Question

Suppose you get for free one of following two securities: (a) an annuity that pays $10,000 at the end of each of the next 6 years; or (b) a perpetuity that pays $10,000 forever, but payments do not begin until 10 years from now (the first cash payment from this security is 11 years from today). Which security would you choose if the annual interest rate is 5%? Does your answer change if the interest rate is 10%? Explain why or why not.

Answer 1

if the interest rate is 5%, I would choose security (b), but if the interest is 10%, then security (a) is a better option

Step-by-step explanation:

security a:

the present value (5%) = $10,000 x 7.7217 (PV annuity factor, 5%, 10 years) = $77,217

the present value (10%) = $10,000 x 6.1446 (PV annuity factor, 10%, 10 years) = $61,446

security b:

terminal value in 10 years, 5% = $10,000 / 5% = $200,000

present value = $200,000 / 1.05¹⁰ = $122,782.65

terminal value in 10 years, 10% = $10,000 / 10% = $100,000

present value = $100,000 / 1.1¹⁰ = $38,554.33