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Value of a single amount versus a mixed stream: Gina Vitale has just contracted

ID: 2643689 • 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?

Suppose that somehow you know that the present value of the entire stream is $32,911.03 and that the discount rate is 4%. What is the amount of the missing cash flow in year 3?

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