Question

Marlene and Darlene are each the recipient of an annuity that pays $1,000 annual payments at the end of each year for 12 years. They both received their first payment on the same day. Explain how Marlene and Darlene could assign different present values to their respective annuities.

Answer 1

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

where P = periodic payment.  

r = periodic rate of interest.

n = number of periods.  

The interest rate is the required return for each investor. The required return is not given. Assume that the required return of Marlene is 5%, and the required return of Darlene is 7%.

Present value of annuity (Marlene) = $1,000 * [1 - (1 + 5%)^-12] / 5% = $8,863.25.

Present value of annuity (Darlene) = $1,000 * [1 - (1 + 7%)^-12] / 7% = $7,942.69.

Thus, the present value of each individual is different due the different required return of each individual.