Question

Norwood Investments is putting out a new product. The product will pay out $25,000 in the first year, and after that, the payouts will grow by an annual rate of 2.5 percent forever. If you can invest the cash flows at 7.5 percent, how much will you be willing to pay for this perpetuity? (Round to the nearest dollar.)

a) $200,000
b) $300,000
c) $400,000
d) $500,000

Answer 1

To calculate the present value of a perpetuity with growing payouts, the formula PV = № / (r - g) is used. For Norwood Investments' product, with a first payout of $25,000 growing at 2.5% annually, and a 7.5% discount rate, you would be willing to pay $500,000 for the perpetuity.

Step-by-step explanation:

To calculate the present value of a perpetuity where the payouts grow at a consistent rate, we can use the formula for the present value of a growing perpetuity:

PV = № / (r - g)

Where:

• PV is the present value of the perpetuity
• № (Cash flow) is the amount of the first payment
• r is the discount rate or the rate of return required
• g is the growth rate of the payments

In this case, Norwood Investments' product will pay out $25,000 in the first year, with a growth rate (g) of 2.5% and a discount rate (r) of 7.5%. By substituting these figures into the formula:

PV = $25,000 / (0.075 - 0.025)

PV = $25,000 / 0.05 = $500,000

Therefore, you would be willing to pay $500,000 for this perpetuity.