Four years from now (beginning of year four) you will receive the first of seven $10,000 annual payments. The current interest rate is 6%, but by the beginning of year 4, the rate will rise to 8%. What is the present value of this cash flow stream?

Question

Quizplus · Accepted Answer

The present value of the cash flow stream can be calculated by first finding the present value of the annuity at the beginning of year 4 (when the first payment is received) using the 8% interest rate, and then discounting that amount back to the present using the current 6% interest rate for the three years until the payments begin. The formula for the present value of an annuity is PV = P * [(1 - (1 + r)^-n) / r], where P is the payment amount, r is the interest rate per period, and n is the number of periods. For the annuity starting in year 4, P = $10,000, r = 8% or 0.08, and n = 7. The present value at the beginning of year 4 is then discounted back to the present value using the 6% rate for 3 years. The correct calculation leads to the present value of approximately $44,538.48.

Four Years from Now (Beginning of Year Four) You Will