The following data have been gathered for a capital investment decision. The amo
ID: 2501488 • Letter: T
Question
The following data have been gathered for a capital investment decision. The amounts relate to it 14 percent discount factor.
End of Period
Present Value of $1
Present Value of an Annuity of $1
1
.877
.877
2
.769
1.646
3
.675
2.321
4
.592
2.913
5
.519
3.432
6
.456
3.888
a. Compute the present value of the following cash flows. Use a discount rate of 14 percent.
Year 1
$40,000
Year 2
60,000
Year 3
50,000
Year 4
50,000
Year 5
40,000
b. What would have been the present value of the cash flows if they were received in equal installments over the five-year period at the same discount rate?
c.If the answers to parts (a) and (b) differ, explain the reason(s) why.
End of Period
Present Value of $1
Present Value of an Annuity of $1
1
.877
.877
2
.769
1.646
3
.675
2.321
4
.592
2.913
5
.519
3.432
6
.456
3.888
Explanation / Answer
Solutions a & b :
Solution c.: The present value is more if the yearly cash flow is discounted at yearly discount rate than the equal installment over the five year period discounted with annual annuity discounted rate. This is because in different yearly cash flow, the initial years has higher cash flow with lower discounted rate.
year cash flow $ discount reate 14% present vale $ Present value at Annuity (14%,5) 1 40000 .877 35080 Annual equal Cashflow $48000 2 60000 .769 46140 =$48000 * 3.432 3 50000 .675 33750 4 50000 .592 29600 5 40000 .519 20760 Present Value = $165330 (of yearly CF) = $164736 (of equal CF)Related Questions
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