Question

Ignatius is evaluating an investment that will provide the following returns at the end of each of the following years: year 1, $12,500; year 2, $9,000; year 3, $7,000; year 4, $5,000; year 5, $2,000; year 6, $0; and year 7, $15,000. Ignatius believes that he should earn an annual rate of 10 percent compounded annually on this investment. How much should he pay for this investment? If he expects to earn an annual return of 10 percent compounded monthly, how much should he pay?

Answer 1

1)

The net present value is equal to CF_n / (1+r)^t

= 12500/(1+0.10)^1 + 9000/(1+0.10)^2 + 7000/(1+0.10)^3 + 5000/(1+0.10)^4 + 2000/(1+0.10)^5 + 0 + 15000/(1+0.10)^7

= $36,415.14

2)

In second part, 0.10/12 as the interest is compounded monthly,

= 12500/(1+0.10/12)^1 + 9000/(1+0.10/12)^2 + 7000/(1+0.10/12)^3 + 5000/(1+0.10/12)^4 + 2000/(1+0.10/12)^5 + 0 + 15000/(1+0.10/12)^7

= $48,985.34