Question

A pension Buyout offer

option a: 50,000 per year for 20 years

Option B : 600,000 buyout

-which one shoudl you tak eid the risk free is at 10%

-what interest rate will you be indifferent between the 2 available options?

please explain your answer and how you go it, Thank you!

Answer 1

(a) When risk-free rate (r) = 10%,

Present value (PV) of Option A = 50,000 x PVIFA(10%, 20) = 50,000 x 8.5136** = 425,680

Since PV of Option B is higher, I should choose Option B.

(b) If the indifference risk-free rate be r, by equivalence,

50,000 x PVIFA(r%, 20) = 600,000

PVIFA(r%, 20) = 12

From PVIFA data table we find that PVIFA(5%, 20) = 12.4622 and PVIFA(6%, 20) = 11.4699. Therefore,

5% < r < 6%. By linear interpolation,

(r - 5) / (6 - 5) = (12 - 12.4622) / (11.4699 - 12.4622)

r - 5 = (- 0.4622) / (- 0.9923)

r - 5 = 0.4658

r = 5.4658%