Question

Uneven Cash Flow Stream

Find the present values of the following cash flow streams. The appropriate interest rate is 10%. (Hint: It is fairly easy to work this problem dealing with the individual cash flows. However, if you have a financial calculator, read the section of the manual that describes how to enter cash flows such as the ones in this problem. This will take a little time, but the investment will pay huge dividends throughout the course. Note that, when working with the calculator's cash flow register, you must enter CF₀ = 0. Note also that it is quite easy to work the problem with Excel, using procedures described in the Ch04 Tool Kit.xlsx.) Do not round intermediate calculations. Round your answers to the nearest cent.

Year	Cash Stream A	Cash Stream B
1	$100	$300
2	400	400
3	400	400
4	400	400
5	300	100

Stream A:

Stream B:

1. What is the value of each cash flow stream at a 0% interest rate? Round your answers to the nearest dollar.

   Stream A   

   Stream B

Answer 1

(a)-The Present value of each cash flow stream at a 10% interest rate

Present Value of the Stream-A

Year	Annual cash flows ($)	Present Value Factor (PVF) at 10.00%	Present Value of the annual cash flows ($) [Annual cash flow x PVF]
1	100	0.909091	90.91
2	400	0.826446	330.58
3	400	0.751315	300.53
4	400	0.683013	273.21
5	300	0.620921	186.28
TOTAL		1,181.50

Present Value of the Stream-A is $1,181.50

Present Value of the Stream-B

Year	Annual cash flows ($)	Present Value Factor (PVF) at 10.00%	Present Value of the annual cash flows ($) [Annual cash flow x PVF]
1	300	0.909091	272.73
2	400	0.826446	330.58
3	400	0.751315	300.53
4	400	0.683013	273.21
5	100	0.620921	62.09
TOTAL		1,239.13

Present Value of the Stream-B is $1,239.13

(b)-The Present value of each cash flow stream at a 0% interest rate

The Present Value of the Stream-A = $1,600 [$100 + 400 + 400 + 400 + 300]

The Present Value of the Stream-B = $1,600 [$300 + 400 + 400 + 400 + 100]

NOTE

The formula for calculating the Present Value Inflow Factor (PVIF) is [1 / (1 + r)n], where “r” is the Discount Rate/Cost of capital and “n” is the number of years.