Chapter 5
Interest Rates

Copyright © 2012 Pearson Prentice Hall. All rights reserved.

Learning Objectives
• Understand the different ways interest rates are quoted
• Use quoted rates to calculate loan payments and balances
• Know how inflation, expectations, and risk combine to determine interest rates
• See the link between interest rates in the market and a firm’s opportunity cost of capital

Copyright © 2012 Pearson Prentice Hall. All rights reserved.

5-2

5.1 Interest Rate Quotes and
Adjustments
• Interest rates are the price of using money
• Effective Annual Rate (EAR) aka Annual
Percentage Yield (APY)
– The total amount of interest that will be earned at the end of one year

Copyright © 2012 Pearson Prentice Hall. All rights reserved.

5-3

5.1 Interest Rate Quotes and
Adjustments
• The Effective Annual Rate
– With an EAR of 5%, a $100 investment grows to: • $100 × (1 + r) = $100 × (1.05) = $105

– After two years it will grow to:
• $100 × (1 + r)2 = $100 × (1.05)2 = $110.25

Copyright © 2012 Pearson Prentice Hall. All rights reserved.

5-4

5.1 Interest Rate Quotes and
Adjustments
• Adjusting the Discount Rate to Different
Time Periods
• (1 + r)0.5 = (1.05)0.5 = $1.0247, so a yearly rate of
5%, is equivalent to a rate of 2.47% every half of a year. $1 × (1.0247)

= $1.0247, × (1.0247) = $1.05

$1

×

(1.0247)2

= $1.05

$1

×

(1.05)

= $1.05

Copyright © 2012 Pearson Prentice Hall. All rights reserved.

5-5

5.1 Interest Rate Quotes and
Adjustments
• Adjusting the Discount Rate to Different Time
Periods
– A discount rate of r for one period can be converted to an equivalent discount rate for n periods:
Equivalent n-Period Discount Rate = (1 + r)n – 1

(Eq. 5.1)

– When computing present or future values, you should adjust the discount rate to match the time period of the cash flows

Copyright © 2012 Pearson Prentice Hall. All rights reserved.

5-6

Example 5.1a Valuing Monthly Cash
Flows
Problem:
• Suppose your bank account pays interest monthly with an effective annual rate of 5%. What amount of interest will you earn each month?
• If you have no money in the bank today, how much will you need to save at the end of each month to accumulate
$150,000 in 20 years?

Copyright © 2012 Pearson Prentice Hall. All rights reserved.

5-7

Example 5.1a Valuing Monthly Cash
Flows
Plan

• That is, we can view the savings plan as a monthly annuity with 20 × 12 = 240 monthly payments.
• The future value of the annuity ($150,000), the length of time (240 months),
• Have the monthly interest rate from the first part of the question. We can then use the future value of annuity formula (Eq. 4.6) to solve for the monthly deposit
Copyright © 2012 Pearson Prentice Hall. All rights reserved.

5-8

Example 5.1a Valuing Monthly Cash
Flows
Execute:
• From Eq. 5.1, a 5% EAR is equivalent to earning (1.05)1/12 –
1 = 0.4074% per month. The exponent in this equation is
1/12 because the period is 1/12th of a year (a month).

FV( annuity) =C × 1r [(1 + r ) n − 1]
• We solve for the payment C using the equivalent monthly interest rate r = 0.4074%, and n = 240 months:
C

FV(annuity)
$150,000
=
= $369.64 per month
1
1
[(1 + r) n − 1]
[(1.004074) 240 − 1] r 0.004074

Copyright © 2012 Pearson Prentice Hall. All rights reserved.

5-9

Example 5.1a Valuing Monthly Cash
Flows
Execute (cont’d):
• We can also compute this result using a financial calculator:

Given:

240

Solve for:

0.4074

0

150,000
-369.64

Excel Formula: =PMT(RATE,NPER,PV,FV)=PMT(.004074,240,0,150000)

Copyright © 2012 Pearson Prentice Hall. All rights reserved.

5-10

5.1 Interest Rate Quotes and
Adjustments
• Annual Percentage Rates (APR)
– Indicates the amount of interest earned in one year without the effect of compounding

• Simple Interest
– Interest earned without the effect of compounding Copyright © 2012 Pearson Prentice Hall. All rights reserved.

5-11

5.1 Interest Rate Quotes and
Adjustments
• Annual Percentage Rates (APR)
– Because the APR does not reflect