You have been given a choice between two retirement policies as described below:

Question

You have been given a choice between two retirement policies as described below:

Policy A: You will recieve equal annual payments of $30,000 in 20 years

Policy B: You will recieve one lump sum of $400,000 now.

1) At what interest rate would you be indifferent in choosing between the two policies?

2) At what interest rate, will you choose Policy A? At whar interest rate will you choose policy B?

3) If you expect to be able to earn 6% annually on your investment over the next 20 years, which policy should you take? why? show your calcualtions

Explanation / Answer

1) 7%

2) When Interest rate Less than  7% then Policy A will be choosed.

3) Policy A will be choosen because 6 % is less than 7%. at 6% Present value under Policy A is higher than POlicy B.

Let the rate is 10% Lump sum Payment =           400,000 (A) Cash flow annually for 30 years =             30,000 Cumulative discount factor @10% for 30 years Cumulative discount factor @5% for 30 years = {1-(1+i)^-n}/i = {1-(1+i)^-n}/i = {1-(1.1)^-30}/.10 = {1-(1.05)^-30}/.05 =               9.427 =             15.372 Present vAlue           282,810 (B) Present vAlue           461,160 IRR = 5+5*{-61160/(-61160-117190)} Difference in cash flow = Difference in cash flow = = 7%           117,190 (A)-(B)           (61,160) Thus, at 7% will be indifferent in choosing between the two policies.

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