Question

Moe purchases a $100 annual perpetuity for which payments begin in one year. Larry purchases a $100 annual perpetuity for which payments begin immediately. If a 10% interest rate is appropriate for both cash flow streams, which of the following statements is true? Multiple Choice Larry's perpetuity is worth $100 more than Moe's Moe's perpetuity is worth $90.91 more than Larry's O The perpetuities are of equal value today,

Moe's perpetuity is worth $100 more than Larry's
O tarry's perpetuity is worth $90.91 more than Moe's.

Answer 1

Larry's perpetuity is worth $100 more than Moe's because it includes one additional payment received immediately. The value of Moe's perpetuity is $1,000, while Larry's is $1,100, due to the immediate start of payments.

Step-by-step explanation:

When evaluating the value of perpetuities, we must take into account the time value of money. Since a perpetuity is a series of infinite payments, its present value can be calculated by dividing the annual payment by the interest rate. In this case, the formula for the present value of a perpetuity is PV = PMT / i, where PMT is the annual payment and i is the interest rate.

For Moe's perpetuity, which starts in one year, the present value is calculated using the formula PV = $100 / 0.10, resulting in a present value of $1,000. However, since the first payment begins one year from now, we do not adjust for the immediate payment. As a result, the present value remains $1,000.

For Larry's perpetuity, which starts immediately, an additional payment is received at the present, so the present value is calculated as PV = $100 / 0.10 + $100, giving us a present value of $1,100.

Therefore, Larry's perpetuity is worth $100 more than Moe's because it includes one additional payment received immediately. The correct answer is that Larry's perpetuity is worth $100 more than Moe's.