Question

You are considering two equally risky annuities, each of which pays $5,000 per year for 10 years. Investment ORD is an ordinary (or deferred) annuity, while Investment DUE is an annuity due. Which of the following statements is CORRECT? Group of answer choices The present value of ORD exceeds the present value of DUE, and the future value of ORD also exceeds the future value of DUE. If the going rate of interest decreases from 10% to 0%, the difference between the present value of ORD and the present value of DUE would remain constant. A rational investor would be willing to pay more for DUE than for ORD, so their market prices should differ. The present value of DUE exceeds the present value of ORD, while the future value of DUE is less than the future value of ORD. The present value of ORD exceeds the present value of DUE, while the future value of DUE exceeds the future value of ORD.

Answer 1

Answer:

A rational investor would be willing to pay more for DUE than for ORD, so their market prices should differ.

Explanation:

If both annuities pay the same amount ($5,000 per year), then the present value of the annuity due will always be higher than the present value of the ordinary annuity. Therefore, an investor will always be willing to pay more (at equal risk) for the annuity due than the ordinary annuity.

E.g. let say that both annuities carry a 10% interest rate.

The present value of the annuity due is:

PV = $5,000 + [$5,000 x 5.7590 (PV annuity factor, 10%, 9 periods)] = $33,795

The present value of the ordinary annuity is:

PV = $5,000 x 6.1446 (PV annuity factor, 10%, 10 periods) = $30,723

The logic behind this is that $1 today is worth more than $1 tomorrow, and the annuity due's first payment is today, while the ordinary annuity's first payment is in 1 year.