Problem 12-3A (Part Level Submission) (a) Problem 12-3A (Part Level Submission)
ID: 2532215 • Letter: P
Question
Problem 12-3A (Part Level Submission)
(a)
Problem 12-3A (Part Level Submission)
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 $189,000 $285,000 Annual cash inflows $71,600 $82,500 Annual cash outflows $28,200 $26,700 Cost to rebuild (end of year 4) $50,100 $0 Salvage value $0 $8,100 Estimated useful life 7 years 7 years
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Explanation / Answer
Solution:-
1. Net present value method:-
Option A
Option B
PV of annual cash inflow(PVAF @ 5% for 7 years *Cash inflow) (PVAF=5.78637)
[5.78637*71600]= 414304
[5.78637*82500] =477375.53
(-) PV of cash annual cash outflow
[5.78637*28200] =163175.63
[5.78637*26700] =154496
(-) PV of cost to rebuild at end of 4 year (PVIF at end of 4th yr = 0.82270)
[50100*0.82270]
=41217.27
---------------------
(+) PV of salvage value (PVIF at end of 7th year = 0.71068)
--------
(8100*0.71068) =5756.51
Net cash inflow (PV)
209911.1
328636.04
(-) Initial cost
189000
285000
Net cash inflow/outflow
20911.1
43636.04
2. Profitability Index:-
Profitability Index = PV of Future Net Cash Flows / Initial Investment Required
Option A
Option B
(A) Initial cost
189000
285000
(B) Net cash inflow (PV)
209911.1
328636.04
PI = B/A
1.11
1.15
3. Internal rate of Return:-
Option A:-
PV of Cash Inflow = Pv of Cash outflow
(71600*PVAF of 7 yrs) – (28200*PVAF of 7 yrs ) – (50100*PVIF of end of 4th yr) = 189000
Let we try @ 8%
(71600*5.20637) – (28200*5.20637) – (50100*0.73503) = 189000
189131 = 189000
Option B:-
PV of Cash Inflow = Pv of Cash outflow
(82500*PVAF of 7 yrs) – (26700*PVAF of 7 yrs ) + (8100*PVIF of end of 7th yr) = 285000
Let we try @ 9%
(82500*5.03295) – (26700*5.03295) + (8100*0.54703) = 285000
285269 = 285000
Net Present Value
Profitability Index
IRR
Option A
20911.1
1.11
8%
Option B
43636.04
1.15
9%
Option A
Option B
PV of annual cash inflow(PVAF @ 5% for 7 years *Cash inflow) (PVAF=5.78637)
[5.78637*71600]= 414304
[5.78637*82500] =477375.53
(-) PV of cash annual cash outflow
[5.78637*28200] =163175.63
[5.78637*26700] =154496
(-) PV of cost to rebuild at end of 4 year (PVIF at end of 4th yr = 0.82270)
[50100*0.82270]
=41217.27
---------------------
(+) PV of salvage value (PVIF at end of 7th year = 0.71068)
--------
(8100*0.71068) =5756.51
Net cash inflow (PV)
209911.1
328636.04
(-) Initial cost
189000
285000
Net cash inflow/outflow
20911.1
43636.04