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Practical financial managment 7e LASHER chapter 7

Chapter 7 - The Valuation and Characteristics of Bonds

A systematic process through which the price at which a security should sell is established - Intrinsic

Real assets (houses, cars) have value due to services they provide
Financial assets (paper) represent rights to future cash flows
Value today is PV

Different opinions about securities’ values come from different assumptions about cash flows and
interest rates

Stocks are hardest to value because future dividends and prices are never guaranteed.

The Basis of Value

Any security’s value is the present value of the cash flows expected from owning

A security should sell for close to that value in financial markets


The Basis of Value



Using a resource to benefit the future
rather than for current satisfaction

What the investor receives for making an

Putting money to work to earn more
Common types of investments

1 year investments
received / $ invested

return = $

Debt investors receive interest. Equity
investors get dividends + price change




The rate of return on an investment is the interest rate that equates the present
value of its expected cash flows with its current price
Return is also known as

Yield, or


Return On One Year Investment

Return is what the investor receives
Can be expressed as a dollar amount or as a rate
Rate of return is what the investor receives divided by what was invested
For debt investments: the interest rate
In terms of the time value of money:
Invest PV at rate k and receive future cash flows of
principal = PV, and
interest = kPV
at the end of a year, so
FV1 = PV + kPV
FV1 = PV(1+k)

PV =

(1 + k)

The Basis for Value

Discount Rate
The term discounted rate is often
used for interest rate

Returns on Longer-Term Investments



Bonds represent a debt relationship in which an issuing company borrows and
buyers lend.

A bond issue represents borrowing from many lenders at one time under a single


Bond Terminology and Practice

A bond’s term (or maturity) is the time from the present until the principal is

A bond’s face (or par) value represents the amount the firm intends to borrow
(the principal) at the coupon rate of interest


Coupon Rates

Coupon Rate – the fixed rate of interest paid by a bond
In the past, bonds had “coupons” attached, today they are “registered”
Most bonds pay coupon interest semiannual


Bond Valuation—Basic Ideas

Adjusting to Interest Rate Changes

Bonds are originally sold in the primary market and trade subsequently among investors
in the secondary market.
Although bonds have fixed coupons, market interest rates constantly change.
How does a bond paying a fixed interest rate remain salable (secondary market) when
interest rates change?


Bond Valuation—Basic Ideas

Bonds adjust to changing yields by changing their prices

Selling at a Premium – bond price above face value
Selling at a Discount – bond price below face value

Bond prices and interest rates move in



Determining the Price of a Bond

The value (price) of a security is equal to the present value of the cash flows
expected from owning it.
In bonds, the expected cash flows are predictable.

Interest payments are fixed, occurring at regular intervals.
Principal is returned along with the last interest payment.


Determining the Price of a Bond
Figure 7-1 Cash Flow Time Line for a Bond

This bond has 10 years until maturity, a par value of $1,000, and a coupon rate of 10%.?


Determining the Price of a Bond

The Bond Valuation Formula

The price of a bond is the present value of a stream of interest payments plus the present
value of the principal repayment

PB = PV(interest payments) + PV(principal repayment)
1 4 4 44 2 4 4 4 43
1 4 4 4 44 2 4 4 4 4 43
Interest payments are annuities--can use
the present value of an annuity form ula:
PMT[PVFA k,n ]

Principal repayment is a lump sum in the
future--can use the future value formula:
FV[PVFk, n ]


Determining the Price of a Bond

Two Interest Rates and One More

Coupon Rate
k - the current market yield on comparable bonds
“Current yield” - annual interest payment divided by bond’s current price

Not used in valuation
Info for investors


Figure 7-2 Bond Cash Flow and
Valuation Concepts


Concept Connection Example 7-1
Finding the Price of a Bond

Emory issued a $1,000, 8%, 25-year bond 15 years ago.
Comparable bonds are yielding 10% today.
What price will yield 10% to buyers today?

What is the bond’s current yield?

Assume the bond pays interest semiannually.

Concept Connection Example 7-1
Finding the Price of a Bond

Must solve for present value of bond’s expected cash flows at today’s interest rate. Use Equation 7.4 :

k represents the periodic current market interest

PB = PMT[PVFA k, n ] + FV[PVFk, n ]

rate, or
10% ÷ 2 = 5%

The payment is 8% x $1,000,
or $80 annually. However, it

n represents the number of

is received in the form of $40
every six months.

The future value is the principal
repayment of $1,000.

interest-paying periods until
maturity, or
10 years x 2 = 20.


Concept Connection Example 7-1
Finding the Price of a Bond

Substituting :

PB = $40[PVFA 5%, 20 ] + $1,000[PVF5%, 20 ]
= $40[12.4622] + $1,000[0.3769]
= $498.49 + $376.90
= $875.39

This is the price at
which the bond must sell
to yield 10%. It is
selling at a discount because
the current interest rate
is above the coupon rate.
The bond’s current yield is
$80 ÷ $875.39, or 9.14%.


Maturity Risk Revisited

Related to the term of the debt

Longer term bond prices fluctuate more in response to changes in interest rates than
shorter term bonds

AKA price risk and interest rate risk


Table 7-1 Price Changes at Different Terms Due to an Interest Rate Increase from 8% to 10%


Figure 7.3 Price Progression with
Constant Interest Rate


Finding the Yield at a Given Price

Calculate a bond’s yield assuming it is selling at a given price
Trial and error – guess a yield – calculate price – compare to price given

PB = PMT PVFA k, n  + FV PVFk, n 
Involves solving for k, which is more complicated
because it involves both an annuity and a FV

Use trial and error to solve for k, or use a financial


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