Question

Ethan got a bad haircut from Sideshow Bob's Barber Shop. It did great harm to his self-esteem and a sympathetic jury awarded him damages, and gave him this choice: He can either receive $85,000 per year for 10 years or $500,000 as a lump sum payment today. If his required rate of return is 12%, what should he do, and why?

Group of answer choices

He should reject the lump sum payment because the sum of the annuity payments is greater than $500,000.

He should reject the lump sum payment because the FV of the annuity is greater than $500,000.

He should take the lump sum payment because the PV of the annuity is less than $500,000.

He should take the lump sum payment because its FV is greater than the sum of the annuity payments.

He should reject the lump sum payment because the PV of the annuity is greater than $500,000.

Answer 1

It is assumed that the annual payments in option 1 will be made at the end of each year (Ordinary Annuity).

Present value of annuity= $480,268.96 as follows:

Accordingly, the answer is 2nd option, “He should take the lump sum payment because the PV of the annuity is less than $500,000.”

Note, in case the yearly payments are at the beginning of each year (Annuity Due), PV will be

$480,268.96 *(1+0.12)= $537,901.23. This being higher than the lump sum amount of $500,000, the answer will be last option viz. “He should reject the lump sum payment because the PV of the annuity is greater than $500,000.”