Question

Your Green Investment Tips subscription is about to expire. You plan to subscribe to the magazine for the rest of your life, and you can renew it by paying $85 annually, beginning immediately, or you can get a lifetime subscription for $850, also payable immediately. Assuming that you can earn 6.0% on your funds and that the annual renewal rate will remain constant, how many years must you live to make the lifetime subscription the better buy?

a. 14.33
b. 7.48
c. 8.80
d. 10.35
e. 12.18

Answer 1

Answer:

The answer is a. 14.33.

Explanation:

We apply the net present value (NPV) methodology to approach the two options.

+ The lifetime subscription's npv = $(850)

+ The annual subscription's npv = - 85 - [ 85/6% * [ 1 - 1.06^(-n) ], with n is the number of years the subscriber still lives.

To make a lifetime subscription a better buy, the NPV of this option should be higher than the NPV of annual subscription or:

85 + [ 85/6% * [ 1 - 1.06^(-n) ] > 850 <=> 1 - 1.06^(-n) > 0.54 <=> 1.06^(-n) < 0.46 <=> -n < -13.33 <=> n > 13.33.

So, the subscriber should live more than 14.33 years ( 13.33 + 1 years for another next year subscription) to make the lifetime subscription a better choice.

So, a is the correct choice.