Question

Mark is due to retire in a month’s time and one of his pension funds has offered him two alternatives. his money can be received either in the form of $16,000 at the end of each of the next 25 years (i.e., a total of $400,000 over 25 years) or as a single lump sum amount of $200,000 paid immediately.

a. if mark can earn 4% annually on his investments over the next 25 years, which alternative he should take? ignore taxes and any other considerations.
b. would mark’s decision in part a change if he could earn 8% rather than 5% on his investments over the next 25 years? why?
c. at approximately what interest rate would mark be indifferent between the two options?

Answer 1

With a 4% annual interest rate, Mark should choose the annuity payments since their present value is higher than the lump sum offer. If the rate was 8%, the annuity is still preferable, but if Mark can earn over 8%, further calculations would be needed to decide.

Step-by-step explanation:

To determine which pension option Mark should select, we must calculate the present value (PV) of the annuity he was offered (the payments of $16,000 for 25 years) and compare it to the lump sum amount of $200,000. Using the formula for the present value of an annuity:

PV = P * [(1 - (1 + r)^(-n)) / r]

Where P is the payment amount, r is the annual interest rate, and n is the number of payments.

For an interest rate of 4%, we calculate:

PV = $16,000 * [(1 - (1 + 0.04)^(-25)) / 0.04] = $267,298.79

Since the present value of the annuity ($267,298.79) at 4% is greater than the lump sum offer ($200,000), Mark should choose the annuity payments.

At 8% interest, the calculation would be:

PV = $16,000 * [(1 - (1 + 0.08)^(-25)) / 0.08] = $202,922.69

At 8%, the present value of the annuity payments is closer to the lump sum amount but still greater, so Mark should still choose the annuity payments. However, if Mark believes he can earn a higher return than 8%, he would need to perform additional calculations to decide.

Mark would be indifferent between the two options when the present value of the annuity payments equals the lump sum offer of $200,000. This would occur at an interest rate where:

$200,000 = $16,000 * [(1 - (1 + r)^(-25)) / r]

By solving this equation, we can find the approximate interest rate that would make both options equivalent.