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
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Chapter 14, Problem 76P
To determine

(a)

The before tax rate of return, ignoring inflation.

Expert Solution
Check Mark

Answer to Problem 76P

The before tax rate of return, ignoring inflation is 3.5%.

Explanation of Solution

Given:

Initial Amount is $10000.

Interest per year is $3.5%.

The MARR is 28%.

Inflation rate is 2%.

Maturity amount received is $10000.

Calculation:

Calculate the return from interest every year.

A=$10000×0.035=$350

Make the table for cash flows.

Year Before tax Cash flow (a) Taxable income (b) Income tax charge (c)(0.28×b) After tax Cash flow c (d)(ac) InflationFactor (e)(1.02)n Present Value at year 0 (f)(d×e)
0 $10000 $10000 1 $10000
1 $350 $350 $98 $252 0.980 $245
2 $350 $350 $98 $252 0.9612 $242.22
3 $350 $350 $98 $252 0.9423 $237.46
4 $350 $350 $98 $252 0.9238 $232.8
5 $350+$10000 $350 $98 $10252 0.9057 $228.24

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

P=A(1+i)n1i(1+i)n+F(1+i)n ...... (I)

Here, the present value is P, the return from interest every year is A, the interest rate is i, the maturity amount is F and the time period is n.

Substitute $10000 for P, $350 for A, $10000 for F and 5 for n in Equation (I).

$10000=$350((1+i)51i(1+i)5)+$10000(1+i)5

Solve the equation for the value of i.

i=0.035i=0.035×100%i=3.5%.

Conclusion:

Thus, the before tax rate of return, ignoring inflation is 3.5%.

To determine

(b)

The after tax rate of return, ignoring inflation.

Expert Solution
Check Mark

Answer to Problem 76P

The after tax rate of return, ignoring inflation is 2.52%.

Explanation of Solution

Calculation:

Calculate the after tax rate of return.

Substitute $10000 for P, $252 for A and 5 for n in Equation (I).

$10000=$252((1+i)51i(1+i)5)+$10000(1+i)5

Solve the equation for the value of i.

i=0.0252i=0.0252×100%i=2.52%.

Conclusion:

The after tax rate of return, ignoring inflation is 2.52%.

To determine

(c)

The after tax rate of return, after taking inflation into account.

Expert Solution
Check Mark

Answer to Problem 76P

The after tax rate of return, after taking inflation into account is 0.51%.

Explanation of Solution

Calculation:

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

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

Substitute $10000 for P, $245 for A1, $242.22 for A2, $237.46 for A3, $232.8 for A4, $228.24 for A5 and $9057.308 for F in Equation (II).

$10000=$245(1+i)1+$242.22(1+i)2+$237.46(1+i)3+$232.8(1+i)4+$228.24(1+i)5+$9057.308(1+i)5

Solve the equation for the value of i.

i=0.00505i0.0051×100%i=0.51%.

Conclusion:

Thus, the after tax rate of return, after taking inflation into account is 0.51%.

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Chapter 14 Solutions

Engineering Economic Analysis

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