Chapter 7 - The Valuation and Characteristics of Bonds

Valuation

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

value

THE BASIS OF VALUE

–

–

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

it.

–

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

3

The Basis of Value

Investing

Return

Using a resource to benefit the future

rather than for current satisfaction

What the investor receives for making an

investment

–

–

Putting money to work to earn more

money

Common types of investments

Debt

–

–

1 year investments

received / $ invested

return = $

Debt investors receive interest. Equity

investors get dividends + price change

Equity

4

Definition

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

Interest

5

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 =

FV1

(1 + k)

The Basis for Value

Discount Rate

The term discounted rate is often

used for interest rate

Returns on Longer-Term Investments

8

Bonds

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

agreement

9

Bond Terminology and Practice

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

returned

A bond’s face (or par) value represents the amount the firm intends to borrow

(the principal) at the coupon rate of interest

10

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

11

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?

12

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

directions

opposite

13

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.

14

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%.?

15

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 ]

16

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

17

Figure 7-2 Bond Cash Flow and

Valuation Concepts

18

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.

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%.

21

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

22

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

23

Figure 7.3 Price Progression with

Constant Interest Rate

24

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

calculator.

25

Valuation

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

value

THE BASIS OF VALUE

–

–

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

it.

–

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

3

The Basis of Value

Investing

Return

Using a resource to benefit the future

rather than for current satisfaction

What the investor receives for making an

investment

–

–

Putting money to work to earn more

money

Common types of investments

Debt

–

–

1 year investments

received / $ invested

return = $

Debt investors receive interest. Equity

investors get dividends + price change

Equity

4

Definition

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

Interest

5

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 =

FV1

(1 + k)

The Basis for Value

Discount Rate

The term discounted rate is often

used for interest rate

Returns on Longer-Term Investments

8

Bonds

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

agreement

9

Bond Terminology and Practice

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

returned

A bond’s face (or par) value represents the amount the firm intends to borrow

(the principal) at the coupon rate of interest

10

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

11

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?

12

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

directions

opposite

13

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.

14

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%.?

15

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 ]

16

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

17

Figure 7-2 Bond Cash Flow and

Valuation Concepts

18

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.

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%.

21

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

22

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

23

Figure 7.3 Price Progression with

Constant Interest Rate

24

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

calculator.

25

## Practical financial manaegment lasher 7th ed chapter 01 foundattions

## Practical financial manaegment lasher 7th ed chapter 02

## Practical financial manaegment lasher 7th ed chapter 03

## Practical financial manaegment lasher 7th ed chapter 04

## Practical financial manaegment lasher 7th ed chapter 05

## Practical financial manaegment lasher 7th ed chapter 06

## Practical financial manaegment lasher 7th ed chapter 07

## Practical financial manaegment lasher 7th ed chapter 08

## Practical financial management lasher 7th ed chapter 09

## Practical financial management lasher 7th ed chapter 010

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