5.0
Chapter
5
McGraw-Hill/Irwin
Discounte
d Cash
Flow
Valuation
©2001 The McGraw-Hill Companies All Rights Reserved
5.1
5.4 Loan Types and Loan Amortization
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5.2
Loan Types and Loan Amortization
 Three
basic types of loans:
Pure Discount Loans
 Interest–Only Loans
 Amortized Loans

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5.3
Pure Discount Loans
 The
pure discount loan is the simplest form of
loan
 The borrower receives money today (a
discounted PV amount) and repays a single
lump sum at some time in the future
 A one year, 10% pure discount loan would
require the borrower to repay $1.10 in one year
for every dollar borrowed today

i.e. borrow $1.00 today and repay $1.10 in one year
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5.4
Pure Discount Loans
Treasury bills are excellent examples of pure discount
loans. The principal amount is repaid at some future date,
without any periodic interest payments.
 Example Page 131: If a T-bill promises to repay
$10,000 in 12 months (1 year) and the market interest rate
is 7 percent, how much will the bill sell for in the market?
 PV = FV/(1+r)t
 PV = 10,000 / (1.07)1 = 9345.79
 Using the Financial Calculator:
 Fv =
10,000
 N =
1
 I
=
7
 PV =
9,345.79
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
5.5
Pure Discount Loans
Example: Bottom Pg 130

Suppose a borrower was able to repay $25,000 in five years.
If we, acting as the lender, wanted a 12 percent interest rate
on the loan, how much would we be willing to lend? Put
another way, what value would we assign today (the present
value) to that $25,000 to be repaid in five years?

Just compute the PV of $25,000 at 12% for 5 yrs.

Using the Formula: PV = FV/(1+r)t
 PV = $25,000 / 1.125
 PV
= $25,000 / 1.7623
 PV = $14,186

Or simply enter into your financial calculator and solve for the PV –
next slide
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5.6
Pure Discount Loans (Financial Calculator)
Example: Bottom Pg 130

Suppose a borrower was able to repay $25,000 in five
years. If we, acting as the lender, wanted a 12 percent
interest rate on the loan, how much would we be willing to
lend? Put another way, what value would we assign today
to that $25,000 to be repaid in five years?
 Just compute the PV of $25,000 at 12% for 5 yrs.
 Using the Financial Calculator:
 n=
5
 i=
12
 FV =
25,000
 PV =
14,186
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5.7
Interest-Only Loans
 A loan
that has a repayment plan that calls for
the borrower to pay interest each period and to
repay the entire principal (the original loan
amount) at some point in the future.
 For example:

With a three-year, 10%, interest-only loan of $1000:

The borrower would pay $100 in interest ($1,000 x .10) at
the end of the first and second years. At the end of the
third year, the borrower would return the $1,000 along with
another $100 in interest for that year.
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5.8
Interest Only Loan - Example
 Consider
a 5-year, interest only loan with a 7%
interest rate. The principal amount is $10,000.
Interest is paid annually.

What would the stream of cash flows be?


Years 1 – 4: Interest payments of .07(10,000) = 700
Year 5: Interest + principal = 10,700
 This
cash flow stream is similar to the cash
flows on corporate bonds and we will talk
about them in greater detail later.
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5.9
Amortized Loans
 With
a pure discount or interest-only loan,
the principal is repaid all at once.
 An alternative is an amortized loan.
 The lender requires the borrower to repay parts
of the loan amount (principal) over time.

(i.e. a home mortgage)
 The
process of paying off a loan by making
regular principal reductions is called
amortizing the loan.
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5.10
Amortized Loans
 The
most common way of amortizing a loan is
to have the borrower make a single, fixed
payment every period.
Consumer Loans (such as car loans)
 Mortgages

 Each
payment covers the interest expense plus
reduces principal
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5.11
Amortized Loan with Fixed Payment
Example: (Using the Financial Calculator)

Consider a 4 year loan with annual payments (ordinary
annuity). The interest rate is 8% and the principal
amount is $5000.
 What is the annual payment?
 Using
the Financial Calculator
n=4
 i=8
 PV = - 5,000
 PMT = $1,509.60

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5.12
Amortization Table:
Year
1
Beg.
Total Fixed Interest Principal End.
Balance
Payment Paid (8%) Paid
Balance
5,000.00
1509.60 400.00 1109.60 3890.40
2
3890.40
1509.60
311.23
1198.37
2692.03
3
2692.03
1509.60
215.36
1294.24
1397.79
4
1397.79
1509.60
111.82
1397.78
.01
6038.40 1038.41
4999.99
Totals
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5.13
Quick Quiz

What is a pure discount loan? What is a good example
of a pure discount loan?



The borrower receives money today and repays a single lump
sum at some time in the future
Treasury Bills
What is an interest only loan? What is a good example
of an interest only loan?


A loan that has a repayment plan that calls for the borrower to
pay interest each period and to repay the entire principal (the
original loan amount) at some point in the future.
Corporate Bonds
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5.14
Quick Quiz
 What
is an amortized loan? What is a good
example of an amortized loan?
The lender requires the borrower to repay parts of the
loan amount over time.
 Mortgages and Consumer Loans (i.e.Car Loans)

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