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.
