The Scampini Clinic recently purchased a new ultrasound machine. The machine cos
ID: 2782223 • Letter: T
Question
The Scampini Clinic recently purchased a new ultrasound machine. The machine cost $80,000, and it is expected to generate net after-tax operating cash flows (including depreciation) of $23,000 per year, starting in Year 1. The machine has a five-year expected life, and the clinic’s cost of capital is 12 percent. The expected salvage values of the machine at the end of each year are given below: Please show answers in excel.
Year
Salvage Value
0
$80,000
1
$62,000
2
$50,000
3
$40,000
4
$18,000
5
$2,000
The clinic must decide whether to operate the machine until the end of its five-year physical life or earlier. The operating cash flows of the ultrasound machine are as follows:
Year
Operating Cash Flow
0
($80,000)
1
$23,000
2
$23,000
3
$23,000
4
$23,000
5
$23,000
For how many years should the clinic operate the ultrasound machine? Please explain and show your work.
Year
Salvage Value
0
$80,000
1
$62,000
2
$50,000
3
$40,000
4
$18,000
5
$2,000
Explanation / Answer
Operate machine for 1 year
PV of Operating Income = 23000/1.12 = 20535.71
PV of Salvage Value = 62000/1.12 = 55357.14
NPV = PV of Operating Income + PV of Salvage Value - Initial Cost = 20535.71 + 55357.14 - 80000 = -4107.15
Operate machine for 2 years
PV of Operating Income = 23000 * ((1-1/(1+12%)2)/12%) = 38871.17
PV of Salvage Value = 50000/1.122 = 39859.69
NPV = PV of Operating Income + PV of Salvage Value - Initial Cost = 38871.17 + 39859.69 - 80000 = -1269.14
Operate machine for 3 years
PV of Operating Income = 23000 * ((1-1/(1+12%)3)/12%) = 55242.12
PV of Salvage Value = 40000/1.123 = 28471.21
NPV = PV of Operating Income + PV of Salvage Value - Initial Cost = 55242.12 + 28471.21 - 80000 = 3713.33
Operate machine for 4 years
PV of Operating Income = 23000 * ((1-1/(1+12%)4)/12%) = 69859.03
PV of Salvage Value = 18000/1.124 = 11439.33
NPV = PV of Operating Income + PV of Salvage Value - Initial Cost = 69859.03 + 11439.33 - 80000 = 1298.36
Operate machine for 5 years
PV of Operating Income = 23000 * ((1-1/(1+12%)5)/12%) = 82909.85
PV of Salvage Value = 2000/1.125 = 1134.85
NPV = PV of Operating Income + PV of Salvage Value - Initial Cost = 82909.85 + 1134.85 - 80000 = 4044.70
Based on the calculations above, NPV is highest for operating the machine for 5 years. So, the clinic should operate the ultrasound machine for 5 years.
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