Question

Clarissa wants to fund a growing perpetuity that will pay $ 4 comma 000 per year to a local​ museum, starting next year. She wants the annual amount paid to the museum to grow by 5​% per year. Given that the interest rate is 8​%, how much does she need to fund this​ perpetuity?

Answer 1

Answer:

To fund this perpetuity, she needs $133,333.33 today.

Explanation:

The growing perpetuity that is growing at a constant rate is just like a constant dividend growth stock. The amount paid to the museum will grow at a constant rate of 5%. Using the same approach as the constant growth model of DDM, the amount of fund needed to be invested for this perpetuity can be calculated as,

PV = Cash flow 1 / i - g

Where,

• Cash flow 1 is the amount that will be paid to the museum next year.
• i is the interest rate
• g is the growth rate in funds

PV = 4000 / (0.08 - 0.05)

PV = $133,333.33