Determine any depreciation recapture or capital gain or capital loss generated by each event described below. Use them to determine the amount of the income tax effect. If the effective tax rate is 40%.

(a) A 21-year-old asset was removed from service and sold for $500. When purchased, the asset was entered on the books with a basis of P = $180,000, S = $5000, and n =18 years. Classical straight line depreciation was used for the entire recovery period.

(b) A high-technology machine was sold internationally for $10,000 more than its purchase price just after it was in service 1 year. The asset had P = $100,000, S = $1000, and n = 5 years and was depreciated by the MACRS method for 1 year.

17.28 Set up a spreadsheet, using a modification of the column headings in Table 17-3(b) to (a) graphically compare the annual CFAT series and (b) numerically compare the total CFAT of two depreciation models MACRS depreciation and SL depreciation with the half-year convention. Use the following asset situation.

First cost = $10,000

Salvage estimate = $500

Recovery period = 5 years

GI — E = $5000 per year for 6 years

The asset was sold for $500 after 6 years of use, the effective tax rate averaged 38% per year over the time of ownership.

17.29 Mercy Hospital, a for-profit corporation, purchased sterilization equipment at a cost of $40,000. MACRS, with a recovery period of 5 years and an estimated salvage of $5000, was used to write off the capital investment. The equipment increased gross income by $20,000 and expenses by $3000 per year. A full 2 years after purchasing it, the hospital sold the equipment to a newly organized clinic for $21,000. The effective tax rate is 35%, determine the (a) income taxes and (b) cash flow after taxes for the asset in the year of the sale.

17.30 A couple of years ago the company Health4All purchased land, a building, and two depreciable assets from another corporation. These have all recently been disposed of. Use the information shown to determine the presence and amount of any capital gain, capital loss, or depreciation recapture.

Asset	Purchase Price, $	Recovery Period, Years	Current Book Value, $	Sales Price, $
Land	-200,000	-		245,000
Building	-800,000	27.5	300,000	255,000
Cleaner	-50,500	3	15,500	18,500
Circulator	-10,000	3	5,000	10,500

 

17.31 In Problem 17.14(b), Hartcourt-Banks sold a 4-year-old asset for $20,000. The asset was depreciated using the 3-year MACRS method. (a) Recalculate the CFAT in the year of sale, taking into account any additional tax effects caused by the $20,000 sale price. (b) What is the change in the CFAT from the amount in Problem 17.14?

17.32 (Uses same asset data as in Problem 16A4.) An asset with a first cost of $45,000 has a life of 5 years, a salvage value of $3000, and an anticipated CFBT of $15.000 per year. Determine the depreciation schedule for classical SL and for switching from DDB to SL to maximize depreciation. Use i = 18% and an effective tax rate of 50% to determine how much the present worth of taxes decreases when switching is allowed. Assume that the asset is sold for $3000 in year 6 and that any negative tax or capital loss at sale time generates a tax savings.

17.33 Retrieve IRS Publication 544 from the Web and use the material in the chapter on reporting gains and losses to explain the calculations necessary to determine net capital gain and net capital loss on Section 1231 property transactions. Describe how they are to be reported on a corporate tax return.

After-Tax Economic Analysis

17.34 Compute the required before-tax return if an after-tax return of 9% per year is expected and the state and local tax rates total 6%. The effective federal tax rate is 35%.

17.35 A division of Texaco Chevron has a TI of $8.95 million for a tax year. If the state tax rate averages 5% for all the states in which the corporation operates, find the equivalent after-tax ROR required of projects that are justified only if they can demonstrate au before-tax return of 22% per year.

17.36 John made an annual return of 8% after taxes on a stock investment. His sister told him this is equivalent to a 12% per year before-tax return. What percent of taxable income is she assuming will be taken by income taxes?

17.37 An engineer co-owns a real estate rental property business, which just purchased an apartment complex for $3,500,000, using all equity capital. For the next 8 years, an annual gross income before taxes of $480,000 is expected. Offset by estimated annual expenses of $100,000. The owners hope to sell the property after & years for the currently appraised value of $4,050,000. The applicable tax rate for ordinary taxable income is 30%. The property will be straight line depreciated over a 20-year life with a salvage value of zero. Neglect the half-year convention in depreciation computations.

(a) Tabulate the after-tax cash flows for the 8 years of ownership, and (b) determine the before-tax and after-tax rates of return. Use either hand or computer presentation of the CFAT tabulation template in Table 17-3, altered to accommodate this situation.

17.38 An asset has the following series of CFBT and CFAT estimates that have been entered into the indicated columns and rows of a spreadsheet. The company uses a rate of return of 14% per year before taxes and 9% per year after taxes. Write the spreadsheet functions for each series that will display the three results of PW, AW, and ROR. In solving this problem, use the spreadsheet functions NPV, PV and IRR at a minimum.

Column
Row 4	A Year	B CFBT, $	C CFAT, $
5	0	-200,000	-200,000
6	1	75,000	62,000
7	2	75,000	60,000
8	3	75,000	52,000
9	4	75,000	53,000
10	5	90,000	65,000

 

17.39 News Record. Inc., has owned two subsidiary companies for the last 4 years and expects to retain ownership for 4 more years of one company and sell the other company now. You have been asked to perform an economic analysis to determine which one to sell. When purchased, North Enterprises (NE) costs $20 million and the Southern Exchange (TSE) costs $40 million. Capital assets cost $10 million for NE and $20 million for TSE when purchased 4 years ago, and they will continue to be MACRS depreciated using n = 7 for the remaining 4 years of their lives. The NE company will require new investment funds of $500.000 immediately due to some bad decisions made previously. TSE does not require new investment funds. Annual estimates of future gross income (revenue) and expenses are made. All values in the table are in $1000 units. The effective tax rate is 35% per year. The board of directors has set the corporate after-tax MARR at 25% per year.

	North Enterprises (NE)				The Southern Exchange (TSE)
Years from Now	1	2	3	4	1	2	3	4
Gross income, $	2000	2500	3000	3500	4000	3000	2000	1000
Expense, $	-500	-800	-1100	-1400	-800	-1200	-1500	-2000

 

To make the retain/sell recommendation, consider only the next 4 years of after-tax cash flows to determine the breakeven ROR value. (Note: Since these are entire corporations being analyzed, a negative income tax should not be considered as a tax savings. In this case, the income tax amount is estimated to be zero for the year. )

17.40 A civil engineer must choose between two pieces of equipment used to supplement the pumping of concrete into foundation settings.

	Machine A	Machine B
First Cost, $	-35,500	-19,000
Salvage, $	4,000	3,000
CFBT/year, $	8,000	65,00
Life, Years	7	7

 

 Both machines have an estimated 7-year useful life; however, MACRS depreciation is over a 5-year recovery period. The effective tax rate is 40%., and the after-tax MARR is 8% per year. Compare the two machines, using present worth after-tax analysis. Perform the analysis (a) by computer and (b) by hand.

17.41 Two alternatives are to be evaluated by Ned. His boss wants to know the rate of return value compared to the corporate after-tax MARR of 7% per year used to decide upon any new capital investment. Perform the analysis (a) before taxes and (b) after taxes with T_e = 50% and classical SL depreciation. (Develop the hand or spreadsheet solution per your instructor.)

	X	Y
First cost, $	-12,000	-25000
AOC, $/year	-3000	1500
Salvage, $	3000	5,000
N, years	10	10

 

17.42 Two machines have the following estimates.

	Machine A	Machine B
First cost, $	-15,000	-22000
Salvage, $	3000	5000
AOC, $/year	-3,000	-1,500
Life, Years	10	10

Either machine is to be used for a total of 10 years, then sold for the estimated salvage value. The before-tax MARR 1s 14% per year, after-tax MARR is 7% per year, and 7, is 50%. Select a machine on the basis of (a) before-tax PW = analysis, (b) after-tax PW analysis using classical SL depreciation over the [0-year life, and (c) after-tax PW analysis using MACRS depreciation with a 5-year recovery period.

17.43 A senior engineer at Tuskegee Industries developed per unit estimates for state-of-the-art truck tire balancing machines to be utilized for the next 3 years. Up to 1000 of these will be purchased for their 450 outlets. If after-tax MARR = 8%, MACRS depreciation (with no G1 — E in year 4) and Te, = 40%, (a) develop a PW versus I chart that shows the after-tax breakeven ROR, and (b) use SOLVER to determine the first cost of B to make the two break even if all other estimates are retained.

	Alternative A	Alternative B
First Cost, $	-10,000	-13,000
Salvage, $	0	2,000
GI-E $/year	4500	5000
Recovery period years	3	3

 

17.44 A European candy manufacturing plant manufacturing must select a new irradiation system to ensure the safety of specific products while being economical. The two alternatives available have the following estimates.

	System A	System B
First Cost, $	-150,000	-85,000
CFBT, $/year	60,000	20,000
Life, years	3	5

 

The company is in the 35%. Tax bracket and assumes classical straight-line depreciation for alternative comparisons performed at an after-tax MARR of 6%. Per year. A salvage value of zero is used when depreciation is calculated. System B can be sold after 5 years for an estimated 10% of its first cost. System A has no anticipated salvage value. Determine which is more economical.

17.45 Use (a) hand calculations and (b) spread-sheet relations to find the after-tax rate of return for the following desalinization plant equipment over a 5-year time period. The equipment, designed for special Jobs, will cost $2500, will have no salvage value, and will last no more than 5 years. Revenue minus expenses is estimated to be $1500 in year 1 and only $300 each additional year of use. The effective tax rate is 30%. (1) Use classical SL depreciation. (2) Use MACRS depreciation.

17.46 Automatic inspection equipment purchased for $78,000 by Stimson Engineering generated an average of $26,080 annually in before-tax cash flow during its 5-year estimated life. This represents a return of 20%. However, the corporate finance officer determined that the CFAT was $18.000 for the first year only and is decreasing by $1000 per year thereafter. If the president wants to realize an after tax return of 12% per year, for how many more years must the equipment remain in service?

17.47 Solve Problem 17.46, using the NPV function in Excel.

17.48 Tabulate CFAT for Problem 17.42 estimates, using classical straight-line depreciation over 10 years. (a) Estimate the breakeven rate of return using a PW versus i graph. (b) Select the better machine at each of the following after-tax MARR values: 5%, 9%, 10%, and 12% per year.

17.49 In Example 17.8, P = $50,000, S = 0, n = 5,CFBT = $20.000, and Te = 40% for a fiber optics cable manufacturer. Straight line depreciation is used to compute an after-tax r* = 18.03%. If the owner requires an after-tax return of 20% per year, determine an estimate allowed for (a) the first cost and (b) the annual CFBT. When you determine one of these values. assume that the other parameter retains the value estimated in Example 17.8. Assume the effective tax rate remains at 40%. Solve this problem by hand.

17.50 Work Problem 17.49, using a spreadsheet and SOLVER for after-tax returns of (a) 20% and (6) 10% per year. Explain why the P and CFBT values have increased or decreased when a ROR value higher and lower than 18.03% is used.

After-Tax Replacement Study

17.51 Scotty Paper Company-Canada employee Stella Needleson was asked to determine if the current process of dying writing paper should be retained or a new environmentally friendly process should be implemented. Estimates or actual values for the two processes are summarized below. She performed an after-tax replacement analysis at 10% per year and the corporation’s effective tax rate of 32% to determine that economically, the new process should be chosen. Was she correct? Why or why not? (Note: Canadian tax law does not impose the half-year convention requirement,)

	Current Process	New Process
First cost 7 years ago, $	-450,000
First cost, $		-700,000
Remaining life, years	5	10
Current market value, $	50,000
AQC, $/year	-160,000	-150,000
Future salvage, $	0	50,000
Depreciation method	SL	SL

 

17.52 (a) The Los Angeles, California, city engineer is analyzing a for-profit public works project at the port authority, using an after-tax replacement analysis of the installed system (defender) and a challenger as detailed below. All values are in $1000 units. The effective state tax rate of 6% is applicable, but no federal taxes are imposed. A municipal after-tax return of 6% per year is required. Assume salvages in the future occur at the estimated amounts and use classical SL depreciation. Perform the analysis.

(b) Would the decision be different if ‘a before-tax replacement analysis were performed at i = 12% per year?

	Defender	Challenger
First Cost, $	-28,000	-15,000
AOC, $/year	-1,200	-1,500
Salvage estimate, $	2,000	3,000
Market value, $	15,000
Life, Years	10	8
Years in Service	5

17.53 In Problem 17.52(a), assume that 5 additional years have passed and the challenger has been in place all 5 years. A new city engineer decides to privatize the for-profit entities of the city government and sells the implemented challenger system for $10,000,000. Was the decision made 5 years earlier to select the challenger an economically correct one? Use the same values as before: 6% effective tax rate, 6% per year after-tax rate of return, and classical SL depreciation.

17.54 Apple Crisp Foods signed a contract some years ago for maintenance services on its fleet of trucks and cars. The contract is up for renewal now for a period of 1 year or 2 years only. The contract quote is $300,000 per year if taken for 1 year and $240,000 per year if taken for 2 years. The finance vice president wants to renew the contract for 2 years without further analysis, but the vice president for engineering believes it is more economical to perform the maintenance in-house. Since much of the fleet 1s aging and must be replaced in the near future, a fixed 3-year study period has been agreed upon. The estimates for the in-house (challenger) alternative are as follows:

First Cost, $	-800,000
AOC, $/year	-120,000
Life, Years	4
Estimated salvage, $	Loses 25% of P annually:
	End year 1 600,000
	End year 2) 400,000
	End year 3) 200,000
	End year 4   0
Macrs depreciation	3-year recovery period

 

The effective tax rate is 35%, and the after-tax MARR 1s 10% per year. Perform an after-tax AW analysis, and determine which vice president has the better economic strategy over the next 3 years.

17.55 Nuclear safety devices installed several years ago have been depreciated from a first cost of $200,000 to zero using MACRS. The devices can be sold on the used equipment market for an estimated $15,000. Or they can be retained in service for 5 more years with a $9000 upgrade now and an AOC of $6000 per year. The upgrade investment will be depreciated over 3 years with no salvage value. The challenger is a replacement with newer technology at the first cost of $40,000, 2 = 5 years, and § = 0. The new units will have operating expenses of $7000 per year.

(a) Use a 5-year study period, an effective tax rate of 40%, an after-tax MARR of 12% per year, and an assumption of classical straight-line depreciation (no half-year convention) to perform an after-tax replacement study.

(b) If the challenger is known to be salable alter 5 years for an amount between $2000 and $4000, will the challenger AW value become more or less costly? Why?

17.56 Develop a spreadsheet like the one in Table 17-8 for Example 17.13. Redo the after-tax replacement analysis, using the estimates that the market value of the defender is only $275,000 and that the challenger will be sold on the international market for $100,000. Salvage value is not considered in computing challenger depreciation.

17.57 Three years ago, Silver House Steel purchased a new quenching system for $550.000. The salvage value after 10 years at that time was estimated to be $50,000. Currently, the expected remaining life is 7 years with an AOC of $27,000 per year. The new president has recommended the early replacement of the system with one that costs $400,000 and has a 12-year life, a $35,000 salvage value, and an estimated AOC of $50,000 per year. The MARR for the corporation 1s 12% per year. The president wishes to know the replacement value that will make the recommendation to replace now economically advantageous. Use a spreadsheet and the SOLVER tool to find the minimum trade in value (a) before taxes and (b) after taxes, using an effective tax rate of 30%. For solution purposes, use classical SL depreciation for both systems. Comment on the difference in replacement value made by the consideration of taxes.

Economic Value Added

17.58 (a) what does the term economic value added (EVA) mean relative to the bottom line of a corporation?

(b) Why might an investor in a public corporation prefer to use the EVA estimates over the CFAT estimates for a project?

17.59 An asset has a first cost of $12,000, SL depreciation of $4000 for each year of its 3-year recovery period and no salvage value, and an estimated CFBT of $5000 per year. The effective tax rate is 50%, and the after-tax MARR of the Harriet Corporation is 10% per year. Use hand or spreadsheet solution as indicated by your instructor to demonstrate (a) that the present worth values of the EVA and CFAT series are identical and (4) that when the equivalent of the first cost is “charged” against annual CFAT, the resulting PW value is equal to the PW of EVA, as discussed in Example 17,14(b).

17.60 For Example 17.3 and an interest rate of 10% per year, do the following: (a) Determine the EVA estimates for each year.

(b) Show that the annual worth of EVA estimates is numerically the same the AW of the CFAT estimates. If the actual salvage value in year 615s zero, not $150,000. (This makes the CFAT value in year 6 equal to $82,588.)

17.61 Sun Microsystems has developed partnerships with several large manufacturing corporations to use Java software in their consumer and industrial products. A new corporation will be formed to man- age these applications. One major project involves using Java in commercial and industrial appliances that store and cook food. The gross income and expenses are expected to follow the relations shown for the estimated life of 6 years. For t = 1 to 6 years,

Annual gross income = 2,800,000 — 100,000

Annual expenses = 950,000 + 50,000t

The effective tax rate is 35%, the interest rate is 12% per year, and the depreciation method chosen for the $3,000,000 in capital investment is the 5-year MACRS alternative that allows straight line write-off with the half-year convention in years 1 and 6. Using a spreadsheet, estimate (a) the annual economic contribution of the project to the new corporation and (b) the equivalent annual worth of these contributions.

17.62 Review the situations in Examples 17.6 and 17.11. Assume the NBA contract is now for 6 years, that the gross income and expenses continue for all 6 years, and that neither analyzer has any realized salvage value. Use an EVA analysis to choose between the two analyzers. The MARR is 10% per year, and Te = 35%.

PROBLEMS

Sensitivity to Parameter Variation

18.1 The Central Drug Distribution Center wants to evaluate a new materials handling system for fragile products. The complete device will cost $62,000 and have an 8-year life and a salvage value of $1500. Annual maintenance, fuel, and overhead costs are estimated at $0.50 per metric ton moved. Labor cost will be $8 per hour for regular wages and $16 for overtime. A total of 20 tons can be moved in an 8-hour period. The center handles from 10 to 30 tons of fragile products per day. The center uses a MARR of 10%. Determine the sensitivity of present worth of costs to the annual volume moved. Assume the operator is paid regular wages for 200 days of work per year. Use a 10-metric-ton increment for the analysis.

18.2 An equipment alternative is being economically evaluated separately by three engineers at Raytheon. The first cost will be $77,000, and the life is estimated at 6 years with a salvage value of $10,000. The engineers disagree, however, on the estimated revenue the equipment will generate. Joe has made an estimate of $10.000 per year. Jane states that this is too low and estimates $14,000, while Carlos estimates $18,000 per year. If the before-tax MARR is 8% per year, use PW to determine if these different estimates will change the decision to purchase the equipment.

18.3 Perform the analysis in Problem 18.2 on a spreadsheet, and make it an after-tax consideration using 5-year MACRS depreciation and a 35% effective tax rate. Use estimated annual expenses of $2000. Determine the effective after-tax MARR of 8%.

18.4 A manufacturing company needs 1000 square meters of storage space. Purchasing land for $80,000 and erecting a temporary metal building at $70 per square meter are one option. The president expects to sell the land for $100,000 and the building for $20,000 after 3 years. Another option is to lease space for $2.50 per square meter per month payable at the beginning of each year. The MARR is 20%. Perform a present worth analysis of the building and leasing alternatives to determine the sensitivity of the decision if construction costs go down 10% and the lease cost goes up to $2.75 per square meter per month.

18.5 A new demonstration system has been designed by Custom Baths & Showers. For the data shown, determine the sensitivity of the rate of return to the amount of the revenue gradient G for values from $1500 to $2500. If the MARR is 18% per year, would this variation in the revenue gradient affect the decision to build the demonstration system? Work this problem (a) by hand and (b) by computer.

P = $74,000 n=10 years s=0

Expense: $30,000 first year, increasing $3000 per year thereafter

Revenue: $63,000 first year, decreasing by G per year thereafter

18.6 Consider the two air conditioning systems detailed below.

	System 1	System 2
First cost, $	— 10,0060	— 17,000
Annual operating cost, $/year	— 600	— 150
Salvage value, $	— 100	— 300
New compressor and motor cost at midlife, $	-1750	-3,000
Life, years	8	12

 

Use AW analysis to determine the sensitivity of the economic decision to MARR values of 4%, 6%, and 8%. Plot the sensitivity curve. Work this problem (a) by hand and (4) by computer.

18.7 Clint and Anne plan to either purchase a weekend home or buy a travel trailer and a four-wheel-drive vehicle to pull the trailer for vacations. They have found a 5-acre tract with a small house 25 miles from their home. It will cost them $130.000, and they estimate they can sell the place for $145,000 in 10 years when their children are grown. The insurance and upkeep costs are estimated at $1500 per year, but this weekend site is expected to save the family $150 every day they don't go on a traveling vacation. The couple estimates that even though the cabin is only 25 miles from home, they will travel 50 miles per day when at the cabin while working on it and visiting neighbors and local events. Their car averages 30 miles per gallon of gas.

The trailer and vehicle combination would cost $75,000 and could be sold for $20,000 in 10 years. Insurance and operating costs will average $1750 per year, but this alternative 1s expected to save $125 per vacation day. On a normal vacation, they travel 300 miles each day. Mileage per gallon for the vehicle and trailer is estimated at 60% that of the family car. Assume gas costs $1.20 per U.S. gallon. The money earmarked for this purchase currently earns 10% per year.

(a) Compute the breakeven number of vacation days per year for the two plans.

(b) Determine the sensitivity of AW for each plan if vacation time may vary as much as +40% from the break-even number.

(c) If Anne just started a new job and will have only 14 days for the next few years, which alternative is less costly?

 

18.8 (a) Calculate by hand and plot the sensitivity of rate of return versus the bond interest rate of a $50,000 fifteen-year bond that has bond interest paid quarterly and is discounted to $42,000. Consider bond rates of 5%, 7%, and 9%. (b) Use a spreadsheet to solve this problem.

18.9 Leona has been offered an investment opportunity that will require a cash out-lay of $30,000 now for a cash inflow of $3500 for each year of investment. However, she must state now the number of years she plans to retain the investment. Additionally, if the investment is retained for 6 years, $25,000 will be returned to investors, but after 10 years the return is anticipated to be only $15.000, and after 12 years it is estimated to be $8000. If money is currently worth 8% per year, is the decision sensitive to the retention period?

18.10 An asset costs $8000 and has a maximum life of 15 years. Its AOC is expected to be $500 the first year and increase by an arithmetic gradient G between $60 and $140 per year thereafter. Determine the sensitivity of the economic service life to the cost gradient in increments of $40, and plot the results on the same graph. Use an interest rate of 5% per year.

18.11 For plans A and B. graph the sensitivity of PW values at 20% per year for the range —50% to + 100% of the following single-point estimates for each of the parameters: (a) first cost, (b) AOC, and (c) annual revenue.

	Plan A	Plan B
First cost. $	-500,000	-375,000
AOC s/year	-75,000	-80,000
Annual revenue, $/year	150,000	130,000
Salvage value, $	50,000	37,000
Expected Life, years	5	5

 

18.12 Use a spreadsheet to determine and graph the sensitivity of the rate of return to a 25% change in (a) purchase price and (b) selling price for the following investment. An engineer purchased an antique car for $25,000 with the plan to “make it original” and sell it at a profit. Improvements cost $5500 the first year, $1500 the second year, and $1300 the third year. He sold the car after 3 years for $35.000.

18.13 Use a spreadsheet to plot on one graph (similar to Figure 18-3) the sensitivity of AW over the range —30% to +50% of the parameters (a) first cost, (b) AOC, and (c) annual revenue. Use a MARR of 18% per year.

Process	Estimate
First Cost, $	-80,000
Salvage value, $	10,000
Life, Years	10
AOC, $/year	-15,000
Annual revenue, $/year	39,000

 

18.14 Graph the sensitivity of what a person should he willing to pay now for a 9% $10,000 bond due in 10 years if there Is a +30% change in (a) face value, (b) dividend rate, or (c) required nominal rate of return, which is expected to be 8% per year, compounded semiannually. The bond dividends are paid semiannually.

Three Estimates

18.15 An engineer must decide between two ways to pump concrete up to the top floors of a seven-story office building to be constructed. Plan 1 requires the purchase of equipment for $6000 which costs between $0.40 and $0.75 per metric ton to operate, with a most likely cost of $0.50 per metric ton. The asset is able to pump 100 metric tons per day. If purchased, the asset will last for 5 years, have no Salvage value, and be used from 50 to 100 days per year. Plan 2 is an equipment-leasing option and is expected to cost the company $2500 per year for equipment with a low cost estimate of $1800 and a high estimate of $3200 per year. In addition, an extra $5 per hour labor cost will be incurred for operating the leased equipment per 8 hour day. Plot the AW of each plan versus total annual operating cost or lease cost at y = 12%. Which plan should the engineer recommend if the most likely estimate of use is (@) 50 days per year and (b) 100 days per year?

18.16 A meat packing plant must decide between two ways to cool cooked hams. Spraying cools to 30°C using approximately 80 liters of water for each ham. The immersion method uses 40 liters per ham, but an extra initial cost for equipment of $2000 and extra maintenance costs of $100 per year for the 10-year life are estimated. Ten million hams per year are cooked, and water costs $0.12 per 1000 liters. Another cost is $0.04 per 1000 liters for wastewater treatment, which is required for either method. The MARR is 15% per year.

If the spray method is selected, the amount of water used can vary from an optimistic value of 40 liters to a pessimistic value of 100 liters with 80 liters being the most likely amount. The immersion technique always takes 40 liters per ham. How will this varying use of water for the spray method affect the economic decision?

18.17 When the country’s economy is expanding. AB Investment Company is optimistic and expects a MARR of 15% for new investments. However, in a receding economy the expected return is 8%. Normally a 10% return is required. An expanding economy causes the estimates of asset life to go down about 20%, and a receding economy makes the n values increase about 10%. Plot the sensitivity of present worth versus (a) the MARR and (b) the life values for the two plans detailed below, using the most likely estimates for the other factors. (c) Considering all the analyses, under which scenario, if any, should plan M or Q be rejected’?

	Plan M	Plan Q
Initial investment, $	-100,000	-110,000
Cash flow, $/year	+15,000	+19,000
Life, Years	20	20

 

Expected Value

18.18 Calculate the expected flow rate for each oil well using the estimated probabilities.

Expected Flow, Barrels/Day
	100	200	300	400
North Well	0.15	0.75	0.10	-
East Well	0.35	0.15	0.45	0.05

 

18.19 There are four estimates made for the anticipated cycle time to produce a subcomponent. The estimates, in seconds, are 10, 20, 30, and /Q. (a) If equal weight is placed on each estimate what is the expected time to plan for? (b) If the largest time is disregarded, estimate the expected time. Does the large estimate seem to significantly increase the expected value?

18.20 The variable Y is defined as 3" for n = 1, 2, 3, 4 with probabilities of 0.4, 0.3. 0.233, and 0.067, respectively. Determine the expected value of Y.

18.21 The AOC value for an alternative is expected to be one of two values. Your office partner told you that the low value is $2800 per year. If her computations show a probability of 0.75 for the high value and an expected AOC of $4575, what is the high AOC value she used in the computation of the average?

18.22 A total of 40 different proposals were evaluated by the IRAD (Industrial Research and Development) committee during the past year. Twenty were funded. Their rate of return estimates are summarized below with the i* values rounded to the nearest integer. For the accepted proposals, calculate the expected rate of return E(i).

Proposal rate of return, %	Number of Proposals
-8	1
-5	1
0	5
5	5
8	2
10	3
15	3 Total =20

 

18.23 Starbreak Foods has performed an economic analysis of proposed service in a new region of the country. The three estimate approach to sensitivity analysis has been applied. The optimistic and pessimistic values each have an estimated 15% chance of occurring. Use the AW values shown to compute the expected AW.

	Optimistic	Most Likely	Pessimistic
AW value, $/year	+30,000	+50,000	-25,000

 

18.24 (a) Determine the expected present worth of the following cash flow series if each series may be realized with the probability shown at the head of each column. Let i = 20% per year.

(b) Determine the expected AW value for the same cash flow series.

Annual Cash Flow, $/year
Year	Prob. = 0.5	Prob. = 0.2	Prob. = 0.3
0	-5000	-6000	-4000
1	1000	500	3000
2	1000	1500	1200
3	1000	2000	-800

 

18.25 A very successful health and recreation club wants to construct a mock mountain for climbing and exercise outside for its customers’ use. Because of its location, there is a 30% chance of a 120-day season of good outdoor weather, a 50% chance of a 150-day season, and a 20% chance of a 165-day season. The mountain will be used by an estimated 350 persons each day of the 4-month (120-day) season, but by only 100 per day for each extra day the season lasts. The feature will cost $375,000 to construct and require a $25,000 rework each 4 years, and the annual maintenance and insurance costs will be $56,000. The climbing fee will be $5 per person. If a life of [0 years is anticipated and a 12% per year return is expected, determine if the addition is economically justified.

18.26 The owner of Ace Roofing may invest $200,000 in new equipment. A life of 6 years and a salvage value of 12% of first cost are anticipated. The annual extra revenue will depend upon the state of the housing and construction industry. The extra revenue is expected to be only $20,000 per year if the current slump in the industry continues. Real estate economists estimate a 50% chance of the slump lasting 3 years and give it a 20% chance of continuing for 3 additional years. However, if the depressed market does improve, during either the first or second 3-year period, the revenue of the investment is expected to increase by a total of $35,000 per year. Can the company expect to make a return of 8% per year on its investment? Use present worth analysis.

18.27 Jeremy has $5000 to invest. If he puts the money in a certificate of deposit (CD), he is assured of receiving an effective 6.35% per year for 5 years. If he invests the money in stocks, he has a 50-50 chance of one of the following cash flow sequences for the next 5 years.

Annual Cash Flow, $/year
Year	Prob. = 0.5	Prob. = 0.5
	Stock 1	Stock 2
0	-5000	-5000
1-4	+250	+600
5	+6800	+4000

 

Finally, Jeremy can invest his $5000 in real estate for the 5 years with the following cash flow and probability estimates.

 

 

	Annual Cash Flow, $/year
Year	Prob. -0.3	Prob. -0.5	Prob. -0.2
0	-5000	-5000	-5000
1	-425	0	+500
2	-425	0	+600
3	-425	0	+700
4	-425	0	+800
5	+9500	+7200	+5200

 

Which of the three investment opportunities offers the best expected rate of return’?

18.28 The California Company has $1 million in an investment pool which the board of directors plans to place in projects with different D-E mixes varying from 20-80 to 80-20. To assist with the decision, the plot shown below, prepared by the chief financial officer, of currently estimated annual equity rates of return (i on equity capital) versus various D-E mixes will be used. All investments will be for 10 years with no intermediate cash flows in or out Of the projects. The motion passed by the board Is to invest as follows:

D-E mix	20-80	50-50	80-20
Percent of Pool	30%	50%	20%

  

(a) What is the current estimate of the expected annual rate of return on the company’s equity capital for the $1 million investments after 10 years?

(b) What is the actual amount of equity capital invested now, and what is the expected total amount after 10 years for the board-approved investment plan?

(c) If inflation is expected to average 4.5% per year over the next 10-year period, determine both the real interest rates at which the equity investment funds will grow and the purchasing power in terms of today’s (constant-value) dollars of the actual amount accumulated after 10 years.

18.29 A flagship hotel in Cedar Falls must construct a retaining wall next to its parking lot due to the widening of the city’s main thoroughfare located in front of the hotel. The amount of rainfall experienced in a short period of time may cause damage in varying amounts, and the wall in-creases in cost in order to protect against larger and faster rainfalls. The probabilities of a specific amount of rainfall in a 30-minute period and wall cost estimates are as follows:

Probability Estimated

Rainfall, of Greater —_ First Cost of

Inches/30 Minutes Rainfall Wall, $

2.0 0.3 — 200,000

2.25 0.) — 225,000

2.5 0.05 ~ 300,000

3.0) 0.01 - 400,000

3.25 0.005 — 450.000

The wall will be financed through a 6% per year loan for the full amount that will be repaid over a 10-year period. Records indicate an average damage of $50,000 has occurred with heavy rains, due to the relatively poor cohesive properties of the soil along the thorough-fare. A discount rate of 6% per year is applicable. Find the amount of rainfall to protect against by choosing the retaining wall with the smallest AW value over the 10-year period.

Decision Trees

18.30 For the decision tree branch shown. Determine the expected values of the two outcomes if decision D3 is already selected and the maximum outcome value is sought. (This decision branch is part of a larger tree.)

18.31 A large decision tree has an outcome branch that is detailed for this problem. If decisions D1, D2, and D3 are all options in a 1-year time period, find the decision path which maximizes the outcome value. There are specific dollar investments necessary for decision nodes D1, D2, and D3 as indicated on each branch.

18.32 Decision D4, which has three possible alternatives—x, y, or z—must be made in year 3 of a 6-year study period in order to maximize the expected value of present worth. Using a rate of return of 15% per year, the investment required in year 3, and the estimated cash flows for years 4 through 6, determine which decision should be made in year 3. (This decision node is part of a larger tree.)

18.33 A total of 5000 mechanical subassemblies are needed annually on a final assembly line. The subassemblies can be obtained in one of three ways: (1) Make them in one of three plants owned by the company; (2) buy them off the shelf from the one and only manufacturer: or (3) contract to have them made to specifications by a vendor. The estimated annual cost for each alternative is dependent upon specific circumstances of the plant, producer. Or contractor. The information shown details the circumstance, a probability of occurrence, and the estimated annual cost. Construct and solve a decision tree to determine the least-cost alternative to provide the subassemblies.

Decision Alternative	Outcomes	Probability	Annual Cost for 5000 Units, $/year
1. Make	Plant: A B C	0.3 0.5 0.2	-250,000 -400,000 -350,000
2. Buy Off the Shelf	Quantity: <5000, pay premium 5000 available>5000, forced to buy	0.2 0.7 0.1	-550,000 -250,000 -290,000
3. Contract	Delivery: Timely delivery Late delivery; then buy some off shelf	0.5 0.5	-175,000 -450,000

 

18.34 The president of ChemTech is trying to decide whether to start a new product line or purchase a small company. It is not financially possible to do both. To make the product for a 3-year period will require an initial investment of $250,000. The expected annual cash flows with probabilities in parentheses are: $75,000 (0.5), $90,000 (0.4), and $150,000 (0.1).

To purchase a small company will cost $450,000 now. Market surveys indicate a 55% chance of increased sales for the company and a 45% chance of severe decreases with an annual cash flow of $25,000. If decreases are experienced in the first year, the company will be sold immediately (during year 1) at a price of $200,000. Increased sales could be $100,000 the first 2 years. If this occurs, a decision to expand after 2 years at an additional investment of $100,000 will be considered. This expansion could generate cash flows with indicated probabilities as follows: $120,000 (0.3), $140.000 (0.3), and $175,000 (0.4). If expansion is not chosen, the current size will be maintained with anticipated sales to continue. Assume there are no salvage values on any investments. Use the description given and a 15% per year return to do the following:

(a) Construct a decision tree with all values and probabilities shown.

(b) Determine the expected PW values at the ““expansion/no expansion” decision node after 2 years provided sales are up.

(c) Determine what decision should be made now to offer the greatest return possible for ChemTech.

(d) Explain in words what would happen to the expected values at each decision node if the planning horizon were extended beyond 3 years and all cash flow values continued as forecasted in the description.

EXTENDED EXERCISE

LOOKING AT ALTERNATIVES FROM DIFFERENT ANGLES

Berkshire Controllers usually finances its engineering projects with a combination of debt and equity capital. The resulting MARR ranges from a low of 8% per year, if the business is slow, to a high of 15% per year. Normally, 10% per year return is expected. Also, the life estimates for assets tend to go down about 20% from normal in a vigorous business environment, and up about 10% in a receding economy. The following estimates are the most likely values for two plans currently being evaluated. Use these data and a spreadsheet to answer the questions below.

		Plan B
	Plan A	Asset 1	Asset 2
First cost, $	-10,000	-30,000	-5000
AOC, $ /year	-500	-100	-200
Salvage value, $	1000	5000	-200
Estimated life, years	40	40	20

 

 

Questions

1. Are the PW values for plans A and B sensitive to changes in the MARR?

2. Are the PW values sensitive to varying life estimates?

3. Plot the results above on separate charts for MARR and life estimates.

4. Is the breakeven point for the first cost of plan A sensitive to the changes in MARR as business goes from vigorous to receding?