An insurance company has made you the following retirement offer. If you pay the

Question

An insurance company has made you the following retirement offer. If you pay them $100,000 now, you will receive payments of $8000 a year for 10 years. After this they will pay you $9000 a year forever. Recall that a “Capitalized Cost” is the amount of money that will provide annual payments indefinitely by paying out the interest.
a) What is the Capitalized Cost of the $9,000 payments in terms of variable (i) at Year 10?
b) Solve for the rate of return (i) for the overall investment to the nearest 0.5%

Explanation / Answer

1. Capitalized cost is calculated by 1/i

Capitalized cost at year 10

interest rate = 8000/100000 = 8%

capitalized cost = -100000+53680.6512+9000*1/0.08 = initial investment + present value of 8000(for 10 years) + present value of 9000 (for ever).

capitalized cost at year 10 = 66180.65

b.

Rate of return = PV of future cashflows/initial investment = 166180.7/100000 = 1.662 = 166%

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