Question

You have been offered the opportunity to purchase one of two select financial products by your favorite Northeastern Mutual sales representative.

Product 1: Perpetuity with annual payments of $78,000 for $1,000,000

Product 2: The same stream of payments but only lasting 25 years.

For you to be indifferent between the two securities, what price would you be willing to pay for the second product?

Answer 1

Value of perpetuity = perpetual payment / discount rate

Implied discount rate in Product 1 = $78,000 / $1,000,000 = 7.8%

Price you would be willing to pay for 2nd product is calculated as below :

PV of annuity = P * [1 - (1 + r)^-n] / r,

where P = periodic payment. We need to calculate this.

r = interest rate per period. This is 7.8%

n = number of periods. This is 25

PV of annuity = $78,000 * [1 - (1 + 7.8%)^-25] / 7.8%

PV of annuity = $847,056.52

Price you would be willing to pay for 2nd product is  $847,056.52