Project's cost at time 0 is $46,272.84
What is profitability index?
Profitability index is the present value of future cash flows divided by the project cost at time 0.
The present value of each future cash flow can be determined using the present value formula of a single cash flow as below;
PV=FV/(1+r)^N
FV=future cash inflows in years 1-4
r=discount rate=8.5%
N=the year of cash flows, 1 for year 1 , 2 for year 2, 3 for year 3 and 4 for year 4.
PV of future cash flows=$12,150/(1+8.5%)^1+$12,600/(1+8.5%)^2+$15,700/(1+8.5%)^3+$10,200/(1+8.5%)^4
PV of future cash flow=$41,553.01
Profitability index=PV of future cash flows/Project cost
Profitability index= .898
Project cost=unknown(assume it is X)
.898=$41,553.01 /X
X=$41,553.01/ .898
X=project's cost=$46,272.84
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