What is the present value of a growing perpetuity that makes a payment of $100 in the first year, which thereafter grows at 3% per year

Answers

the present value of a growing perpetuity is $2,060

Explanation:

If a cash flow is growing at a constant rate, then we call this a growing perpetuity.

Present Value = PMT ( 1 + g) ÷ (r - g)

where,

g = constant growth rate

  = 0.03

r = discount rate

 = 0.08

Then,

Present Value = $100 (1,03) ÷ (0.08 - 0.03)

                        = $2,060

present value  = $2500

Explanation:

given data

Dividend D = $100

grows g = 3% per year

solution

we consider here discount rate that is ke = 7%

so now we apply here present value  formula that is

present value  = \frac{D}{ke-g}    ..............................1

put here value and we will get

present value  = \frac{100}{0.07-0.03}

solve it and we will get

present value  = $2500



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