FI3300 Corporation Finance – Chapter 9

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FI3300 Corporation Finance Chapter 9

• Bond and Stock Valuation

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Learning objectives

• Describe the concepts underlying the cost of
  capital.
• Compute the price of a consol and a preferred
  stock.
• Compute the price of a zero-coupon bond.
• Compute the price of a fixed-coupon bond.
• Know the pricing properties of a fixed-coupon
  bond.
• Compute the price of common stock under various
  assumptions about dividend growth.

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Cost of capital 1

• Cost of capital
• How much the firm is willing to pay to get funds
  from investors
• In other words, it is the cost to the firm for
  acquiring money from investors
• Usually expressed as a percentage

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Cost of capital 2

• An investor will provide funds to the firm only
  if she earns her required rate of return
• If investor provides funds to the firm (i.e., a
  financial security was bought and sold), the
  following must be true
• Investor earns her required rate of return from
  the transaction
• Firm pays just its cost of capital for the funds
• Thus investors required rate of return firms
  cost of capital

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Cost of capital 3

• Capital can be provided either by issuing debt
  (e.g., bonds) or equity (common stock).
• If debt is issued,
• Investors required rate of return on debt
  security
• firms cost of debt
• If equity is issued,
• Investors required rate of return on equity
  security
• firms cost of equity

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Blast from the past last lecture

• Required rate of return on debt security is also
  known as
• Cost of debt
• Yield-to-maturity (YTM for short)
• Discount rate
• Required rate of return on equity security is
  also known as
• Cost of equity
• Discount rate

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Bond Valuation

• Consols, Preferred stock
• Zero-coupon bonds
• Fixed-coupon bonds

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Consols 1

• Pays a fixed coupon every period forever.
• Has no maturity.
• Investor who buys a consol is buying the
  perpetuity of the fixed coupon.
• So, use PV formula of a perpetuity to find the
  present value/price of the consol
• Price of consol

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Consols 2

• Remember earlier that cost of capital
  investors required rate of return. So, we can
  re-arrange the equation to find the firms cost
  of consol capital.
• Cost of consol capital
• We can apply the same ideas to value preferred
  stocks. This is because the cash flows from a
  preferred stock is also a perpetuity!

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Preferred stock

• Pays a fixed dividend forever.
• Price of preferred stock is simply the present
  value of a perpetuity.
• Required rate of return on preferred stock.

Preferred stock dividend
Price of preferred stock
Required rate of return on preferred stock/ cost
of capital for preferred stock
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Consol problem 1

• Problem 9.2 ABC Corp. wants to issue perpetual
  debt in order to raise capital. It plans to pay
  a coupon of 90 per year on each bond with face
  value 1,000. Consols of a comparable firm with
  a coupon of 100 per year are selling at 1,050.
  What is the cost of debt capital for ABC? What
  will be the price at which it will issue its
  consols?
• Verify that cost of debt 0.0952 or 9.52
• Use cost of debt from above to find price of
  consol.Verify that price of consol 90/0.0952
  945.38

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Consol problem 2

• Problem 9.3 If ABC (from the problem above)
  wanted to raise 100 million dollars in debt, how
  many such consols would it have to issue (to
  nearest whole number)?
• No. of consols 100 million/ consol price
  105,778
• Problem 9.4 If ABC wanted to issue its consols
  at par, that is, at a price of 1,000, what
  coupon must it pay?
• Use coupon price x required rate of return
• Verify that coupon 95.20 per year

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Zero-coupon bond (ZCB) 1

• Call this ZCB for short.
• Zero coupon rate, no coupon paid during bonds
  life.
• Bond holder receives one payment at maturity, the
  face value (usually 1000).
• Price of a ZCB, PZCB

F face value of the bond
N number of years to maturity
cost of ZCB debt capital (in decimals)
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Zero-coupon bond (ZCB) 2

• As long as interest rates are positive, the price
  of a ZCB must be less than its face value.
• Why? With positive interest rates, the present
  value of the face value (i.e., the price) has to
  be less than the face value.

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ZCB Problems
These problems are just basic TVM problems where
you receive one lump sum in the future.

• 1) Find the price of a ZCB with 20 years to
  maturity, par value of 1000 and a required rate
  of return of 15 p.a.
• N20, I/Y15, FV1000, PMT0. Price 61.10
• 2) XYZ Corp.s ZCB has a market price of 354.
  The bond has 16 years to maturity and its face
  value is 1000. What is the cost of debt for the
  ZCB (i.e., the required rate of return).
• PV-354, FV1000, N16, PMT0.
• Required rate of return/ Cost of debt 6.71 p.a.

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Fixed-coupon bond (FCB) 1

• Call this FCB for short.
• Firm pays a fixed amount (coupon) to the
  investor every period until bond matures.
• At maturity, firm pays face value of the bond to
  investor.
• Face value also called par value. Unless
  otherwise stated, always assume face value to be
  1000.
• Period can be year, half-year (6 months),
  quarter (3 months).

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Fixed-coupon bond (FCB) 2

• FCB gives you a stream of fixed payments plus a
  lump sum payment (face value) at maturity.
• This cash flow stream is just an annuity plus a
  lump sum at maturity.
• Therefore, we calculate the price of a FCB by
  finding the PV of the annuity and lump sum.
• We use the financial calculator to compute the
  price of the FCB.

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Fixed-coupon bond (FCB) 2

• Price of the FCB, PFCB

Fixed periodic coupon
Number of periods to maturity
Face value
Cost of debt capital
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Find FCB price

• A 1,000 par value bond has coupon rate of 5 and
  the coupon is paid semi-annually. The bond
  matures in 20 years and has a required rate of
  return of 10. Compute the current price of this
  bond.
• PMT 25. Why?
• FV1000, PMT 25, I/Y5, N40. CPT, then PV.
• PV -571.02. Thus, price 571.02 lt par value

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Useful property 1

• Go back to the bond in the last problem.
• Suppose annual coupon rate 10.
• Verify that price 1000 par value
• Suppose annual coupon rate 12
• Verify that price 1,171.59 gt par value.
• It turns out that the following property is true.

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Useful property 2
Note discount rate cost of debt required
rate of return yield to maturity
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Apply what we learnt

• A 10-year annual coupon bond was issued four
  years ago at par. Since then the bonds yield to
  maturity (YTM) has decreased from 9 to 7. Which
  of the following statements is true about the
  current market price of the bond?
• The bond is selling at a discount
• The bond is selling at par
• The bond is selling at a premium
• The bond is selling at book value
• Insufficient information

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Try one more

• One year ago Pell Inc. sold 20-year, 1,000 par
  value, annual coupon bonds at a price of 931.54
  per bond. At that time the market rate (i.e.,
  yield to maturity) was 9 percent. Today the
  market rate is 9.5 percent therefore the bonds
  are currently selling
• at a discount.
• at a premium.
• at par.
• above the market price.
• not enough information.

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Find YTM, Coupon rate

• 1)A 1,000 par value bond sells for 863.05. It
  matures in 20 years, has a 10 percent coupon
  rate, and pays interest semi-annually. What is
  the bonds yield to maturity on a per annum basis
  (to 2 decimal places)?
• Verify that YTM 11.80
• 2) ABC Inc. just issued a twenty-year semi-annual
  coupon bond at a price of 787.39. The face value
  of the bond is 1,000, and the market interest
  rate is 9. What is the annual coupon rate (in
  percent, to 2 decimal places)?
• Verify that annual coupon rate 6.69
• What happens if bond pays coupon annually?
  Quarterly?

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Long FCB question

• HMV Inc. needs to raise funds for an expansion
  project. The company can choose to issue either
  zero-coupon bonds or semi-annual coupon bonds. In
  either case the bonds would have the SAME nominal
  required rate of return, a 20-year maturity and a
  par value of 1,000. If the company issues the
  zero-coupon bonds, they would sell for 153.81.
  If it issues the semi-annual coupon bonds, they
  would sell for 756.32. What annual coupon rate
  is Camden Inc. planning to offer on the coupon
  bonds? State your answer in percentage terms,
  rounded to 2 decimal places.
• Verify that annual coupon rate 7.01

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Common stock

• For common stock, the future cash flows are
• Dividends
• Selling price
• These cash flows are highly uncertain.
• To find the value of common stock, we make
  assumptions about how dividends evolve in the
  future. We look at 3 set of assumptions
• Constant dividend stream
• Dividends grow at constant rate (constant
  dividend growth model)
• Non-constant dividend growth

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Constant dividend stream

• Same amount of dividend is paid for ever.
• Cash flow stream resembles a perpetuity.
• Thus, we value the common stock in the same way
  as we value the preferred stock.
• Common stock price, Pe
• Cost of equity capital, re

Common stock dividend
Cost of equity capital or required rate of return
on equity
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Dividends grow at constant rate 1

• Assume that dividends grow at a constant rate, g,
  per period forever.
• Given this assumption, the price of common stock
  equals

Dont panic. D1 D0(1 g)
D0 Dividend that the firm just paid
Required rate of return on equity
Dividend growth rate
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Dividends grow at constant rate 2

• Useful properties.
• All other things unchanged,
• If D0 increases (decreases), Pe increases
  (decreases).
• If g increases (decreases), Pe increases
  (decreases).
• If re increases (decreases), Pe decreases
  (increases).

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Dividends grow at constant rate 2

• By rearranging the above equation, we can find
  the required rate of return on equity
• For the constant growth model to work, re gt g.

Capital gains yield
Required rate of return on equity
Dividend yield
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Constant growth problems 1

• Jarrow Company will pay an annual dividend of 3
  per share one year from today. The dividend is
  expected to grow at a constant rate of 7
  permanently. The market requires 15 What is the
  current price of the stock (to 2 decimal places)?
• In this question D1 is already given to you.
• Verify that Price 37.5

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Constant growth problems 2

• Johnson Foods Inc. just paid a dividend of 10
  (i.e., D0 10.00). Its dividends are expected
  to grow at a 4 annual rate forever. If you
  require a 15 rate of return on investments of
  this risk level, what is Johnson Foodss current
  stock price? (to 2 decimal places)
• Straightforward application of price formula.
• Verify that price 94.55

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Constant growth problems 3

• The price of a stock in the market is 62. You
  know that the firm has just paid a dividend of 5
  per share (i.e., D0 5). The dividend growth
  rate is expected to be 6 percent forever. What is
  the investors required rate of return for this
  stock (to 2 decimal places)?
• Use re (D1/P) g.
• Verify that re 14.55

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Constant growth problems 4

• A firm is expected to pay a dividend of 5.00 on
  its stock next year. The price of this stock is
  40 and the investors required rate of return is
  20. The firms dividends grow at a constant
  rate. What is this constant dividend growth rate
  (g)?
• use re (D1/P) g
• Verify that g 7.5

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Non-constant dividend growth 1

• With this assumption, dividends grow at different
  rates for different periods of time. Eventually,
  dividends will grow at a constant rate forever.
• Time line is very useful for valuing this type of
  stocks.
• To value such stocks, also need the constant
  growth formula.
• Best way to learn is through an example.

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Non-constant dividend growth 2

• Consider ABC Co.s dividend stream
• Discount rate is 15.

Dividends grow at 5 forever
2.00
3.00
3.50
T 1
T 2
T 3
T 4
T 0
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What to do?

• Use constant growth formula to find stock price
  at the end of year 3. Call this stock price P3.
• Add P3 to dividend received at t3. This sum is
  the cash flow for t3. Find PV of this cash flow.
  
• Find PV of dividends at t1, t2.
• Current stock price sum of 2 and 3.

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Apply the method to find ABCs stock price

• P3 (3.5 x (1.05))/(0.15 0.05) 36.75
• Find cash flow at t3
• 36.75 3.50 40.25
• Current stock price, P0

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Another type of non-constant growth problem

• Malcolm Manufacturing, Inc. just paid a 2.00
  annual dividend (that is, D0 2.00). Investors
  believe that the firm will grow at 10 annually
  for the next 2 years and 6 annually forever
  thereafter. Assuming a required return of 15,
  what is the current price of the stock (to 2
  decimal places)?
• Use timeline to see the problem better.
• Verify that stock price 25.29

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Summary

• Find the price/ present value of debt and equity
  securities
• Consols, preferred stock are valued using the
  same techniques.
• Fixed-coupon bonds are valued as an annuity plus
  a lump sum (face value at maturity)
• Common stocks are valued under 3 different
  assumptions about dividends
• Constant dividends
• Dividends grow at constant rate
• Dividends grow at different rates