Introduction to Corporate Finance

PART 1: INTRODUCTION

You wish to save money on a regular basis to finance an exotic vacation in five years. You are confident that, with

sacrifice and discipline, you can force yourself to deposit $1,000 annually, at the end of each of the next five years,

into a savings account paying 7% annual interest. This situation is depicted graphically at the top of Figure 3.8.

Compute the future value (FV) of this ordinary annuity using Equation 3.3. Use the assumed interest rate (r)

of 7% and plug in the known values of each of the five yearly (n = 5) cash flows (CF^1 to CF^5 ), as follows:

FV CF rCFr CF r

FV CF rCFr CF r

(1 )(1) (1 )

(1 )(1) (1 )

$1,000(1.07) $1,000(1.07) $1,000(1.07) $1,000(1.07) $1, 000

$1,310.80 $1,225.04 $144.90 $1,070 $1,000 $5,750.40

nn

n

nn

n

1

1

2

2

1

51

2

52 55

4321

......

......

=×++×+ ++×+

=×++×+ ++ ×+

= ++++

=++++=

−− −

−− −

The year 1 cash flow of $1,000 earns 7% interest for four years, the year 2 cash flow earns 7% interest for

three years, and so on. The future value of the ordinary annuity is $5,750.74.

example

FIGURE 3.8 FUTURE VALUE AT THE END OF FIVE YEARS OF AN ORDINARY ANNUITY OF $1,000 PER YEAR

INVESTED AT 7%

The future value of the five-year, $1,000 ordinary annuity at 7% interest at the end of year 5 is $5,750.74, which is well

above the $5,000 sum of the annual deposits.

Formula B4: =FV(B3,B2,B1)

Future value $5,750.74

Interest rate 7%

5

–$1,000

Number of periods

Payment

Input

Solution

–1,000

5

7

PMT

N

I

CPT

FV

5,750.74

Function

Row

Column

Calculator Spreadsheet

1

2

3

4

5

A B

0 1 2 3 4 5

End of year

FV = $5,750.74

$1,000 $1,000 $1,000 $1,000 $1,000

$1,310.80

$1,255.04

$1,144.90

$1,070.00

$1,000.00