Engineering Economy
Engineering Economy
8th Edition
ISBN: 9780073523439
Author: Leland T Blank Professor Emeritus, Anthony Tarquin
Publisher: McGraw-Hill Education
Question
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Chapter 17, Problem 51P

(a):

To determine

Calculate the present worth.

(a):

Expert Solution
Check Mark

Explanation of Solution

The recovery rate for year 1 (RR1) is 0.3333, year 2 (RR2) is 0.4445, year 3 (RR3) is 0.1481, and year 4 (rr4) is 0.0741. Time period is indicated by ‘n’ and MARR is indicated by ‘i’.

Depreciation (D) can be calculated using the following formula:

D=First cost×RR        (1)

Substitute the respective value in Equation (1) to calculate the depreciation in year 1.

D=8,000×0.3333=2,666

The first year’s depreciation is $2,666.

The taxable income (TI) can be calculated using the following formula:

TI=(GIOE)D        (2)

Substitute the respective value in Equation (2) to calculate the taxable income in year 1.

TI=3,5002,666=834

The first year’s taxable income is $834.

Tax (T) can be calculated using the following formula:

T=TI×Te        (3)

Substitute the respective value in Equation (3) to calculate the tax in year 1.

T=834×0.4=333

The first year’s tax is $333.

The cash flow after tax (CFATI) can be calculated using the following formula:

CFAT=(GIOE)T        (4)

Substitute the respective value in Equation (4) to calculate the cash flow after tax in year 1.

CFAT=3,500333=3,167

The first year’s cash flow after tax is $3,167.

Table 1 shows the depreciation, taxable income, tax, and CFAT obtained using Equations (1), (2), (3) and (4).

Table 1

YearPGI-OEDTITCFAT
0-8,000    -8,000
1 3,5002,6668343333,167
2 3,500,3,556-56-223,522
3 3,5001,1852,3159262,574
400593-593-237237

The present worth (PW) can be calculated as follows:

PW=CFAT0+CFAT2(1+i)2+CFAT2(1+i)2+CFAT3(1+i)3++CFAT4(1+i)4=8,000+3,167(1+0.08)1+3,522(1+0.08)2+2,574(1+0.08)3+237(1+0.08)4=8,000+3,1671.08+3,5221.1664+2,5741.259712+2371.360489=169

The present worth of alternate X is $169.

Table 2 shows the depreciation, taxable income, tax, and CFAT of alternate Y obtained using Equations (1), (2), (3), and (4).

Table 2

YearPGI-OEDTITCFAT
0-13,000    -13,000
1 5,0004,3336672674,733
2 5,0005,779-779-3115,311
3 5,0001,9253,0751,2303,770
402,0009631,0374151,585

The present worth (PW) can be calculated as follows:

PW=CFAT0+CFAT2(1+i)2+CFAT2(1+i)2+CFAT3(1+i)3++CFAT4(1+i)4=13,000+4,733(1+0.08)1+5,311(1+0.08)2+3,770(1+0.08)3+1,585(1+0.08)4=8,000+4,7331.08+5,3111.1664+3,7701.259712+1,5851.360489=93

The present worth of project Y is $93. Since the present worth of project X is greater than project Y, select project X.

(a):

To determine

Calculate the time period.

(a):

Expert Solution
Check Mark

Explanation of Solution

The present worth of alternate X and Y can be calculated using spreadsheet as follows:

Engineering Economy, Chapter 17, Problem 51P

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Chapter 17 Solutions

Engineering Economy

Ch. 17 - Prob. 11PCh. 17 - Prob. 12PCh. 17 - Prob. 13PCh. 17 - Prob. 14PCh. 17 - Prob. 15PCh. 17 - Prob. 16PCh. 17 - Prob. 17PCh. 17 - Prob. 18PCh. 17 - Prob. 19PCh. 17 - Prob. 20PCh. 17 - Prob. 21PCh. 17 - Prob. 22PCh. 17 - Prob. 23PCh. 17 - Prob. 24PCh. 17 - Prob. 25PCh. 17 - Prob. 26PCh. 17 - Prob. 27PCh. 17 - Prob. 28PCh. 17 - Prob. 29PCh. 17 - Prob. 30PCh. 17 - Prob. 31PCh. 17 - Prob. 32PCh. 17 - Prob. 33PCh. 17 - Prob. 34PCh. 17 - Prob. 35PCh. 17 - Prob. 36PCh. 17 - Prob. 37PCh. 17 - Prob. 38PCh. 17 - Prob. 39PCh. 17 - Prob. 40PCh. 17 - Prob. 41PCh. 17 - Prob. 42PCh. 17 - Prob. 43PCh. 17 - Prob. 44PCh. 17 - Prob. 45PCh. 17 - Prob. 46PCh. 17 - Prob. 47PCh. 17 - Prob. 48PCh. 17 - Prob. 49PCh. 17 - Prob. 50PCh. 17 - Prob. 51PCh. 17 - Prob. 52PCh. 17 - Prob. 53PCh. 17 - Prob. 54PCh. 17 - Prob. 55PCh. 17 - Prob. 56PCh. 17 - Prob. 57PCh. 17 - Prob. 58PCh. 17 - Prob. 59PCh. 17 - Prob. 60PCh. 17 - Prob. 61PCh. 17 - Prob. 62PCh. 17 - Prob. 63PCh. 17 - Prob. 64PCh. 17 - Prob. 65PCh. 17 - Prob. 66PCh. 17 - Prob. 67PCh. 17 - Prob. 68PCh. 17 - Prob. 69PCh. 17 - Prob. 70PCh. 17 - Prob. 71PCh. 17 - Prob. 72PCh. 17 - Prob. 73PCh. 17 - Prob. 74PCh. 17 - Prob. 75PCh. 17 - Prob. 76APQCh. 17 - Prob. 77APQCh. 17 - Prob. 78APQCh. 17 - Prob. 79APQCh. 17 - Prob. 80APQCh. 17 - Prob. 81APQCh. 17 - Prob. 82APQCh. 17 - Prob. 83APQCh. 17 - Prob. 84APQCh. 17 - Prob. 85APQCh. 17 - Prob. 86APQCh. 17 - Prob. 87APQCh. 17 - Prob. 88APQCh. 17 - Prob. 1CSCh. 17 - Prob. 2CSCh. 17 - Prob. 3CSCh. 17 - Prob. 4CS
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