ENGINEERING ECONOMIC ENHANCED EBOOK
ENGINEERING ECONOMIC ENHANCED EBOOK
14th Edition
ISBN: 9780190931940
Author: NEWNAN
Publisher: OXF
Question
Book Icon
Chapter 12, Problem 20P
To determine

The after tax rate of return.

Expert Solution & Answer
Check Mark

Answer to Problem 20P

The after tax rate of return is 11.62%.

Explanation of Solution

Concept used:

Write the expression for depreciation.

D=2n×BVt1 ....... (I)

Here, book value is BV and useful life is n.

Write the expression for taxable income.

(Taxable income)t=BTCFtDt ....... (II)

Here before tax cash flow is BTCF.

Write the expression for income tax.

(Tax)t=(Taxable income)t×tax rate ....... (III)

Write the expression for after tax cash flow.

(ATCF)t=BTCFtTaxt ....... (IV)

Write the expression for after tax rate of return.

P=[F1(P/F,i,n)+F2(P/F,i,n)+F3(P/F,i,n)+F4(P/F,i,n)+F5(P/F,i,n)+F6(P/F,i,n)] ....... (V)

Here, the present value of the annuity is P, future value of the series is F, interest rate is i and number of periods is n.

Write the expression for rate of return by linear interpolation.

IRR=i%low+(i%highi%low)[FlowPFlowFhigh] ....... (VI)

Here, lower interest rate is i%low, higher interest rate is i%high, factor of lower interest rate is Flow, factor of higher interest rate is Fhigh, .

Calculation:

Calculate depreciation.

Substitute $100000 for BVt1, 4 for n and 1 for t in Equation (I).

D1=24×$100000=$50000

Substitute $50000 for BVt1, 4 for n and 2 for t in Equation (I).

D2=24×$50000=$25000

Substitute $25000 for BVt1, 4 for n and 3 for t in Equation (I).

D3=24×$25000=$12500

Substitute $12500 for BVt1, 4 for n and 4 for t in Equation (I).

D4=24×$12500=$6250

Calculate taxable income.

Substitute $30000 for BTCF, $50000 for D1 and 1 for t in Equation (II).

(Taxable income)1=$30000$50000=$20000

Substitute $30000 for BTCF, $25000 for D2 and 2 for t in Equation (II).

(Taxable income)2=$30000$25000=$5000

Substitute $35000 for BTCF, $12500 for D3 and 3 for t in Equation (II).

(Taxable income)3=$35000$12500=$22500

Substitute $40000 for BTCF, $62500 for D4 and 4 for t in Equation (II).

(Taxable income)4=$40000$62500=$33750

Substitute $10000 for BTCF, 0 for D5 and 5 for t in Equation (II).

(Taxable income)5=$100000=$10000

Substitute $10000 for BTCF, 0 for D6 and 6 for t in Equation (II).

(Taxable income)6=$100000=$10000

Calculate income tax.

Substitute $20000 for taxable income, 0.46 for tax rate and 1 for t in Equation (III).

(Tax)1=$20000×0.46=$9200

Substitute $5000 for taxable income, 0.46 for tax rate and 2 for t in Equation (III).

(Tax)2=$5000×0.46=$2300

Substitute $22500 for taxable income, 0.46 for tax rate and 3 for t in Equation (III).

(Tax)3=$22500×0.46=$10350

Substitute $33750 for taxable income, 0.46 for tax rate and 4 for t in Equation (III).

(Tax)4=$33750×0.46=$15525

Substitute $10000 for taxable income, 0.46 for tax rate and 5 for t in Equation (III).

(Tax)5=$10000×0.46=$4600

Substitute $10000 for taxable income, 0.46 for tax rate and 6 for t in Equation (III).

(Tax)6=$10000×0.46=$4600

Calculate after tax cash flow.

Substitute $30000 for BTCF, $9200 and 1 for t for tax in Equation (IV).

(ATCF)1=$30000($9200)=$39200

Substitute $30000 for BTCF, $2300 and 2 for t for tax in Equation (IV).

(ATCF)2=$30000$2300=$27700

Substitute $35000 for BTCF, $10350 and 3 for t for tax in Equation (IV).

(ATCF)3=$35000$10350=$24650

Substitute $40000 for BTCF, $15525 and 4 for t for tax in Equation (IV).

(ATCF)4=$40000$15525=$24475

Substitute $10000 for BTCF, $4600 and 5 for t for tax in Equation (IV).

(ATCF)5=$10000$4600=5400

Substitute $10000 for BTCF, $4600 and 6 for t tax in Equation (IV).

(ATCF)6=$10000$4600+$6250=$11650

The table for the calculated values is shown below.

Year BTCF D Taxable income Tax ATCF
0 $100000 $100000
1 $30000 $50000 $20000 $9200 $39200
2 $30000 $25000 $5000 $2300 $27700
3 $35000 $12500 $22500 $10350 $24650
4 $40000 $6250 $33750 $15525 $24475
5 $10000 0 $10000 $4600 $5400
6 $10000 0 $10000 $4600 $11650

Table (1)

Calculate the after tax rate of return.

Substitute $100000 for P, $39200 for F1, $27700 for F2, $24650 for F3, $24475 for F4, $5400 for F5, $11650 for F6 in Equation (V).

$100000=[$39200( P/F,i,1)+$27700( P/F,i,2)+$24650( P/F,i,3)+$24475( P/F,i,4)+$5400( P/F,i,5)+$11650( P/F,i,6)] ....... (VII)

Consider the table and apply trial and error method equalizing the equation (VII).

Determine an interest rate which equalizes left hand side and right hand side of Equation (VII).

Substitute the tabular values into the right hand side of the equation (VII).

The table for values close to the left hand side of the equation (VII) is shown below.

Interest rate Value
10% $103693.30
12% $99149.70

Table (2)

Calculate the rate of return by linear interpolation.

Substitute $100000 for P, 10% for i%low, 12% for i%high, $103693.30 for Flow and $99149.70 for Fhigh in Equation (VI).

IRR=10%+(12%10%)[$103693.30$100000$103693.30$99149.70]=10%+2%[$3693.30$4543.60]=0.1+0.02×0.8218=0.1162.

Conclusion:

The internal rate if return is 11.62%.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Knowledge Booster
Background pattern image
Recommended textbooks for you
Text book image
ENGR.ECONOMIC ANALYSIS
Economics
ISBN:9780190931919
Author:NEWNAN
Publisher:Oxford University Press
Text book image
Principles of Economics (12th Edition)
Economics
ISBN:9780134078779
Author:Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:PEARSON
Text book image
Engineering Economy (17th Edition)
Economics
ISBN:9780134870069
Author:William G. Sullivan, Elin M. Wicks, C. Patrick Koelling
Publisher:PEARSON
Text book image
Principles of Economics (MindTap Course List)
Economics
ISBN:9781305585126
Author:N. Gregory Mankiw
Publisher:Cengage Learning
Text book image
Managerial Economics: A Problem Solving Approach
Economics
ISBN:9781337106665
Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher:Cengage Learning
Text book image
Managerial Economics & Business Strategy (Mcgraw-...
Economics
ISBN:9781259290619
Author:Michael Baye, Jeff Prince
Publisher:McGraw-Hill Education