Question

A rich relative has bequeathed you a growing perpetuity. The first payment will occur one year from now and will be $1,000. Each year after that, you will receive a payment on the anniversary of the previous payment that is 8% larger than the previous payment. This pattern of payments will go on forever. Assume that the interest rate is 12% per year.

Required:
a. What is today's value of the bequest?
b. What is the value of the bequest immediately after the first payment is made?

Answer 1

a.

PV = $25000

b.

PV one year from today = $27000

Step-by-step explanation:

a.

A perpetuity is a series of cash flows that are constant in nature, occur after equal interval of time and are for an infinite period of time. A growing perpetuity is a perpetuity that grows at a proportionate rate for an infinite period of time. The formula to calculate the present value of a growing perpetuity is,

PV = CF1 / r - g

Where,

• CF1 is the cash flow in the coming period or period 1
• r is the required rate of return or interest rate
• g is the growth rate of perpetuity

PV = 1000 / (0.12 - 0.08)

PV = $25000

b.

After the first payment is made, the value of the growing perpetuity can be calculated using CF2. The value that will come will be the value of perpetuity 1 year from today.

PV one year from today = CF2 / (r - g)

PV one year from today = 1000 * (1+0.08) / (0.12 - 0.08)

PV one year from today = $27000