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?

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,

PV = 4000 / (0.08 - 0.05)

PV = $133,333.33

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