Problem 12-3A Problem 12-3A Brooks Clinic is considering investing in new heart-
ID: 2392509 • Letter: P
Question
Problem 12-3A
Problem 12-3A
Brooks Clinic is considering investing in new heart-monitoring equipment. It has two options. Option A would have an initial lower cost but would require a significant expenditure for rebuilding after 4 years. Option B would require no rebuilding expenditure, but its maintenance costs would be higher. Since the Option B machine is of initial higher quality, it is expected to have a salvage value at the end of its useful life. The following estimates were made of the cash flows. The company’s cost of capital is 5%.Option A Option B Initial cost $183,000 $281,000 Annual cash inflows $70,000 $80,000 Annual cash outflows $28,000 $25,000 Cost to rebuild (end of year 4) $48,000 $0 Salvage value $0 $7,000 Estimated useful life 7 years 7 years
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Explanation / Answer
1. NPV
Option A
NPV = $20538
Option B
NPV = $42225
2. Profitability index
PI = (NPV + Initial Investment) / Initial Investment
Option A:
= (20538 + 183000)/ 183000
= 1.11
Option B:
= (42225 + 281000)/ 281000
= 1.15
3. IRR
Option A:
NPV @ 7% (in the same way as calculated in point 1)
= -183000 + (42000 x 5.38929) + (-48000 x 0.76290)
= $6731
NPV @ 9%
= -183000 + (42000 x 5.03295) + (-48000 x 0.70843)
= -$5621
IRR = Lower rate + [NPV at lower rate/ (NPV at lower rate - NPV at higher rate)] x Difference in rates
= 7% + [6731/ (6731 + 5621)] x 2
= 8.09%
Option B:
NPV @ 7% (in the same way as calculated in point 1)
= -281000 + (55000 x 5.38929) + (7000 x 0.62275)
= $19770
NPV @ 9%
= -281000 + (55000 x 5.03295) + (7000 x 0.54703)
= -$359
IRR = Lower rate + [NPV at lower rate/ (NPV at lower rate - NPV at higher rate)] x Difference in rates
= 7% + [19770/ (19770 + 359)] x 2
= 8.96%
Option B should be accepted.
Year 0 Year 1 to 7 Year 4 Year 7 Initial cost -183000 Annual cash inflows 70000 Annual cash outflows -28000 Cost to rebuild -48000 Salvage value 0 Total cash flows -183000 42000 -48000 0 PVF @ 5% 1.00000 5.78637 0.82270 0.71068 Present value -183000 243027.54 -39489.6 0