Ross et al.: Fundamentals
of Corporate Finance, Sixth
Edition, Alternate EditionIII. Valuation of Future
Cash Flows- Discounted Cash Flow
Valuation
(^214) © The McGraw−Hill
Companies, 2002
Because the loan balance declines to zero, the five equal payments do pay off the loan.
Notice that the interest paid declines each period. This isn’t surprising because the loan
balance is going down. Given that the total payment is fixed, the principal paid must be
rising each period.
If you compare the two loan amortizations in this section, you will see that the total in-
terest is greater for the equal total payment case, $1,427.31 versus $1,350. The reason for
this is that the loan is repaid more slowly early on, so the interest is somewhat higher. This
doesn’t mean that one loan is better than the other; it simply means that one is effectively
paid off faster than the other. For example, the principal reduction in the first year is
$835.46 in the equal total payment case as compared to $1,000 in the first case. Many web
sites offer loan amortization schedules. See our nearby Work the Webbox for an example.
184 PART THREE Valuation of Future Cash Flows
Beginning Total Interest Principal Ending
Year Balance Payment Paid Paid Balance
1 $5,000.00 $1,285.46 $ 450.00 $ 835.46 $4,164.54
2 4,164.54 1,285.46 374.81 910.65 3,253.88
3 3,253.88 1,285.46 292.85 992.61 2,261.27
4 2,261.27 1,285.46 203.51 1,081.95 1,179.32
5 1,179.32 1,285.46 106.14 1,179.32 0.00
Totals $6,427.30 $1,427.31 $5,000.00
Preparing an amortization tableis one of the more tedious time
value of money applications. Using a spreadsheet makes it relatively easy,
but there are also web sites available that will prepare an amortization
table very quickly and simply. One such site is CMB Mortgage. Their web site
http://www.cmbmortgage.comhas a mortgage calculator for home loans, but the same
calculations apply to most other types of loans such as car loans and student loans.
Suppose you graduate with a student loan of $30,000 and will repay the loan over
the next 10 years at 7.63 percent. What are your monthly payments? Using the calcu-
lator, we get:
Try this example yourself and hit the “Payment Schedule” button. You will find that
your first payment will consist of $167.39 in principal and $190.75 in interest. Over
the life of the loan you will pay a total of $12,977.57 in interest.
Work the Web