Fundamentals of Financial Management (Concise 6th Edition)

132 Part 2 Fundamental Concepts in Financial Management

The top section of Table 5-2 calculates the PV using the step-by-step approach.

When we found the future value in the previous section, we worked from left to

right, multiplying the initial amount and each subsequent amount by (1 # I). To

! nd present values, we work backward, or from right to left, dividing the future

value and each subsequent amount by (1 # I). This procedure shows exactly what’s

happening, which can be quite useful when you are working complex problems.

However, it’s inef! cient, especially when you are dealing with a number of years.

With the formula approach, we use Equation 5-2, simply dividing the future

value by (1 # I)N. This is more ef! cient than the step-by-step approach, and it gives

the same result. Equation 5-2 is built into! nancial calculators; and as shown in

Table 5-2, we can! nd the PV by entering values for N, I/YR, PMT, and FV and

then pressing the PV key. Finally, spreadsheets have a function that’s essentially

the same as the calculator, which also solves Equation 5-2.

The fundamental goal of! nancial management is to maximize the! rm’s

value, and the value of a business (or any asset, including stocks and bonds) is the

present value of its expected future cash " ows. Because present value lies at the

heart of the valuation process, we will have much more to say about it in the re-

mainder of this chapter and throughout the book.

5-3a Graphic View of the Discounting Process

Figure 5-2 shows that the present value of a sum to be received in the future

decreases and approaches zero as the payment date is extended further into the

future and that the present value falls faster at higher interest rates. At relatively

high rates, funds due in the future are worth very little today; and even at rela-

tively low rates, present values of sums due in the very distant future are quite

small. For example, at a 20% discount rate, $1 million due in 100 years would be

worth only $0.0121 today. This is because $0.0121 would grow to $1 million in 100

years when compounded at 20%.

Present Value of $1

10 20 30 40 50

0.20

0

0.40

0.60

0.80

1.00

I = 20%

I = 10%

I = 5%

I = 0%

Periods

Present Value of $1 at Various Interest Rates and Time Periods

F I G U R E 5! 2