Compute the present value of a perpetuity that grows at the rate of 10% for the...

Compute the present value of a perpetuity that grows at the rate of 10% for the first 10 years and at the rate of 15% from year 11 onwards. The first payment for this perpetuity to be received in one year from now is $1,000 and the required rate of return is 20%.

Expert Solution

Year	Cashflows	PVF at 20%	Present value
1	1000	0.833333	833.3333
2	1100	0.694444	763.8889
3	1210	0.578704	700.2315
4	1331	0.482253	641.8789
5	1464.1	0.401878	588.389
6	1610.51	0.334898	539.3565
7	1771.561	0.279082	494.4102
8	1948.717	0.232568	453.2093
9	2143.589	0.193807	415.4419
10	2357.948	0.161506	380.8217
10	54232.8	0.161506	8758.923
Present value of Caashflows			14569.88

Present value of Prepetuity: $ 14569.88



Note:
Cash flows from Year-2 to Year-10 is computed with the following formula:
Cashflows of Year = Cashflows of Previous yr + 10%

Now, Cashflows of Year11= Cashflows of Year-10+15%
			2357.95+15% = 2711.64
And cashflows for Year-15 - Cashflows of Year-14 = 154002.6
As, from Year-11 onwards, the cashflows generates in perpetuity wth the 15%,
therefore, the price of future cashflows at the end of Year-10 is computed as under:
Price at the end of Year-10 = 2711.64 / (20-5)% = 54232.8

jeff jeffy answered 1 year ago

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