Which is greater, the present value of a five-year ordinary annuity of $300 discounted at 10%, or the present value of a five-year ordinary annuity of $300 discounted at 0% that has its first cash flow six years from today?
A) The first annuity because the cash flows occur sooner.
B) The second annuity because the cash flows are discounted at a lower interest rate.
C) The two annuities are of equal value.
D) The answer to this question cannot be determined.

Question

Quizplus · Accepted Answer

The present value of the second annuity can be calculated using the formula: PV = $300/ (1+0%) + $300/(1+10%)^2 + $300/(1+10%)^3 + $300/(1+10%)^4 + $300/(1+10%)^5 = $1,413.87. 
The present value of the first annuity can be calculated using the formula: PV = $300/(1+10%) + $300/(1+10%)^2 + $300/(1+10%)^3 + $300/(1+10%)^4 + $300/(1+10%)^5 = $1,153.09. 
Therefore, the second annuity has a greater present value because the discount rate is lower, even though the first cash flow is delayed by a year.

Which Is Greater, the Present Value of a Five-Year Ordinary