Engineering Economic Analysis
Engineering Economic Analysis
13th Edition
ISBN: 9780190296902
Author: Donald G. Newnan, Ted G. Eschenbach, Jerome P. Lavelle
Publisher: Oxford University Press
Question
Book Icon
Chapter 14, Problem 83P
To determine

(a)

The actual dollar after tax rate of return.

Expert Solution
Check Mark

Answer to Problem 83P

The actual dollar after tax rate of return is 16.17%.

Explanation of Solution

Given:

Net annual income to the owner is 10.5% of the market value.

Purchase amount of the property is $150000.

Cost of the land is $46500.

The selling price 59 months later is equal to the original purchase price.

The income tax rate is 35%.

Calculation:

Calculate the before tax cash flow for year 1.

BTCF1=f×150000 ...... (I)

Here, the inflation rate is f.

Substitute 8% for f in Equation (I).

BTCF1=0.08×$150000=$12000

Calculate the before tax cash flow for year 2.

BTCF2=f×150000+(f×BTCF1)+(f1×BTCF1) ...... (II)

Here, the inflation rate is f and the market interest rate is f1.

Substitute 10% for f, 2% for f1 and $12000 for BTCF in Equation (II).

BTCF2=$12000+(0.10×$12000)+(0.02×$12000)=$12000+$1200+$240=$13440

Calculate the before tax cash flow for year 3.

BTCF3=BTCF2+(BTCF2×012) ...... (III)

Substitute $13440 for BTCF2 in Equation (III).

BTCF3=$13440+($13440×0.12)=$15053

Calculate the before tax cash flow for year 4.

BTCF4=BTCF3+(BTCF3×0.12) ...... (IV)

Substitute $15053 for BTCF3 in Equation (IV).

BTCF4=$15053+($15053×0.12)=$16859

Calculate the before tax cash flow for year 5.

BTCF5=BTCF4+(BTCF4×0.12) ...... (V)

Substitute $16859 for BTCF4 in Equation (V).

BTCF5=$16859+($16859×0.12)=$18882

Calculate the cost of home.

HomeCost=PCLC ..... (VI)

Here, the property cost is PC and land cost is LC.

Substitute $150000 for PC and $46500 for LC in Equation (VI).

HomeCost=PCLC=$150000$46500=$103500

Write the expression to calculate the market value plus 12% per year.

MV+12%=((MVn1)+(0.12×MVn1)) ...... (VII)

Here, the market value of the precious year is MVn1 and the market value of the present year with 12% increase is MV+12%.

Calculate the market value plus 12% per year for year 1.

Substitute $150000 for MVn1 in Equation (VII).

MV+12%=(($150000)+(0.12×$150000))=$168000

Calculate the market value plus 12% per year for year 2.

Substitute $168000 for MVn1 in Equation (VII).

MV+12%=(($168000)+(0.12×$168000))=$188160

Calculate the market value plus 12% per year for year 3.

Substitute $188160 for MVn1 in Equation (VII).

MV+12%=(($188160)+(0.12×$188160))=$210775.2

Calculate the market value plus 12% per year for year 3.

Substitute $188160 for MVn1 in Equation (VII).

MV+12%=(($188160)+(0.12×$188160))=$210739

Calculate the market value plus 12% per year for year 4.

Substitute $210739 for MVn1 in Equation (VII).

MV+12%=(($210739)+(0.12×$210739))=$236028

Calculate the market value plus 12% per year for year 5.

Substitute $236028 for MVn1 in Equation (VII).

MV+12%=(($236028)+(0.12×$236028))=$264351

Make the table to calculate the MARCS 5 year depreciation using values for residential property.

Year Initial Cost (a) MARCS rate (b) Depreciation (c)(a×b)
0
1 $103500 3.485% $3607
2 $103500 3.636% $3763
3 $103500 3.636% $3763
4 $103500 3.636% $3763
5 $103500 3.485% $3607

Make the table to calculate the after tax cash flow.

Year BTCF (a) Market Value of property +12% Depreciation (b) TaxableIncome (c) Income taxes (d)(c×0.35) ATCF (e)(a+d)
0 $150000 $150000 $150000
1 $12000 $168000 $3607 $8393 $2938 $9062
2 $13440 $188160 $3763 $9677 $3387 $10053
3 $15053 $210739 $3763 $11290 $3951 $11101
4 $16859 $236028 $3763 $13096 $4584 $12275
5 $18882 $264351 $3607 $245469

The ATCF5 is $254469 as mentioned and it will be equal to the original price of the property.

Thus the selling price of the property is $261991.

Write the expression to calculate the capital gain.

Capitalgain=(SellingPrice)(Costoftheproperty) ..... (VIII)

Substitute $261991 for SellingPrice and $150000 for Costoftheproperty in Equation (VIII).

Capitalgain=$261991$150000=$111991

Calculate the tax on capital gain.

Taxoncapitalgain=0.02×$111991=$22398

Write the expression to calculate the recaptured depreciation.

RD=MACRdepreciation

Substitute $18503 for MACRdepreciation in Equation (IV).

RD=$18503

Calculate the tax on recaptured depreciation.

TaxonRD=0.35×$18503=$6476

Calculate the total tax on disposal.

Totaltaxondisposal=(Taxoncapitalgain)+(TaxonRD) ....... (IX)

Substitute $22398 for Taxoncapitalgain and $6476 for TaxonRD in Equation (IX).

Totaltaxondisposal=$22398+$6476=$28874

Calculate the rate of return.

P=A(1+i)n1(1+i)i ....... (X)

Here, the property cost is P and the land cost is A.

Substitute $150000 for P, $46500 for A and 4.92 for n in Equation (X).

$150000=$46500(1+i)4.921(1+i)4.92i

Solve the equation for the value of i.

i=0.1617×100%i=16.17%

Here, the value of n has been taken 4.92years because the rate of return has to be calculated for 59months which is equal to 4.92years.

Conclusion:

The actual dollar after tax rate of return is 16.17%.

To determine

(b)

The after tax return for the owner.

Expert Solution
Check Mark

Answer to Problem 83P

The after tax return for the owner is 21.9%.

Explanation of Solution

Year ATCF (a) ATCF Year 0 (b)(a×1.07n)
0 $150000 $150000
1 $9062 $8469
2 $10053 $8781
3 $11101 $9061
4 $12275 $9365
5 $245469 $344283

Calculate the after tax rate of return in year 0.

Write the expression to calculate the after tax rate of return.

P=A1(1+i)1+A2(1+i)2+A3(1+i)3+A4(1+i)4+A5(1+i)5 ...... (XI)

Here, the present worth is P, the after tax cash flow is A, the rate of return is i.

Substitute $150000 for P, $8469 for A1

$8781 for A2, $9061 for A3, $9365 for A4 and $344283 for A5 in Equation (XI).

$150000=$8469(1+i)1+$8781(1+i)2+$9061(1+i)3+$9365(1+i)4+$344283(1+i)5

Salve for the value of i

i=0.219=0.219×100%=21.9%.

Conclusion:

The after tax return of the owner is 21.9%.

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Chapter 14 Solutions

Engineering Economic Analysis

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