You are negotiating to make a 7-year loan of $25,000 to Breck Inc.To repay you,Breck will pay $2,500 at the end of Year 1,$5,000 at the end of Year 2,and $7,500 at the end of Year 3,plus a fixed but currently unspecified cash flow,X,at the end of Years 4 through 7.Breck is essentially riskless,so you are confident the payments will be made,and you regard 8% as an appropriate rate of return on low-risk 7-year loans.What cash flow must the investment provide at the end of each of the final four years; that is,what is X?
A)$4,271.67
B)$4,496.49
C)$4,733.15
D)$4,969.81

Question

Quizplus · Accepted Answer

First, we need to find the present value of the payments at the end of Year 1, Year 2, and Year 3. We'll use the present value formula:
PV = FV / (1 + r)^n
Where PV is the present value, FV is the future value, r is the interest rate, and n is the number of years.
So, for Year 1:
PV1 = 2,500 / (1 + 0.08)^1 = 2,314.81
For Year 2:
PV2 = 5,000 / (1 + 0.08)^2 = 4,407.86
For Year 3:
PV3 = 7,500 / (1 + 0.08)^3 = 6,391.25
The total present value of these three payments is:
Total PV = PV1 + PV2 + PV3 = 13,113.92
Now we can use the present value formula again to solve for X, the cash flow Breck must provide at the end of each of the final four years:
Total PV = X / (1 + 0.08)^4 + X / (1 + 0.08)^5 + X / (1 + 0.08)^6 + X / (1 + 0.08)^7
13,113.92 = X / 1.3605 + X / 1.5869 + X / 1.855 + X / 2.1544
13,113.92 = 0.7357X + 0.6299X + 0.5383X + 0.4592X
13,113.92 = 2.3631X
X = 5,544.73
So Breck must provide a cash flow of $5,544.73 at the end of each of the final four years.
Therefore, the best choice is C.

You Are Negotiating to Make a 7-Year Loan of $25,000