Introduction to Corporate Finance

PART 1: INTRODUCTION

Letting CFt represent the cash flow at the end of year t, the future value of an n-year mixed stream

of cash flows (FV) is shown in Equation 3.3:

Eq. 3.3 FV=CF 1 ×+() 11 rCnn––^1 +×Fr 2 ()+1^2 ++...... CFn×+()rnn–

Substituting the annual cash flows and the 9% interest rate into Equation 3.3, we would calculate

the value for each year (shown to the right of the time line). These values would total $2,930.70.

We can simplify the notation for Equation 3.3, as shown in Equation 3.3a, by using summation

notation, which uses the Greek letter, capital sigma (Σ), as a shorthand way of saying that the future

value of this n-year mixed stream is equal to the sum of the future values of individual cash flows from

periods 1, 2, 3,..., n:

Eq. 3.3a FV CF rnt–

t=

n

=(t 1+)

1

∑ ×

Although summations economise on the notation needed to express most of the equations presented

in this chapter, for clarity we present equations in their non-condensed format wherever possible, and we

use the summation notation sparingly.

Sometimes it is necessary to blend the techniques that we have covered thus far to solve a problem.

The following example illustrates how this works.

example

FIGURE 3.7 FUTURE VALUE AT THE END OF FIVE YEARS OF A MIXED CASH FLOW STREAM INVESTED AT 9%

The future value of a mixed stream of cash flows equals the sum of the future values of the individual cash flows. For the

cash flows shown on the timeline, the individual future values compounded at 9% interest to the end of year 5 are shown at

the end of the arrows. Their total of $2,930.70 represents the future mixed stream.

0 1 2 3 4 5

End of year

FV = $2,930.70

$400 $800 $500 $400 $300

$564.63

$1,036.02

$594.05

$436.00

$300.00

Our company invests money

each month to pay future

retirement benefits that are fixed

contractually. If the return on our

investment goes up, how does

that affect the amount we must

set aside each month?

thinking cap

question