Introduction to Corporate Finance

PART 1: INTRODUCTION

As was the case with the future value of an annuity, a shortcut formula is available to simplify the

present-value calculation for an annuity. Using the symbol PMT to denote the annual cash flow, the

formula for the present value of an n-year ordinary annuity (PV) appears in Equation 3.7.

Eq. 3.7 PV

PMT

rr

1

1

(1+)

=×− n













example

FIGURE 3.11 CONTINUED

Formula B4: =PV(B3,B2,B1,0,0)

Present value $27,948.97

Interest rate 8%

5

–$7,000

Number of periods

Payment

Input

Solution

–7,000

5

8

PMT

N

I

CPT

PV

27,948.97

Function

Row

Column

Calculator Spreadsheet

1

2

3

4

5

A B

We can use Equation 3.7 to calculate the present

value of the service contract EM has offered to the

Koalaburra Company. Substituting in n = 5 years,

r = 0.08 and PMT = $7,000, we find the present

value (PV) of this ordinary annuity to be $27,948.97,

as shown below:

PV

$7,000

0.08

1

1

(0.08)

$7,000

0.08

[1 0.680583]

$27,948.97

=×− 5











=×−

=

Alternatively, we could use Excel’s PV (present

value) function, entering 8% for the rate, 5 for the

number of periods, negative $7,000 for the payment,

and 0 for the future value and type of annuity

=pv(0.08,5,–7,000,0,0). This yields the answer

$27,948.97.

example

In some applications, the present value of the annuity is known, along with the number and size of

the annual payments. What is missing is the rate of return.