# M05Berk148315 02 CorpFin C05concise 20lecture 1 Essay examples

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Pages: 15

Chapter 5
Interest Rates

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

5-2

5.1 Interest Rate Quotes and
• 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

5-3

5.1 Interest Rate Quotes and
• 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

5-4

5.1 Interest Rate Quotes and
• 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

5-5

5.1 Interest Rate Quotes and
• 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

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?

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

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

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)

5-10

5.1 Interest Rate Quotes and