Given two alternatives: Data A B First Cost $4,000 $6,000 Annual Cost $1,000 $50
ID: 1091678 • Letter: G
Question
Given two alternatives:
Data
A
B
First Cost
$4,000
$6,000
Annual Cost
$1,000
$500
Annual Benefit
$2,000
$2,200
Life, Years
4
10
Salvage Value
$3,000
$1,000
Assuming hat alternatives are replaced at the end of their useful life, determine the better alternative using annual cash flow analysis at an interest rate of 10%.
Alternative A, $786
Alternative B, $786
Alternative A, $384
Alternative B, $384
Data
A
B
First Cost
$4,000
$6,000
Annual Cost
$1,000
$500
Annual Benefit
$2,000
$2,200
Life, Years
4
10
Salvage Value
$3,000
$1,000
Explanation / Answer
First find Annual Net Present Value of both projects.
Both projects have same format, initial cost + annual cash flow (benefit - cost) + salvage value (at last year of project). Salvage value of Project a at year 4, salvage value for b at year 10.
NPV Project A = -4,000 + (2,000 - 1,000) * [(1+0.10)^4-1] / [0.10 (1+0.10)^4] + 3,000 / (1+0.10)^4
NPV Project A = -4,000 + 3,169.87 + 2,049.04
NPV Project A = $1,218.91
NPV Project B = -6,000 + (2,200 - 500) * [(1+0.10)^10-1] / [0.10 (1+0.10)^10] + 1,000 / (1+0.10)^10
NPV Project B = -6,000 + 10,445.76 + 385.54
NPV Project B = $4,831.30
Now NPV is calculates, using those NPV's as PV, find the yearly annuity for Annual cash flow of each project.
PV = A [(1+r)^n-1] / [r (1+r)^n]
Project A: 1,218.91 = EACF [(1+0.10)^4-1] / [0.10 (1+0.10)^4]
EACF Project A = 384.53
Project B: 4,831.30 = EACF [(1+0.10)^10-1] / [0.10 (1+0.10)^10]
EACF Project B = 786.27
EACF = Equivalent Annual Cash Flow
B. Alternative B, $786.................(answer)
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.