A company has set aside $10,000 as an endowment in order to pay a cash award of $R every month to the "employee of the month" forever.If the first award is paid one month from now and the company can earn j₁₂ = 8.4% for the first 24 months and j₁₂ = 6% thereafter,what is R?

Question

Quizplus · Accepted Answer

Let's first calculate the present value of the perpetual cash flow using a formula for a perpetuity:

PV = R / i, where PV is present value, R is the cash flow, and i is the discount rate.

Since the discount rate changes after 24 months, we need to calculate the present value for two time periods separately:

PV1 = R / 0.07, where 0.07 is the monthly discount rate for the first 24 months (8.4% annual rate).
PV2 = R / 0.005, where 0.005 is the monthly discount rate after 24 months (6% annual rate).

The sum of PV1 and PV2 should be equal to the initial endowment:

PV1 + PV2 = $10,000

Substituting the formulas for PV1 and PV2, we get:

R / 0.07 + R / 0.005 = $10,000

Solving for R, we get:

R = $52.30

Therefore, the answer is C: $52.30.

A Company Has Set Aside $10,000 as an Endowment in Order