What Do Interest Rates Mean and What IsTheir Role in

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CHAPTER 3

What Do Interest Rates

Mean and What Is Their

Role

in Valuation?

© 2013 Pearson Education, Inc. All rights reserved.4-3

LEARNING OBJECTIVES

• Explain the present value concept and the meaning of the term

interest rate.

• Present different ways of measuring the interest rate.

• Distinguish between the four types of credit market instruments

• Explain the difference between nominal and real interest rates.

• Compute the yield to maturity for different credit market

instruments.

CHAPTER PREVIEW

• Interest rates are among the most closely watched variables in the economy.

• Their movements are reported almost daily as they directly affect our everyday

lives and have important consequences for the health of theeconomy.

• They affect personal decisions such as whether to consume or save, whether to

buy a house, or to purchase bonds orput funds into a savings account.

• They also affect the economic decisions of businesses such as to invest in new

equipment for factories or to save their money in a bank

Present Value Introduction

Different debt instruments have very different streams of cash payments to the holder

known as cash flows (CF).

All else being equal, debt instruments are evaluated against one another based on the

amount of each cash flow and the timing of each cash flow.

This evaluation, where the analysis of the amount and timing of a debt instrument’s

cash flows lead to its yield to maturity or interest rate, is called present value analysis.

Present Value

▪Present Value or Present discounted value is based on the commonsense notion that a dollar of cash flow paid to you one year from now is worth less than a dollar paid to you today.

▪Why?Because you could invest the dollar in a savings account that earns interest and have more than a dollar in one year.

▪The term present value (PV) can be extended to mean the PV of a single cash flow or the sum of a sequence or group of cash flows.

Present Value Concept:

▪Loan Principal: the amount of funds the lender provides to the

borrower.

▪Maturity Date: the date the loan must be repaid; the Loan Term

is from initiation to maturity date.

▪Interest Payment: the cash amount that the borrower must pay

the lender for the use of the loan principal.

▪Simple Interest Rate: the interest payment divided by the loan

principal; the percentage of principal that must be paid as

interest to the lender. Convention is to express on an annual

basis, irrespective of the loan term.

SOME BASIC TERMINOLOGY

• Principal: initial value of the loan.

• Face value or par value is equal to a bond's price when it is first issued.

• Cash flows are the cash payments to the holder of debt instruments.

•Maturity date: is the date on which the principal amount of a bond or another

debt instrument becomes due and is repaid to the investor.

Present Value Example4-9

• Thus, at the end of the year, you receive 110( principal 100+10

interest)

• Assume that you lend you friend a simple loan $100 for one

year.

• You would require her to repay the principal of $100 in one year

time along with an additional payment for interest say,$10.

• Simple interest rate, i, is:

Let i = .10

In one year $100 X (1+ 0.10) = $110

In two years $110 X (1 + 0.10) =$121

or 100 X (1 +0.10)2

In three years $121 X (1 + 0.10) =$133

or 100 X (1 + 0.10)3

In n years

$100 X (1 + i)n

DISCOUNTING THE FUTURE

PRESENT VALUE

( 1 + i ) n

• Having $100 today as having $110 a year from now or $121 two

years from now (of course, as long as you are sure that the

borrower will pay you back).

✓ This process is called discounting the future.P V = t o d a y ‘ s ( p r e s e n t )v a l u e

C F = f u t u r e c a s h f l o w ( p a y m e n t )

i = the interestC F

P V =

• The amounts you would have at the end of each year bymaking

the $100 loan today can be seen in the followingtimeline:

Present Value of Cash Flows: Example

What is the present value of $250 to be paid in two years if the interest rate is 15%?

FOUR TYPES OF CREDIT MARKET

INSTRUMENTS

• Simple Loan

• Fixed Payment Loan

• Coupon Bond

• Discount Bond

TYPES OF CREDIT MARKET INSTRUMENTS-

CONTINUED4-9

The simple loan: ,which we have already discussed , the lender provides the

borrower with an amount of funds (called the principal) that must be repaid

to the lender at the maturity date, along with an additional payment for the

interest.

• For example, commercial loans to businesses.


CONTINUED

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4-8

• Fixed-payment loan: the lender provides the borrower with an amount of funds,

which must be repaid by making the same payment every period (such as a

month) consisting of part of the principal and interest for a set number of years.

• For example, if you borrowed $1000 for 5 years, and the interest rate is 10%, a

fixed-payment loan might require you to pay $300 every year for 5 years.

• Instalment loans and mortgages are frequently of the fixed- payment type.


CONTINUED

• A coupon bond pays the owner of the bond a fixed interest

payment (coupon payment) every year until the maturity date,

when a specified final amount (face value or par value) is repaid.

• Face value is the nominal value or dollar value of a security

stated by the issuer.

• A coupon bond with $1000 face value, for example, might pay

you a coupon payment of $100 per year for ten years and at the

maturity date repay you the face value amount of $1000.

A coupon bond is identified by three pieces of information

1.First is the corporation or government agency that issues the bond.

2. Second is the maturity date of the bond.

3.Third is the bond’s coupon rate, The dollar amount of the yearly coupon payment

expressed as a percentage of the face value of the bond.

In our example, the coupon bond has a yearly coupon payment of $100 and a face value

of $1,000. The coupon rate is then $100/$1,000 = 0.10, or 10%.

Capital market instruments such as U.S. Treasury bonds and notes and corporate bonds

are examples of coupon bonds.


CONTINUED

4-10

• Discount bond (a zero-coupon bond): is bought at a price below its face value (at a

discount), and the face value is repaid at the maturity date.

• discount bond does not make any interest payments; it just pays off the face value.

• For example, a discount bond with a face value of $1000 might be bought for $900

and in a year s time the owner would be repaid the face value of $1000.

• Canadian government treasury bills and long-term zero-coupon bonds are examples

of discount bonds.

These four types of instruments require payments at different times

1. Simple loans and discount bonds make payment only at their

maturity dates.

2. Fixed- payment loans and coupon bonds have payments

periodically until maturity.

How would you decide which of these instruments would provide you with more income?

With an interest rate of 6 percent, the present value of $100 next year

is approximately

A) $106.

B) $100.

C) $94.

D) $92.

4-21 © 2013 Pearson Education, Inc. All rights reserved.


What is the present value of $500.00 to be paid in two years if the

interest rate is 5 percent?A) $453.51

B) $500.00

C) $476.25

D) $550.00



1. A credit market instrument that provides the borrower with

an amount of funds that must be repaid at the maturity

date along with an interest payment is known as a


A) simple loan.

C) coupon bond.

B) fixed-payment loan.

D) discount bond.

2. A credit market instrument that requires the borrower to

make the same payment every period until the maturity date is

known as a

A) simple loan.

C) coupon bond.

B) fixed-payment loan.

D) discount bond.

A credit market instrument that pays the owner a fixed coupon payment every year until the maturity date and then repays the face value is called aA) simple loan.B) fixed-payment loan.C) coupon bond.D) discount bond.

A credit market instrument that repays the face value to the owner at the maturity date is called aA) simple loan.B) fixed-payment loan.C) coupon bond.D) discount bond.

• How would you decide which of these instruments provides

you with more income? They all seem so different because

they make payments at different times.

• To solve this problem, we use the concept of present value to

provide us with a procedure for measuring interest rates on

these different types of instruments.

4-27

MEASURING OF INTEREST RATES


flow

• The yield to maturity is the most accurate measure of interest rates.

• Yield to maturity (YTM): is the total expected return of a Debt

instrument if it is held until the end of its lifetime.

• YTM is the interest rate that equates the present value of cash

payments received from a debt instrument with its value today.

• Different debt instruments have very different cash payments to the

holder (known as cash flows) with very different timing.

MEASURING INTEREST RATES

4-29

• Present Value (or present discounted value):

• A dollar paid to you one year from now is less valuablethan a dollar

paid to you today. Why?

• You can deposit a dollar in a savings account that earns interest and

have more than a dollar in oneyear.

– After 1 year: you will have $1 ×(1+i).

➢ Example: if you deposit $1000 and interest rate = 10%

– After 1 year: you will have $1000 ×(1+10%)=

1000+100=1100

YIELD TO MATURITY (YTM)


✓ Economists consider YTM the most accurate measure of

interest rates.

✓ To understand yield to maturity better, we look at how it is

calculated for the four types of credit market instruments.

✓ In all these examples, the key to understanding the

calculation of the YTM is equating today’s value of the debt

instrument with the present value of all of its future cash

flows.

YIELD TO MATURITY (YTM)- CONTINUED

SIMPLE LOAN

4-27

• The YTM on a simple loan is easy to calculate.

• For the one-year loan we discussed, today’s value is $100, and

the payments in one year’s time would be $110 (the

repayment of $100 + the interest payment of $10).

• We can use this information to solve for the YTM i by

recognizing that the present value of the future payments

must equal today’s value of a loan.

• For the simple loan the YTM = the simple interest rate

If Pete borrows $100 from his sister and next year she wants

$110 back from him, what is the yield to maturity on this loan?

simple loan the YTM Example


SOLUTION

YIELD TO MATURITY (YTM)- CONTINUED

FIXED-PAYMENT LOAN

• The borrower makes the same payment to the bank every month

until the maturity date, when the loan will be completely paid off.

• we follow the same strategy we used for the simple loan we equate

today’s value of the loan with its present value.

• Because the fixed-payment loan involves more than one cash flow

payment, the present value of the fixed-payment loan is calculated

as the sum of the present values of all payments (using Equation 1).

LV = loan value

FP = fixed yearly payment

n = number of years until maturity


SOLUTION


TO CALCULATE THE FIXED PAYMENT, WE NEED TO USE THE

FINANCIAL CALCULATOR https://www.calculator.net/loan-

calculator.html


To find the yearly payment for the loan using a financial calculator:

n = number of years = 20PV = amount of the loan (LV) = -100,000 FV = amount of the loan after 20 years = 0i = annual interest rate = .07 Then push the PMT button = fixed yearly payment (FP) = $9,439.29.

https://www.calculator.net/loan-calculator.html

Coupon Bond

➢ To calculate the yield to maturity for a coupon bond, follow the same strategy used for the fixed-payment loan

➢ Present value of the bond is calculated as the sum of the present values of all the coupon payments plus the present value of the final payment of the face value of the bond.

Where P = price of coupon bondC = yearly coupon payment F = face value of the bond n = years to maturity date

RELATIONSHIP BETWEEN PRICE AND YIELDTO MATURITY

▪ Three interesting facts in Table 3.1

1. When the coupon bond is priced at its face value, the yield to maturity equals the coupon rate.

2. The price of a coupon bond and the yield to maturity are negatively related; that is, as the yield to

maturity rises, the price of the bond falls. If the yield to maturity falls, the price of the bond rises.

3. The yield to maturity is greater than the coupon rate when the bond price is below its face value.

The yield-to-maturity calculation for a discount bond is similar to that for the simple loan.

DISCOUNT B O N D

Let’s consider a discount bond such as a one-year U.S. Treasury bill, which pays a face value of $1,000 in one year’s time. If the current purchase price of this bill is $900, then equating this price to the present value of the $1,000 received in one year,

$900 = $1,000 / 1+i

DISCOUNT BOND

For any one year discountbond

i = F - P

P

F = Face value of the discountbond

P = current price of the discount bond

The yield to maturity equals the increase

in price over the year divided by the initialprice.

As with a coupon bond, the yield to maturity is

negatively related to the current bondprice.


THE DISTINCTION BETWEEN REAL AND

NOMINAL INTEREST RATES


FIGURE 1 REAL AND NOMINAL INTEREST RATES

(THREE-MONTH TREASURY BILL), 1953–2011


Sources: Nominal rates from www.federalreserve.gov/releases/H15 and inflation from ftp://ftp.bis.gov/special.requests/cpi/cpia.txt. The real rate is constructed using the procedure outlined in Frederic S. Mishkin, “The Real Interest Rate: An Empirical Investigation,” Carnegie-Rochester Conference Series on Public Policy 15 (1981): 151–200. This procedure involves estimating expected inflation as a function of past interest rates, inflation, and time trends and then subtracting the expected inflation measure from the nominal interest rate.

http://www.federalreserve.gov/releases/H15and

• Would it make sense to buy a house when mortgage rates are 14% and

expected inflation is 15%?

Even though the nominal rate for the mortgage appears high, the real cost of borrowing

the funds is -1%.Yes,under this circumstance it would be reasonable to make this purchase.

1) The concept of is based on the common-sense notion

that a dollar paid to you in the future is less valuable to you than a

dollar today.

A) present value

B) future value

C) interest

D) deflation

2) The present value of an expected future payment as

the interest rate increases.

A) falls

B) rises

C) is constant

D) is unaffected


5)A pays the owner a fixed coupon payment every

year until the maturity date, when the value is repaid.

A) coupon bond; discount

B) discount bond; discount

C) coupon bond; face

D) discount bond; face

6) If a $5,000 coupon bond has a coupon rate of 13 percent, then

the coupon payment every year is

A) $650.

B) $1,300.

C) $130.

D) $13.


future payment


3) An increase in the time to the promised

the present value of the payment.

A) decreases

B) increases

C) has no effect on

D) is irrelevant to

4) To claim that a lottery winner who is to receive $1 million per

year for twenty years has won $20 million ignores the process of

A) face value.

B) par value.

C) deflation.

D) discounting the future.

7)For a 3-year simple loan of $10,000 at 10 percent, the amount

to be repaid is

A) $10,030.

B) $10,300.

C) $13,000.

D) $13,310.

8) The present value of a fixed-payment loan is calculated as the

of the present value of all cash flow payments.

A) sum

B) difference

C) multiple

D) log


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What Do Interest Rates Mean and What IsTheir Role in