Tim Smunt has been asked to evaluate two machines. After some investigation, he
ID: 468466 • Letter: T
Question
Tim Smunt has been asked to evaluate two machines. After some investigation, he determines that they have the costs shown in the following table:
Machine A Machine B
Original Cost $10,000 $28,000
Labor per year $2,000 $4,800
Maintenance per year $4,300 $1,000
Salvage value $2,000 $7,000
He is told to assume that:
1. The life of each machine is 3 years.
2. The company thinks it knows how to make 14% on investments no more risky than this one.
3. Labor and maintenance are paid at the end of the year.
The NPV for Machine A= _____ (round your response to the nearest whole number and include a minus sign if necessary).
The NPV for Machine B= _____ (round your response to the nearest whole number and include a minus sign if necessary).
Explanation / Answer
Machine A
Machine B
Original Cost
$10,000
$28,000
Labor per year
$2,000
$4,800
Maintenance per year
$4,300
$1,000
Salvage value
$2,000
$7,000
Total Annual operating cost for Machine = Labor + maintenance
Total Annual operating cost for Machine A = $2,000 + $4,300 = $6,300
Total Annual operating cost for Machine B = $4,800 + $1,000 = $5,800
Interest rate = i = 14%
Present value factors (X) for year 1, 2, and 3 are 0.877, 0.769, and 0.675.
Present value of expense/receipt (S) = PV factor x Receipts (R)
S = XR
Year
Cost Type
Present value factor (14%)
Receipts
Present value
X
R
S
0
Expense
1.000
$10,000
$10,000
1
Expense
0.877
$6,300
$5,525
2
Expense
0.769
$6,300
$4,845
3
Expense
0.675
$6,300
$4,253
Total present value of Expenses
$24,622
3
Salvage Revenue
0.675
-$2,000
-$1,350
Net Present Value
$23,272
NPV of Machine A = Total PV of expenses – Total PV of Receipts
NPV of Machine A = $24,622 - $1,350 = $23,272
Year
Cost Type
Present value factor (14%)
Receipts
Present value
X
R
S
0
Expense
1.000
$28,000
$28,000
1
Expense
0.877
$5,800
$5,087
2
Expense
0.769
$5,800
$4,460
3
Expense
0.675
$5,800
$3,915
Total present value of Expenses
$41,462
3
Salvage Revenue
0.675
-$7,000
-$4,725
Net Present Value
$36,737
NPV of Machine B = Total PV of expenses – Total PV of Receipts
NPV of Machine B = $14,462 - $4,725 = $36,737
NPV of Machine B > NPV of Machine A, thus accept investment in Machine B.
Answer:
NPV of Machine A = $23,272
NPV of Machine B = $36,737
Machine A
Machine B
Original Cost
$10,000
$28,000
Labor per year
$2,000
$4,800
Maintenance per year
$4,300
$1,000
Salvage value
$2,000
$7,000