Value of a single amount versus a mixed stream Gina Vitale has just contracted t
ID: 2451752 • Letter: V
Question
Value of a single amount versus a mixed stream Gina Vitale has just contracted
to sell a small parcel of land that she inherited a few years ago. The buyer is willing to
pay $24,000 at the closing of the transaction or will pay the amounts shown in the
following table at the beginning of each of the next 5 years. Because Gina doesn’t
really need the money today, she plans to let it accumulate in an account that earns
7% annual interest. Given her desire to buy a house at the end of 5 years after closing
on the sale of the lot, she decides to choose the payment alternative—$24,000 single
amount or the mixed stream of payments in the following table—that provides the
higher future value at the end of 5 years. Which alternative will she choose?
Mixed stream
Beginning of year Cash flow
1 $ 2,000
2 4,000
3 6,000
4 8,000
5 10,000
Explanation / Answer
1)
Present value of cash stream
= 2000/1.07 + 4000/1.07^2 + 6000/1.07^3 + 8000/1.07^4 + 10000/1.07^5
= 23493.72
Present value of closing price = 24000/1.07^5 = 17111.67
she will choose Stream of cash flows
2)
let X be the missing amount
2000/1.04 + 4000/1.04^2 + X/1.04^3 + 8000/1.04^4 + 10000/1.04^5 = 32911.03
X= $13759.36
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