Posted: August 3rd, 2022

go to the university library and perform research on an applied case that brings the concepts learned in any chapter (or multiple) of the ones covered in this class. Make sure you read the course objectives and assure you satisfy at least one of them. Cite the case, add it as an attachment, and provide a write-up connecting the case with concepts learned. The case should be from additional resources different from the book used for this class.

You can access research cases or papers in related manners, it can be a peer-reviewed article, journal, or corporate filings like 10K or 10Q.

The length is up to you. Master level quality is expected

class name Applied Managerial Finance

Chapter 7

Equity Markets and Stock Valuation

SLO: Synthesize and apply financial data to Bonds and Stock Valuations

©2020 McGraw-Hill Education. All rights reserved. Authorized only for instructor use in the classroom. No reproduction or further distribution permitted without the prior written consent of McGraw-Hill Education.

1

Key Concepts and Skills

Understand how stock prices depend on future dividends and dividend growth.

Be able to compute stock prices using the dividend growth model.

Understand how corporate directors are elected.

Understand how stock markets work.

Understand how stock prices are quoted.

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Chapter Outline

7.1 Common Stock Valuation.

7.2 Some Features of Common and Preferred Stock.

7.3 The Stock Markets.

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Cash Flows for Stockholders

If you own a share of stock, you can receive cash in two ways.

The company pays dividends.

You sell your shares, either to another investor in the market or back to the company.

As with bonds, the price of the stock is the present value of these expected cash flows.

Dividends → cash income.

Selling → capital gains.

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One-Period Example 1

Suppose you are thinking of purchasing the stock of Moore Oil, Inc.

You expect it to pay a $2 dividend in one year.

You believe you can sell the stock for $14 at that time.

You require a return of 20% on investments of this risk.

What is the maximum you would be willing to pay?

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One-Period Example 2

D1 = $2 dividend expected in one year.

R = 20%.

P1 = $14.

CF1 = $2 + $14 = $16.

Compute the PV of the expected cash flows.

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Two-Period Example

What if you decide to hold the stock for two years?

D1 = $2.00 CF1 = $2.00.

D2 = $2.10.

P2 = $14.70.

Now how much would you be willing to pay?

CF2 = $2.10 + $14.70 = $16.80

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Three-Period Example

What if you decide to hold the stock for three years?

D1 = $2.00 CF1 = $2.00.

D2 = $2.10 CF2 = $2.10.

D3 = $2.205.

P3 = $15.435.

Now how much would you be willing to pay?

CF3 = $2.205 + $15.435 = $17.640

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Three-Period Example

Using TI BAII + Cash Flow Worksheet

Cash Flows:

CF0 = 0

CF1 = 2.00

CF2 = 2.10

CF3 = 17.64

Display You Enter

CF

C00 0 Enter, Down

C01 2 Enter, Down

F01 1 Enter, Down

C02 2.10 Enter, Down

F02 1 Enter, Down

C03 17.64 Enter, Down

F03 1 Enter, Down NPV

I 20 Enter, Down CPT

NPV 13.33

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Developing the Model

You could continue to push back when you would sell the stock.

You would find that the price of the stock is really just the present value of all expected future dividends.

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Stock Value = PV of Dividends

How can we estimate all future dividend

payments?

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Estimating Dividends Special Cases

Constant dividend/Zero Growth.

Firm will pay a constant dividend forever.

Like preferred stock.

Price is computed using the perpetuity formula.

Constant dividend growth.

Firm will increase the dividend by a constant percent every period.

Supernormal growth.

Dividend growth is not consistent initially, but settles down to constant growth eventually.

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Zero Growth

Dividends expected at regular intervals

forever = perpetuity.

P0 = D / R

Suppose stock is expected to pay a $0.50 dividend every quarter and the required return is 10% with quarterly compounding. What is the price?

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Constant Growth Stock

One whose dividends are expected togrow forever at a constant rate, g.

D1 = D0(1 + g)1

D2 = D0(1 + g)2

Dt = D0(1 + g)t

D0 = Dividend JUST PAID.

D1 to Dt = Expected dividends.

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Projected Dividends

D0 = $2.00 and constant g = 6%.

D1 = D0(1+g) = 2(1.06) = $2.12.

D2 = D1(1+g) = 2.12(1.06) = $2.2472.

D3 = D2(1+g) = 2.2472(1.06) = $2.3820.

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Dividend Growth Model

“Gordon Growth Model”

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DGM: Example 1

Suppose Big D, Inc. just paid a dividend of $.50. It is expected to increase its dividend by 2% per year. If the market requires a return of 15% on assets of this risk, how much should the stock be selling for?

D0= $0.50

g = 2%

R = 15%

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DGM: Example 2

Suppose TB Pirates, Inc. is expected to pay a $2 dividend in one year. If the dividend is expected to grow at 5% per year and the required return is 20%, what is the price?

D1 = $2.00

g = 5%

r = 20%

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Stock Price Sensitivity to Dividend Growth, g

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Stock Price Sensitivity to Required Return, R

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Example 7.3

Gordon Growth Company I

Gordon Growth Company is expected to pay a dividend of $4 next period and dividends are expected to grow at 6% per year. The required return is 16%.

What is the current price?

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Example 7.3

Gordon Growth Company II 1

What is the price expected to be in year 4?

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Example 7.3

Gordon Growth Company II 2

What is the implied return given the change in price during the four year period?

50.50 = 40(1 + return)4; return = 6%

4 N; −40 PV; 50.50 FV; 0 PMT; CPT I/Y = 6%

The price grows at the same rate as dividends.

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Constant Growth Model Conditions

Dividend expected to grow at g forever.

Stock price expected to grow at g forever.

Expected dividend yield is constant.

Expected capital gains yield is constant and

equal to g.

Expected total return, R, must be > g.

Expected total return (R):

= expected dividend yield (DY).

+ expected growth rate (g).

= dividend yield + g.

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Nonconstant Growth

Suppose a firm is expected to increase dividends by 20% in one year and by 15% in two years. After that dividends will increase at a rate of 5% per year indefinitely. If the last dividend was $1 and the required return is 20%, what is the price of the stock?

Remember that we have to find the PV of all expected future dividends.

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Nonconstant Growth – Solution

Compute the dividends until growth levels off.

D1 = 1(1.2) = $1.20.

D2 = 1.20(1.15) = $1.38.

D3 = 1.38(1.05) = $1.449.

Find the expected future price at the beginning of the constant growth period:

P2 = D3 / (R – g) = 1.449 / (.2 − .05) = 9.66.

Find the present value of the expected future cash flows.

P0 = 1.20 / (1.2) + (1.38 + 9.66) / (1.2)2 = 8.67.

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Nonconstant + Constant Growth 1

Basic PV of all Future Dividends Formula

Dividend Growth Model

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Nonconstant + Constant Growth 2

+

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Nonconstant Growth Followed by Constant Growth

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Quick Quiz: Part 1

What is the value of a stock that is expected to pay a constant dividend of $2 per year if the required return is 15%?

What if the company starts increasing dividends by 3% per year beginning with the next dividend? The required return remains at 15%.

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Using the DGM to Find R

Start with the DGM:

Rearrange and solve for R:

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Finding the Required Return

Example 1

A firm’s stock is selling for $10.50. They just paid a $1 dividend and dividends are expected to grow at 5% per year.

What is the required return?

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Finding the Required Return

Example 2

P0 = $10.50.

D0 = $1.

g = 5% per year.

What is the required return?

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Finding the Required Return

Example 3

P0 = $10.50.

D0 = $1.

g = 5% per year.

What is the dividend yield?

1(1.05) / 10.50 = 10%.

What is the capital gains yield?

g = 5%.

Dividend Yield

Capital Gains

Yield

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Valuation Using Multiples

For stocks that don’t pay dividends (or have erratic dividend growth rates), we can value them using the price-earnings (PE) ratio and/or the price-sales ratio:

Price at time t = Pt

= Benchmark PE ratio × Earnings per sharet

Price at time t = Pt

= Benchmark price-sales ratio × Sales per sharet

The price-sales ratio can be especially useful when earnings are negative.

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Valuation Using Multiples

Example

Suppose we are trying to value the company Inactivision, a video game developer that does not pay dividends. If the appropriate industry PE for this type of company is 20 and you predict earnings to be $2.50 per share for the coming year, then the forecasted stock price for a year from now, or target price, is the following:

Target price = 20 × $2.50 = $50

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Table 7.1

TABLE 7.1 Summary of stock valuation

The general case

In general, the price today of a share of stock, P0, is the present value of all of its future dividends, D1, D2, D3, … :

where R is the required return.

Constant growth case

If the dividend is constant and equal to D, then the price can be written as:

If the dividend grows at a steady rate g, then the price can be written as:

This result is called the dividend growth model.

Nonconstant Growth

If the dividend grows steadily after t periods, then the price can be written as:

where:

The required return, R, can be written as the sum of two things:

R = D1 / P0 + g

where D1/P0 is the dividend yield and g is the capital gains yield (which is the same thing as the growth rate in dividends for the steady growth case).

Valuation Using Comparables

For stocks that don’t pay dividends (or have erratic dividend growth rates), we can value them using the PE ratio and/or the price-sales ratio:

Pt = Benchmark PE ratio × EPSt

Pt = Benchmark price – sales ratio × Sales per sharet

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Features of Common Stock 1

Voting Rights.

Stockholders elect directors.

Cumulative voting versus Straight voting.

Boards are often staggered, or “classified.”

Proxy voting.

Classes of stock.

Founders’ shares.

Class A and Class B shares.

Return to Quick Quiz

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Features of Common Stock 2

Other Rights.

Share proportionally in declared dividends.

Share proportionally in remaining assets during liquidation.

Preemptive right.

Right of first refusal to buy new stock issue to maintain proportional ownership if desired.

Return to Quick Quiz

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Dividend Characteristics

Dividends are not a liability of the firm until declared by the Board of Directors.

A firm cannot go bankrupt for not declaring dividends.

Dividends and Taxes.

Dividends are not tax deductible for firm.

Taxed as ordinary income for individuals.

Dividends received by corporations have a minimum 70% exclusion from taxable income.

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Features of Preferred Stock

Dividends.

Must be paid before dividends can be paid to common stockholders.

Not a liability of the firm.

Can be deferred indefinitely.

Most preferred dividends are cumulative.

Missed preferred dividends have to be paid before common dividends can be paid.

Preferred stock generally does not carry voting rights.

Return to Quick Quiz

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The Stock Markets

Primary versus Secondary Markets.

Primary = new-issue market.

Secondary = existing shares traded among investors.

Dealers versus Brokers.

Dealer: Maintains an inventor.

Ready to buy or sell at any time.

Think “Used car dealer.”

Broker: Brings buyers and sellers together.

Think “Real estate broker.”

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New York Stock Exchange (NYSE)

NYSE.

Merged with Euronext in 2007.

NYSE Euronext merged with the American Stock Exchange in 2008.

Members (Historically).

Buy a trading license (own a seat).

Designated market makers, DMMs (formerly known as “specialists”).

Floor brokers.

Supplemental liquidity providers (SLPs).

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NYSE Operations

Operational goal = attract order flow.

NYSE DMMs:

Assigned broker/dealer.

Each stock has one assigned DMM.

All trading in that stock occurs at the “DMM’s post.”

Trading takes place between customer orders placed with the DMMs and “the crowd.”

“Crowd”= Floor brokers and SLPs.

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NASDAQ

NASDAQ OMX (merged 2007).

Computer-based quotation system.

Multiple market makers.

Electronic Communications Networks.

Three levels of information.

Level 1 – median quotes, registered representatives.

Level 2 – view quotes, brokers & dealers.

Level 3 – view and update quotes, dealers only.

Large portion of technology stocks.

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ECNs

Electronic Communications Networks provide direct trading among investors.

Developed in late 1990s.

ECN orders transmitted to NASDAQ.

Observe live trading online at Batstrading.com.

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Reading Stock Quotes

What information is provided in the stock quote?

Click on this link to go to Bloomberg for current stock quotes.

Access the text alternative for these images

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Work the Web

Not only are stock price quotes readily available online. Some online trading sites display their “order book” or “limit order book” live online.

The BATS Exchange was one of these websites until it was purchased by the CBOE in 2016.

Follow this link to see current buy and sell orders for Microsoft (MSFT).

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Quick Quiz: Part 2 1

You observe a stock price of $18.75. You expect a dividend growth rate of 5% and the most recent dividend was $1.50. What is the required return?

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Quick Quiz: Part 2 2

What are some of the major characteristics of common stock? (Slide 38 and Slide 39).

What are some of the major characteristics of preferred stock? (Slide 41).

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Chapter 7

END

©2020 McGraw-Hill Education. All rights reserved. Authorized only for instructor use in the classroom. No reproduction or further distribution permitted without the prior written consent of McGraw-Hill Education.

Accessibility Content:

Text Alternatives for Images

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Reading Stock Quotes Text Alternative

Data are listed and graphed and include previous close, open, bid, ask, day’s range, 52-week range, ex-dividend date, and so on.

Return to slide containing original image

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Chapter 6

Interest Rates and Bond Valuation

SLO: Synthesize and apply financial data to Bonds and Stock Valuations

©2020 McGraw-Hill Education. All rights reserved. Authorized only for instructor use in the classroom. No reproduction or further distribution permitted without the prior written consent of McGraw-Hill Education.

1

Key Concepts and Skills

After studying this chapter, you should be able to:

Identify important bond features and types of bonds.

Describe bond values and why they fluctuate.

Discuss bond ratings and what they mean.

Evaluate the impact of inflation on interest rates.

Explain the term structure of interest rates and the determinants of bond yields.

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Chapter Outline

6.1 Bonds and Bond Valuation.

6.2 More on Bond Features.

6.3 Bond Ratings.

6.4 Some Different Types of Bonds.

6.5 Bond Markets.

6.6 Inflation and Interest Rates.

6.7 Determinants of Bond Yields.

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Bond Definitions

Bond.

Debt contract.

Interest-only loan.

Par value (face value) approximately $1,000.

Coupon rate.

Coupon payment.

Maturity date.

Yield to maturity.

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Key Features of a Bond 1

Par value:

Face amount.

Re-paid at maturity.

Assume $1,000 for corporate bonds.

Coupon interest rate:

Stated interest rate.

Usually = YTM at issue.

Multiply by par value to get coupon payment.

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Key Features of a Bond 2

Maturity:

Years until bond must be repaid.

Yield to maturity (YTM):

The market required rate of return for bonds of similar risk and maturity.

The discount rate used to value a bond.

Return if bond held to maturity.

Usually = coupon rate at issue.

Quoted as an APR.

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Bond Value

Bond Value = PV(coupons) + PV(par).

Bond Value = PV(annuity) + PV(lump sum)

Remember:

As interest rates increase present values decrease.

( r → PV )

As interest rates increase, bond prices decrease

and vice versa.

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The Bond-Pricing Equation

PV(Annuity)

PV(lump sum)

C = Coupon payment; F = Face value

Return to Quiz

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Texas Instruments BA-II Plus

N = number of periods to maturity.

I/Y = period interest rate = YTM.

PV = present value = bond value.

PMT = coupon payment.

FV = future value = face value = par value.

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Spreadsheet Formulas

=FV(Rate,Nper,Pmt,PV,0/1).

=PV(Rate,Nper,Pmt,FV,0/1).

=RATE(Nper,Pmt,PV,FV,0/1).

=NPER(Rate,Pmt,PV,FV,0/1).

=PMT(Rate,Nper,PV,FV,0/1).

Inside parens: (RATE,NPER,PMT,PV,FV,0/1).

“0/1” Ordinary annuity = 0 (default).

Annuity Due = 1 (must be entered).

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Pricing Specific Bonds on the TI BAII+

Bond Worksheet: 2nd BOND (above “9”).

SDT CPN RDT RV ACT 2/Y YLD PRI.

SDT = Actual Settlement date (enter MM.DDYY).

CPN = Annual rate in %.

RDT = Actual Redemption (maturity) date.

RV = Redemption value as a % of par.

ACT = ACT/360 day count setting.

2/Y = 2/Y – 1/Y coupons per year.

YLD = Yield to redemption.

PRI = Dollar price per $100 of par value.

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Pricing Specific Bonds in Excel

=PRICE(Settlement,Maturity,Rate,Yld,Redemption, Frequency,Basis).

=YIELD(Settlement,Maturity,Rate,Pr,Redemption, Frequency,Basis).

Settlement = actual date as a serial number.

Maturity = actual date as a serial number.

Redemption and Pr(ice) = % of par value.

Rate (coupon) and Yld = annual rates as decimals.

Frequency = # of coupons per year.

Basis = day count convention (enter “2” for ACT/360).

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Valuing a Discount Bond with Annual Coupons

Coupon rate = 10%

Annual coupons

Par = $1,000

Maturity = 5 years

YTM = 11%

5 N

11 I/Y

100 PMT

1000 FV

CPT PV = − 963.04

Using the calculator:

Using the formula:

B = PV(annuity) + PV(lump sum)

B = 369.59 + 593.45 = 963.04

Using Excel: =PV(0.11, 5, 100, 1000, 0)

Note: When YTM > Coupon rate Price < Par = “Discount Bond”
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Valuing a Premium Bond with Annual Coupons
Coupon rate = 10%
Annual coupons
Par = $1,000
Maturity = 20 years
YTM = 8%
20 N
8 I/Y
100 PMT
1000 FV
CPT PV = − 1196.36
Using the calculator:
Using the formula:
B = PV(annuity) + PV(lump sum)
B = 981.81 + 214.55 = 1196.36
Using Excel: =PV(0.08, 20, 100, 1000, 0)
Note: When YTM < Coupon rate Price > Par = “Premium Bond”

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Graphical Relationship Between Price and Yield-to-Maturity

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Bond Prices: Relationship

Between Coupon and Yield

Coupon rate = YTM Price = Par.

Coupon rate < YTM Price < Par.
“Discount bond” … Why?
Coupon rate > YTM Price > Par.

“Premium bond” … Why?

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Bond Value ($) versus Years Remaining to Maturity

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The Bond-Pricing Equation

Adjusted for Semiannual Coupons

C = Annual coupon payment C/2 = Semi-annual coupon

YTM = Annual YTM (as an APR) YTM/2 = Semi-annual YTM

t = Years to maturity 2t = Number of 6-month

periods to maturity

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Semiannual Bonds

Example 6.1

Coupon rate = 14% − Semiannual.

YTM = 16% (APR).

Maturity = 7 years

Number of coupon payments? (2t or N).

14 = 2 × 7 years.

Semiannual coupon payment? (C/2 or PMT).

$70 = (14% × Face Value)/2.

Semiannual yield? (YTM/2 or I/Y).

8% = 16%/2

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Example 6.1

Semiannual coupon = $70.

Semiannual yield = 8%.

Periods to maturity = 14.

Bond value =

70[1 – 1/(1.08)14] / .08 + 1000 / (1.08)14 = 917.56.

Using Excel: =PV(0.08, 14, 70, 1000, 0).

Using the calculator:

14 N

8 I/Y

70 PMT

1000 FV

CPT PV = −917.56

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Interest Rate Risk 1

Price Risk.

Change in price due to changes in interest rates.

Long-term bonds have more price risk than short-term bonds.

Low coupon rate bonds have more price risk than high coupon rate bonds.

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Interest Rate Risk 2

Reinvestment Rate Risk.

Uncertainty concerning rates at which cash flows can be reinvested.

Short-term bonds have more reinvestment rate risk than long-term bonds.

High coupon rate bonds have more reinvestment rate risk than low coupon rate bonds.

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Figure 6.2

Access the text alternative for these images

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Computing Yield-to-Maturity (YTM)

Yield-to-maturity (YTM) = the market required rate of return implied by the current bond price

With a financial calculator,

Enter N, PV, PMT, and FV.

Remember the sign convention.

PMT and FV need to have the same sign (+).

PV the opposite sign (−).

CPT I/Y for the yield.

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YTM with Annual Coupons

Consider a bond with a 10% annual coupon rate, 15 years to maturity and a par value of $1000. The current price is $928.09.

Will the yield be more or less than 10%?

15 N

1000 FV

100 PMT

CPT PV = 11% Result = YTM

928.09 PV (enter as a negative)

Using Excel: =RATE(15, 100, −928.09, 1000, 0).

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YTM with Semiannual Coupons 1

Suppose a bond with a 10% coupon rate and semiannual coupons, has a face value of $1000, 20 years to maturity and is selling for $1197.93.

Is the YTM more or less than 10%?

What is the semiannual coupon payment?

How many periods are there?

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YTM with Semiannual Coupons 2

Suppose a bond with a 10% coupon rate and semiannual coupons, has a face value of $1,000, 20 years to maturity and is selling for $1,197.93.

40 N

1197.93 PV (negative)

1000 FV

50 PMT

CPT PV 4% (= ½ YTM)

YTM = 4%*2 = 8%

Using Excel: =RATE(40, 50, −1197.93, 1000, 0) = 4%.

NOTE: Solving a semi-annual payer for YTM results in a 6-month yield.

The calculator & Excel solve what you enter.

©2020 McGraw-Hill Education

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Table 6.1

TABLE 6.1 Summary of bond valuation

Finding the value of a bond

Bond value = C × [1 − 1/(1 + r)t]/r + F/(1 + r)t

where:

C = Coupon paid each period

r = Rate per period

t = Number of periods

F = Bond’s face value

Finding the yield on a bond

Given a bond value, coupon, time to maturity, and face value, it is possible to find the implicit discount rate, or yield to maturity, by trial and error only. To do this, try different discount rates in the preceding formula until the calculated bond value equals the given bond value. Remember that increasing the rate decreases the bond value.

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Debt or Equity

Debt.

Not an ownership interest.

No voting rights.

Interest is tax-deductible.

Creditors have legal recourse if interest or principal payments are missed.

Excess debt can lead to financial distress and bankruptcy.

Equity.

Ownership interest.

Common stockholders vote to elect the board of directors and on other issues.

Dividends are not tax deductible.

Dividends are not a liability of the firm until declared. Stockholders have no legal recourse if dividends are not declared.

An all-equity firm cannot go bankrupt.

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The Bond Indenture

“Deed of Trust”

Contract between issuing company and

bondholders includes:

Basic terms of the bonds.

Total amount of bonds issued.

Secured versus Unsecured.

Sinking fund provisions.

Call provisions.

Deferred call.

Call premium.

Details of protective covenants.

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Bond Classifications

Registered versus Bearer Bonds.

Security.

Collateral – secured by financial securities.

Mortgage – secured by real property, normally land or buildings.

Debentures – unsecured.

Notes – unsecured debt with original maturity less than 10 years.

Seniority.

Senior versus Junior, Subordinated.

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Bond Characteristics and

Required Returns

Coupon rate.

(risk characteristics of the bond when issued).

Usually ≈ yield at issue.

Which bonds will have the higher coupon, all else equal?

Secured debt versus a debenture.

Subordinated debenture versus senior debt.

A bond with a sinking fund versus one without.

A callable bond versus a non-callable bond.

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Bond Ratings – Investment Quality

High Grade.

Moody’s Aaa and S&P AAA – capacity to pay is extremely strong.

Moody’s Aa and S&P AA – capacity to pay is very strong.

Medium Grade.

Moody’s A and S&P A – capacity to pay is strong, but

more susceptible to changes in circumstances.

Moody’s Baa and S&P BBB – capacity to pay is adequate, adverse conditions will have more impact on the firm’s ability to pay.

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Bond Ratings – Speculative

Low Grade.

Moody’s Ba, B, Caa and Ca.

S&P BB, B, CCC, CC.

Considered speculative with respect to capacity to pay. The “B” ratings are the lowest degree of speculation.

Very Low Grade.

Moody’s C and S&P C – income bonds with no interest being paid.

Moody’s D and S&P D – in default with principal and interest in arrears.

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Government Bonds 1

Municipal Securities.

Debt of state and local governments.

Varying degrees of default risk, rated similar to corporate debt.

Interest received is tax-exempt at the federal level.

Interest usually exempt from state tax in issuing state.

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Government Bonds 2

Treasury Securities = Federal government debt.

Treasury Bills (T-bills).

Pure discount bonds.

Original maturity of one year or less.

Treasury notes.

Coupon debt.

Original maturity between one and ten years.

Treasury bonds.

Coupon debt.

Original maturity greater than ten years.

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Example 6.4

A taxable bond has a yield of 8% and a municipal bond has a yield of 6%

If you are in a 40% tax bracket, which bond do you prefer?

8%(1 − .4) = 4.8%.

The after-tax return on the corporate bond is 4.8%, compared to a 6% return on the municipal.

At what tax rate would you be indifferent between the two bonds?

8%(1 − T) = 6%.

T = 25%.

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Zero Coupon Bonds

Make no periodic interest payments (coupon rate = 0%).

Entire yield-to-maturity comes from the difference between the purchase price and the par value (capital gains).

Cannot sell for more than par value.

Sometimes called zeroes, or deep discount bonds.

Treasury Bills and U.S. Savings bonds are good examples of zeroes.

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Floating Rate Bonds

Coupon rate floats depending on some index value.

Examples – adjustable rate mortgages and inflation-linked Treasuries.

Less price risk with floating rate bonds.

Coupon floats, so is less likely to differ substantially from the yield-to-maturity.

Coupons may have a “collar” – the rate cannot go above a specified “ceiling” or below a specified “floor.”

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Other Bond Types

Structured notes.

Convertible bonds.

Put bonds.

Many types of provisions can be added to a bond.

Important to recognize how these provisions affect required returns.

Who does the provision benefit?

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Bond Markets

Primarily over-the-counter transactions with dealers connected electronically.

Extremely large number of bond issues, but generally low daily volume in single issues.

Getting up-to-date prices difficult, particularly on small company or municipal issues.

Treasury securities are an exception.

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Work the Web Example

Bond information is available online.

One good site:

http://finra-markets.morningstar.com/BondCenter/Default.jsp

Click on this link to go to the site.

Use “Quick Bond Search” to observe the yields for various bond types, and the shape of the yield curve.

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Corporate Bond Quotations

ABC 8.375 Jul 15, 2033 100.641 8.316 362 30 763,528

What company are we looking at?

What is the coupon rate? If the bond has a $1000 face value, what is the coupon payment each year?

When does the bond mature?

What was the trading volume on that day?

What is the quoted price? (Ask price).

How does the bond’s yield compare to a comparable

Treasury note/bond?

8.316 = Last yield.

362 = basis point difference versus 30-yr T-Bond.

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Treasury Quotations 1

FIGURE 6.3 Sample Wall Street Journal U.S. Treasury note and bond prices

U.S. Treasury Quotes

Treasury note and bond data are representative over-the-counter quotations as of 3 p.m. Eastern time.

Maturity Coupon Bid Asked Chg Asked Yield

1/31/2019 1.500 99.5469 99.5625 −0.0078 2.205

12/31/2021 2.125 97.8906 97.9063 0.0703 2.749

1/31/2022 1.500 95.6563 95.6719 0.0547 2.762

2/28/2023 2.625 99.2109 99.2266 0.1172 2.801

9/30/2023 1.375 92.7969 92.8125 0.1172 2.847

2/29/2024 2.125 96.1172 96.1328 0.1484 2.864

7/31/2024 2.125 95.7344 95.7500 0.1172 2.887

1/31/2025 2.500 97.6328 97.6484 0.1953 2.892

4/30/2025 2.875 99.8359 99.8516 0.2109 2.899

11/15/2026 6.500 126.6406 126.6563 0.3125 2.906

2/15/2029 5.250 120.9453 121.0078 0.4063 2.941

5/15/2030 6.250 132.8984 132.9609 0.4688 2.949

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Treasury Quotations 2

FIGURE 6.3 Sample Wall Street Journal U.S. Treasury note and bond prices (Continued)

U.S. Treasury Quotes

Treasury note and bond data are representative over-the-counter quotations as of 3 p.m. Eastern time.

Maturity Coupon Bid Asked Chg Asked Yield

2/15/2036 4.500 120.9375 121.0000 0.5625 2.964

5/15/2037 5.000 129.0938 129.1563 0.6641 2.973

11/15/2039 4.375 121.3047 121.3672 0.6953 3.014

5/15/2040 4.375 121.5313 121.5938 0.7500 3.021

8/15/2041 3.750 111.6875 111.7500 0.7500 3.040

5/15/2042 3.000 99.1875 99.2188 0.7266 3.046

2/15/2043 3.125 101.1641 101.1953 0.7344 3.056

2/15/2044 3.625 110.0313 110.0625 0.6875 3.056

8/15/2046 2.250 84.6797 84.7109 0.6016 3.064

5/15/2047 3.000 98.7578 98.7891 0.6953 3.063

5/15/2048 3.125 101.1875 101.2188 0.7422 3.062

Source: www.wsj.com, 6/14/2018.

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Treasury Quotations 3

Highlighted quote in Figure 6.3.

5/15/2030 6.250 132.8984 132.9609 0.4688 2.949

When does the bond mature?

What is the coupon rate on the bond?

What is the bid price? What does this mean?

What is the ask price? What does this mean?

How much did the price change from the previous day?

What is the YTM based on Ask price?

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Treasury Quotations 4

5/15/2030 6.250 132.8984 132.9609 0.4688 2.949

Maturity = May 15, 2030.

Coupon rate = 6.250% per year.

Bid price = 132.8984% of par.

Price at which dealer is willing to buy from you.

Ask price = 132.9609% of par.

Price at which dealer is willing to sell to you.

Bid-Ask Spread = Dealer’s profit.

Change = ask price is up .4688% since the previous day.

Asked Yield = 2.949%.

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Quoted Price versus Invoice Price

Quoted bond prices = “clean” price.

Net of accrued interest.

Invoice Price = “dirty” or “full” price.

Price actually paid.

Includes accrued interest.

Accrued Interest.

Interest earned since last coupon payment is owed to bond seller at time of sale.

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Inflation and Interest Rates

Real rate of interest.

= Change in purchasing power.

Nominal rate of interest.

= Quoted rate of interest.

= Change in purchasing power and inflation.

The ex ante nominal rate of interest includes our desired real rate of return plus an adjustment for expected inflation.

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The Fisher Effect

The Fisher Effect defines the relationship between real rates, nominal rates and Inflation.

(1 + R) = (1 + r)(1 + h).

R = nominal rate (Quoted rate).

r = real rate.

h = expected inflation rate.

Approximation: R = r + h.

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Example 6.6

If we require a 10% real return and we expect inflation to be 8%, what is the nominal rate?

R = (1.1)(1.08) – 1 = .188 = 18.8%.

Approximation: R = 10% + 8% = 18%.

Because the real return and expected inflation are relatively high, there is significant difference between the actual Fisher Effect and the approximation.

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Term Structure of Interest Rates

Term structure: The relationship between time to maturity and yields, all else equal.

The effect of default risk, different coupons, etc., has been removed.

Yield curve: Graphical representation of the term structure.

Normal = upward-sloping L/T > S/T.

Inverted = downward-sloping L/T < S/T.
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Figure 6.5 A: Upward-Sloping Yield Curve
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Figure 6.5 B: Downward-Sloping Yield Curve
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Figure 6.6: Treasury Yield Curve
More information can be found at this link.
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Factors Effecting Required Return
Default risk premium – bond ratings.
Taxability premium – municipal versus taxable.
Liquidity premium – bonds that have more frequent trading will generally have lower required returns.
Maturity premium – longer term bonds will tend to have higher required returns.
Anything else that affects the risk of the cash flows to the bondholders will affect the required returns.
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Quick Quiz
How do you find the value of a bond and why do bond prices change? (Slide 6.8).
What is a bond indenture and what are some of the important features? (Slide 6.30).
What are bond ratings and why are they important? (Slide 6.33).
How does inflation affect interest rates? (Slide 6.50).
What is the term structure of interest rates? (Slide 6.52).
What factors determine the required return on bonds? (Slide 6.56).
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Chapter 6
END
©2020 McGraw-Hill Education. All rights reserved. Authorized only for instructor use in the classroom. No reproduction or further distribution permitted without the prior written consent of McGraw-Hill Education.
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Figure 6.2 Text Alternative
This graph has the interest rate (percent) on the x-axis and the bond value (in dollars) on the y-axis. The x-axis goes from zero to twenty counting by fives. The y-axis goes from zero to $2,000 counting by $500. The graph displays two intersecting curves. The curve for the 1-year bond is so slight that it almost looks like a line with a slight negative slope. If interest rates are 5%, a 1-year bond with a 10% rate has a value of $1,047.62. If interest rates are 20%, a 1-year bond with a 10% rate has a value of $916.67. The curve for a 30-year bond is much steeper. If interest rates are 5%, a 30-year bond with a 10% rate has a value of $1768.62. If interest rates are 20%, a 30-year bond with a 10% rate has a value of $502.11.
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Figure 6.5 A: Upward-Sloping Yield Curve Text Alternative
Both graphs have the x-axis labeled as "time to maturity" with no values indicated on the axis. The y-axis is labeled "interest rate" also with no labeled values. In both graphs the real rate is plotted first as a horizontal line about one-quarter of the way up the y-axis. In the upward-sloping term structure, the line indicating the inflation premium is vertically higher than the real rate, and has a positive slope, showing that inflation is anticipated to increase over time. Starting at the same location on the y-axis and increasing in a concave down fashion is a curve that describes the interest rate risk premium. As the inflation premium increases, so does the interest rate premium, but at a less rapid rate over time. Overall, in the upward-sloping term structure, the nominal interest rate increases.
In the downward-sloping term structure graph, the line indicating the inflation premium intersects the y-axis as high as possible for the unmarked axis and decreases over time in a linear manner indicating that inflation is anticipated to decrease over time. Starting at the same location on the y-axis and decreasing in a concave down fashion is a curve that describes the interest rate risk premium. Overall, in the downward-sloping term structure the nominal interest rate decreases.
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Figure 6.6: Treasury Yield Curve
Text Alternative
The x-axis shows maturity dates in 1 mo, 3 mo, 6 mo, 1yr, 2 yr, 3 yr, 5 yr, 7 yr, 10 yr, 20 yr, and 30 yr. The y-axis shows yield % for zero to 3 percent in 0.5% increments. Both nominal and real plots are shown. The nominal plot starts at 1.4 for 1 month and steadily rises to 3.0% for 30 yr on Date 2/1/2018. The real plot starts at 0.6% for 5 yr and rises to 0.85% for 30 yr.
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Bond Price
You are looking at a bond that has 25 years to maturity. The coupon rate is 9% and coupons are paid semiannually. The yield-to-maturity is 8%. What is the current price?
Settlement Date: 09/15/05 (Choose a date)
Maturity Date: 09/15/30 (Choose a date 25 years after settlement)
Coupon Rate: 9% (Same as .09, needs to be annual rate)
YTM: 8% (Same as .08, needs to be annual rate)
Face Value (% of par): 100
Coupons per year: 2
Price(% of par): 110.7410923083
Formula: =PRICE(B3,B4,B5,B6,B7,B8)
Yield
You are looking at a bond that has 25 years to maturity. The coupon rate is 9% and coupons are paid semiannually. The current price is $950. What is the yield to maturity?
Settlement Date: 03/15/02 (Choose a date)
Maturity Date: 03/15/27 (Choose a date 25 years after settlement)
Coupon Rate: 9% (Same as .09, needs to be annual rate)
Bond Price (% of par): 95
Face Value (% of par): 100
Coupons per year: 2
Yield to maturity: 9.53% (The answer is returned as a decimal; format the cell to get a percent.)
Formula: =YIELD(B3,B4,B5,B6,B7,B8)
TVM
You are looking at a bond that has 25 years to maturity. The coupon rate is 9% and coupons are paid semiannually. The yield-to-maturity is 8%. What is the current price?
RATE 4.00% (8%/2)
NPER 50 (25*2)
PMT 4.5 (9%*100/2)
FV 100 (Using 100 par so that PV will give price as % of par)
Price $110.74 Formula: -PV(B3,B4,B5,B6)
You are looking at a bond that has 25 years to maturity. The coupon rate is 9% and coupons are paid semiannually. The current price is $950. What is the yield to maturity?
NPER 50 (25*2)
PMT 4.5 (9%*100/2)
PV -95 (Entered as a % of par and negative for sign convention)
FV 100
YTM 9.53% (Returns as a whole percent, format to get decimal places)
Formula: =2*RATE(B11,B12,B13,B14)
(Have to multiply by 2 because it returns a semiannual rate)

Place an order in 3 easy steps. Takes less than 5 mins.