Week 7 Uneven Cash Flow Streams

Week 7: Lecture

Uneven Cash Flow Streams

Quite often you encounter situations in which you want to know the present value or future value of a stream of future cash flows, but the cash flows are not regular and even and thus do not constitute an annuity. In situations like this the PV or FV of each individual cash flow is calculated separately and then added up to get the total PV. Here are two examples:

Example 1: What's the FV at the end of the fifth year of the following cash flow stream: (assume your required rate of return is 10%)

Year Cash Flow
1 100
2 400
5 300

On a timeline the problem looks like this:

tvm_uneven_cash_flow_timeline.jpg

To calculate the total FV of the stream of cash flows at the end of year 5, proceed as follows, using the FV of an individual cash flow formula that you learned about last week:

FV of 100 @ Yr 1 = 100 * (1+.10)4 = 146.41
FV of 400 @ Yr 2 = 400 * (1+.10)3 = 532.40
FV of 300 @ Yr 5 = 300 = 300.00
Sum = total PV = 978.81

 

Example 2: What's the PV of the following cash flow stream: (assume your required rate of return is 10%)

Year Cash Flow
1 100
2 400
5 300

On a timeline the problem looks like this:

tvm_uneven_cash_flow_timeline_present_value.jpg

To calculate the total PV of the stream of cash flows, proceed as follows, using the PV of an individual cash flow formula that you learned about last week:

PV of 100 @ Yr 1 = 100 *(1 / (1+.10)1) = 90.909
PV of 400 @ Yr 2 = 400 * (1 / (1+.10)2) = 330.578
PV of 300 @ Yr 5 = 300 * (1 / (1+.10)5) = 186.276
Sum = total PV = 607.76

 

Important Observation
The procedure to calculate the PV of an uneven cash flow stream illustrates how the fundamental value of a business is calculated. In week 1 of the course we established that the value of a business is the present value of all the cash flows that could be expected to accrue to the firm in the future. The PV of an uneven cash flow stream procedure shown here illustrates how it works. More importantly, the procedure illustrates what factors influence the present value of the business:

  • The size of the future cash flows: the larger the future cash flows, the higher the PV
  • When the future cash flows occur: the sooner the cash flows occur the higher the PV
  • The required rate of return: the lower the required rate of return, the higher the PV (the value of the required rate of return depends on the degree of uncertainty, or riskiness associated with the future cash flows. The more uncertain, or risky the value of a future cash flow is, the higher the rate of return investors will require to obtain that cash flow and the lower its present value will be. This establishes what risk has to do with the value of a business

Since the basic objective of a firm’s managers is to maximize the value of the firm you can see that what managers should be doing is

  • Seeking to increase the firm’s future cash flows,
  • Seeking to shorten the time the firm has to wait to get the cash flows, and
  • To minimize the riskiness associated with the cash flows.