Question

Evans Ltd. is now considering the possibility of offering a lifetime membership option to its subscribers. Under this proposal, subscribers could receive the monthly newsletter throughout their lives by paying a flat fee of $480. The one-year subscription rate of $40 would continue to apply to new and existing subscribers who choose to subscribe on an annual basis. Assume that the average age of Evans Ltd.'s current subscribers is 38 and their average life expectancy is 78 years. Evans Ltd.'s average interest rate on long-term debt is 12%.
Using the information given, calculate the present value of a lifetime membership for an average. (Round PV factors to 4 decimal places and final answer to 2 decimal places.)

Answer 1

Answer: $329.75

Explanation:

The one year subscription is $40 per year. It is estimated that the average age of current subscribers is 38 and they will leave on average to 78. This means that they will leave for,

= 78 - 38

= 40 years

Evans Ltd  average interest rate on long-term debt is 12% so this means that we can use that 12% as a discount rate for the cash-flow expected.

I have attached a Present Value Interest Factor of an Annuity table to this question. It helps calculate annuities faster.

The above can be treated as an annuity because the $40 is constant every year.

The present value of the $40 over 40 years can be calculated by,

= $40 * present value Interest Factor of an Annuity for 40 years at 12% (look at the table for where 40 years on the y axis intersects with 12% on the x axis)

= $40 * 8.2438 (this is the figure when it is not rounded off to 3 dp)

= $329.752

= $329.75

This shows that the lifetime flat fee of $480 is more profitable for Evans Ltd as opposed to the yearly subscription. They should therefore try to sell more of the lifetime contract with the flat fee.