Introduction to Corporate Finance

Ross et al.: Fundamentals

of Corporate Finance, Sixth

Edition, Alternate Edition

III. Valuation of Future

Cash Flows

6. Discounted Cash Flow
   Valuation

© The McGraw−Hill^213

Companies, 2002

$360, and the total payment is $1,360. We can calculate the total payment in each of the
remaining years by preparing a simple amortization scheduleas follows:

Notice that in each year, the interest paid is given by the beginning balance multiplied
by the interest rate. Also notice that the beginning balance is given by the ending bal-
ance from the previous year.
Probably the most common way of amortizing a loan is to have the borrower make a
single, fixed payment every period. Almost all consumer loans (such as car loans) and
mortgages work this way. For example, suppose our five-year, 9 percent, $5,000 loan
was amortized this way. How would the amortization schedule look?
We first need to determine the payment. From our discussion earlier in the chapter,
we know that this loan’s cash flows are in the form of an ordinary annuity. In this case,
we can solve for the payment as follows:

$5,000 C{[1 
(1/1.09^5 )]/.09}

C[(1 
.6499)/.09]

This gives us:

C$5,000/3.8897

$1,285.46

The borrower will therefore make five equal payments of $1,285.46. Will this pay off
the loan? We will check by filling in an amortization schedule.
In our previous example, we knew the principal reduction each year. We then calcu-
lated the interest owed to get the total payment. In this example, we know the total pay-
ment. We will thus calculate the interest and then subtract it from the total payment to
calculate the principal portion in each payment.
In the first year, the interest is $450, as we calculated before. Because the total pay-
ment is $1,285.46, the principal paid in the first year must be:

Principal paid $1,285.46 
 450 $835.46

The ending loan balance is thus:

Ending balance $5,000 
835.46 $4,164.54

The interest in the second year is $4,164.54 .09 $374.81, and the loan balance de-
clines by $1,285.46
374.81 $910.65. We can summarize all of the relevant calcu-
lations in the following schedule:

CHAPTER 6 Discounted Cash Flow Valuation 183

Beginning Total Interest Principal Ending

Year Balance Payment Paid Paid Balance

1 $5,000 $1,450 $ 450 $1,000 $4,000

2 4,000 1,360 360 1,000 3,000

3 3,000 1,270 270 1,000 2,000

4 2,000 1,180 180 1,000 1,000

5 1,000 1,090 90 1,000 0

Totals $6,350 $1,350 $5,000