Question

1.Suppose that one year from now you receive $350. At the end of the next nine years you receive a payment that is 4% larger than the prior year. If the cost of capital is 14% what is this stream of cash flows worth today?

2.Suppose that one year from now you will receive $1000 and that at the end of every year thereafter you will receive a payment that is 3% larger than the prior payment. If the cost of capital is 9% what is this stream of cash flows worth today?

3.Suppose that one year from now you will receive $700. At the end of each of the next four years you will receive a payment that is 1% bigger than the prior payment. Following year five you will receive a payment at the end of every year that is 4% larger than the prior payment. If the cost of capital is 7% what is the this stream of cash flows worth today?

Answer 1

(1) First Payment = $ 350 received at t=1 assuming current time is t=0. Tenure of Payment Receipts = 10 years. Growth Rate of Payment Stream = 4 % and Cost of Capital = 14 %

Present Worth of the Payment Stream = 350 x [1/(0.14-0.04)] x [1-{(1.04)/(1.14)}^(10)] = $ 2102.496 ~ $ 2102.5

(2) First payment = $ 1000 received at t=1 assuming current time is t=0. The stream of payment has a constant growth of 3 % and is perpetual in nature. Cost of Capital is 9%. This stream is an example of a constant growth perpetuity.

Present Worth of the Perpetuity = 1000 / (0.09 - 0.03) = $ 16666.67

(3) The stream of payment is perpetual in nature. However, it is a constant growth perpetuity with two different rates of growth. The first growth rate is 1 % which prevails between year 1 and year 5. Post Year 5 the growth rate is 4% in perpetuity. Cost of Capital = 7 %

Year 1 Payment = $ 700, Year 5 Payment = (1.01)^(4) x 700 = $ 728.4228 and Year 6 Payment = 728.4228 x (1.04) = $ 757.5597

PV at the end of Year 5 of the perptual payment stream growing at 4 % = PV5) = 757.5597 / (0.09 - 0.04) = $ 15151.9

Present value at t=0 of the perpetual payment stream growing at 4 % = PV(5) / (1.09)^(5) = 15151.9 / (1.09)^(5) = $ 9847.237

Present Value of the Payment Stream growing at 1 % = 700 x [1/(0.09-0.01)] x [1-{(1.01)/(1.09)]^(5)] = $ 2773.011

Total Present value of payment stream = 9847.237 + 2773.011 = $ 12620.25