Consider the following EOY cash flows for two mutually exclusive alternatives(on
ID: 1250513 • Letter: C
Question
Consider the following EOY cash flows for two mutually exclusive alternatives(one must be chosen):
Machine X
Machine Y
Capital investment
$6,000
$14,000
Annual expenses
$2,500
$2,400
Useful life
12 years
18 years
Market value at end of useful life
0
$2,800
The MARR is 5% per year
a). Determine which alternative should be selected if the repeatability assumption applies.
b). Determine which alternative should be selected if the analysis period is 18 years, the repeatability assumption does not apply, and a machine can be leased for $8,000 per year after the useful life of either machine is over.
Machine X
Machine Y
Capital investment
$6,000
$14,000
Annual expenses
$2,500
$2,400
Useful life
12 years
18 years
Market value at end of useful life
0
$2,800
Explanation / Answer
a) repeatability applies. So, we assume common period of 36 years with 3 nos. of X and 2 nos. of Y with same costs, benefits and salvage value as given. MARR = 5% =0.05 .
Total NPV of X = NPV of first unit at t=0 +NPV of 2nd unit at t=12,/(1+k)^12
+ NPV of 3rd unit at t=24,/(1+k)^24
NPV of 1st unit at t=0 = (- 6000 +2500(1.05^12-1)/(0.05*1.05^12))
=> = 16158.13 ($)
NPV of 2nd unit at t=18, = NPV of 1st unit at t=0, = 16158.13 ($)
NPV of 3rd unit at t=24, = NPV of 1st unit at t=0, = 16158.13 ($)
So, Total NPV of X = 16158.13 +16158.13/1.05^12 + 16158.13/1.05^24
=> = 30165.7 ($)
Total NPV of Y = NPV of first unit at t=0 +NPV of 2nd unit at t=18,/(1+k)^18
NPV of 1st unit at t=0 = - 14000 +2400((1.05^18-1)/(0.05*1.05^18)) +2800/1.05^18
=> = 15217.47 ($)
NPV of 2nd unit at t=18, = NPV of 1st unit at t=0, = 15217.47 ($)
So, Total NPV of Y = 15217.47 +15217.47/1.05^18
=> = 21540.64 ($)
Hence, Machine X is better and recommended. (ANSWER)
b)
NPV of X = (NPV of first unit in (a) above, 16158.13) - (8000/1.05^12 = 11703.43 ($)
NPV of Y = NPV of first unit in (a) above, 15217.47 ($)
So, Machine Y is better and recommended. (ANSWER)
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