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
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
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
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)
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
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?
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
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
