Question

You are currently willing to pay $25,000 to purchase a perpetuity which will pay you and your heirs $2,250 each year forever (the first $2,250 payment will be received one year from today). If your required rate of return does not change, how much would you currently be willing to pay if this were a 10-year ordinary annuity of $2,250 per year instead of a perpetuity? (Select the range in which the correct answer falls)

 

A. Less than $14,200

B. Greater than or equal to $14,200 but less than $14,300

C. Greater than or equal to $14,300 but less than $14,400

D. Greater than or equal to $14,400 but less than $14,500

E. Greater than or equal to $14,500

Answer 1

The best option is (d).

 

Explanation:

Calculation of required rate of return:

Currently willing to pay per perpetuity (Value of Perpetuity) = $25,000

Perpetual Cash flow = $2,250

Value of Perpetuity = Cash flow/Return

Substitute values 

$25,000 = $2,250/Return

Return = $2,250/$25,000 = 0.09 or 9%

 

Calculation of value of 10 year ordinary annuity

Required rate of return does not change

Return = 9%

Cash flow = $2,250

Value of annuity = present value annuity factor * Cash flow

Present value annuity factor = 1/(1+9%)1 + 1/(1+9%)2 +  1/(1+9%)3...........+1/(1+9%)10 = 6.418

 

Value of 10 year ordinary annuity = 6.418 * $2,250 = $14,440.5

 

Hence the best option is (D) Greater than $14,400 but Less than $14,500.

The best option is (d).

Hence the best option is (D) Greater than $14,400 but Less than $14,500.