FIN 319: Intermediate Financial Management Spring 2006

1
FIN 319 Intermediate Financial
ManagementSpring 2006

• SLIDE SET 3 Bond and Stock Valuation
• (BASED ON RWJ CHAPTER 5)

2

• The Discounted Cash Flow Approach to Valuation
• Estimate The Size And Timing Of Future Cash Flows
  
• Determine The Required Rate Of Return or Discount
  Rate For Each Cash Flow.
• Based on current interest rates, and the
  riskiness of the cash flow
• Different Discount Rates May Be Appropriate For
  Different Cash Flows
• Discount Each Cash Flow To Present
• Sum The Present Values Of The Cash Flows.

3
First, Bond Valuation. The terminology

• Par or Face Value (F) The Bond promises to pay
  its face value at the Maturity Date.
• Coupon Interest. The bond makes interest
  payments at a rate of C per year, with actual
  payments of C/2 every six months. C/F is defined
  as the coupon interest rate. Note that the
  coupon rate is constant over the life of the
  bond.
• Call Provision Call Protection Call Premium
• Default Risk
• Discount Rate, r.
• This changes day to day.
• Yield to maturity. The discount rate that
  equates the bonds promised payments to its
  observed price, V.
• Current yield C/V.

4
Valuing a semiannual coupon bond

• Valuation of a semiannual coupon bond with annual
  coupon payment C, maturity value of F, N years to
  maturity, and annual discount rate r.
• Two components.
• The coupon payments comprise an annuity.
• Lump sum payment of face value at maturity

5
Value of a semiannual coupon bond

• Two Pieces
• Annuity of C/2 for 2N periods.
• Lump sum of F received at the end of 2N periods.

Technical note Here r is the stated annual
discount rate, but we are implicitly using
semiannual compounding.
6
Bond Pricing Example

• Dupont issued 30-year bonds with a coupon rate of
  7.95. These bonds currently have 28 years
  remaining to maturity and are rated AA. Newly
  issued AA bonds with similar maturities are
  currently yielding 7.73. The bonds have a face
  value of 1000. What is the value of a Dupont
  bond today?

7
Bond Example (continued)

• Annual coupon payment0.0795100079.50
• Semiannual coupon payment39.75
• Semiannual discount rate0.0773/20.03865
• Number of semiannual periods28256

8
Bond Prices And Interest (Discount) Rates

• When The Discount Rate Is Equal To The Coupon
  Rate The Bond Will Sell At Par
• When The Discount Rate Is Above The Coupon Rate
  The Bond Will Sell At A Discount To Par
• When The Discount Rate Is Below The Coupon Rate
  The Bond Will Sell At A Premium To Par
• At The Instant Before Maturity The Bond Will Sell
  At Par

9
Bond Prices and Time to Maturity
Discount Rates
What is the coupon rate?
10
Bond Prices and Interest (Discount) Rates
Years to maturity
What is the coupon rate? Why is the long maturity
bond more volatile?
11
Yield To Maturity/Call

• The Yield To Maturity Is The Discount Rate That
  Equates The Bonds Current Price With Its Stream
  of Promised Future Cash Flows.
• The Yield To Call Is The Discount Rate That
  Equates the Bonds Current Price With Its Stream
  of Promised Cash Flows until the expected Call
  Date.
• Given Two Bonds Equivalent in all Respects Except
  That One Is Callable, Which Bond Will Have A
  Higher Price?

12
Yield to Maturity Example

• On 9/1/95, PGE bonds with a maturity date of
  3/01/25 and a coupon rate of 7.25 were selling
  for 92.847 of par, or 928.47 each. What is the
  YTM on these bonds?
• Semiannual coupon payment0.07251000/236.25
• number of semiannual periods302-159

13
Yield to Maturity Example (cont.)

• r/2 can only be found by trial and error.
  Calculators and spread sheets have algorithms to
  speed up the search.
• Searching reveals that r/23.939, or r7.877.
• This is an effective annual rate of
• (1.03939)2 - 1 8.03.

14
Determinants of a Bonds YTM

• 1. The time to maturity
• Typically long-term bonds have higher yields
• 2. The risk of default
• Measured by bond ratings
• Add a default risk premium to the government bond
  yield of similar maturity (risk-free rate)

15
Treasury Yield Curve 4/06/2006
16
(No Transcript)
17
(No Transcript)
18
(No Transcript)
19
Preferred Stock Valuation

• Preferred Stock
• preferred stock has a fixed dividend payment
• preferred dividends can be omitted without
  placing the firm in bankruptcy
• preferred stock has no maturity date
• Does preferred stock have the same risk as the
  firms debt?
• Preferred stock looks like a perpetuity

20
Preferred Stock Valuation

• Preferred stock is typically valued as a
  perpetuity. Given the promised dividend payment,
  Divp, and the discount rate, rp, the value of a
  share of preferred stock is

21
Preferred Stock Example

• Example
• On 8/24/95 Sears preferred stock had a dividend
  of 2.22 per share and was selling at 26.25 per
  share. What rate of return were investors
  requiring on Sears preferred stock?

22
Common Stock Valuation Terminology

• Dt dividend per share of stock at time t
• P0market price of the stock at time 0.
• Ptmarket price of the stock at time t. (Prior
  to date t, this would be the expected price).
• gexpected growth rate in dividend payments
• rsrequired rate of return
• D1/P0dividend yield during period 1.
• P1 - P0/P0 capital gain rate during period 1.

23
Apple Computer(Historical Stock Price)
24
Common Stock Valuation

• The return on a share of stock is given by

• Before date 1 this is the expected return, after
  date 1 this is the realized return.
• Let rs denote the expected return required by
  investors, i.e., the appropriate discount rate.
  Then,

25
Common Stock Valuation (continued)

• What determines P1?
• An investor purchasing the stock at time 1 and
  holding it until time 2 would be willing to pay

• Substituting into the equation for P0, the price
  at time zero is

26
Common Stock Valuation (continued)

• Repeat this process H times and we have

• If we continue to apply the same logic (let H go
  to infinity), we get

• The current market value of a share of stock is
  the present value of all its expected future
  dividends!

27
Bristol Myers Squibb Dividends
28
Stock Valuation if Dividends display constant
growth (forever)

• If the dividend payments on a stock are expected
  to grow at a constant rate, g, and the discount
  rate is rs, the value of the stock at time 0 is

• g must be less than rs to use this formula
• If g0 then the formula reduces to the perpetuity
  formula

29
Example

• Geneva steel just paid a dividend of 2.10.
  Genevas dividend payments are expected to grow
  at a constant rate of 6. The appropriate
  discount rate is 12. What is the price of
  Geneva Stock?
• D0 2.10 D1 2.10(1.06) 2.226

30
Estimating the Required Return from the Price.

• We are focusing on valuation -- determination of
  the price.
• Suppose you observe a price that you consider
  reliable, and instead wish to infer rs.
  Rearrange the constant growth valuation formula
  to obtain
• rs D1/ P0 g.
• Example US East stock currently sells for 22.
  Its most recent dividend was 1.50, and dividend
  growth of 6 is expected.
• D1 1.501.06 1.59
• rs 1.59/22 .06 .0723 .06 13.23
• This method is often used in utility regulation.

31
Back to Valuation. Estimating the growth rate.

• A starting point for estimating the growth rate
  is to assume
• (1) The firms ROE is constant over time and
  across projects.
• (2) The proportion of the firms income paid as
  dividends is also constant.
• (3) The firm will have no future financings.
• Then, income and dividends will both grow at the
  same rate as owners equity, and owners equity
  will grow only due to retained earnings.
• The growth rate will be ROE(1 - d), where d is
  the dividend payout ratio (proportion of earnings
  paid out).
• Be cautious about using this technique in cases
  where the assumptions may be way off base!

32
Common Stock Valuation Example Sears

• As of early 1986,
• ROE 13, d 45,
• implying g .13(1-.45) .0715.
• 1995 dividend was 1.64,
• so D1 1.64(1.0715) 1.757.
• Assuming rs .11, we have
• P0 1.757/(.11 - .0715) 45.64.
• (The actual share price was 45)

33
Stock Valuation Based on Dividends, with
Nonconstant Growth

• Firms often go through lifecycles
• Fast growth
• Growth that matches the economy
• Slower growth or decline.
• A supernormal growth stock is one experiencing
  rapid growth. But, supernormal growth is
  generally only temporary.

34
Valuation of Nonconstant Growth Stocks

• Find the present value of the dividends during
  the period of rapid growth.
• Project the stock price at the end of the rapid
  growth period. This will be the discounted value
  of the subsequent dividends. Discount this price
  back to the present.
• Add these two present values to find the
  intrinsic value (price) of the stock.

35
Example

• Batesco Inc. just paid a dividend of 1. The
  dividends of Batesco are expected to grow by 50
  next year (year1) and 25 the year after that
  (year 2). Subsequently, Batescos dividends are
  expected to grow at 6 per year in perpetuity.
• The proper discount rate for Batesco is 13.
• What is a fair price for a share of Batesco stock?

36
Example (continued)

• First, determine the dividends.
• D01 g150
• D11(1.50)1.50 g225
• D21.50(1.25)1.875 g36
• D31.875(1.06)1.9875

37
Example (continued)

• Supernormal growth period

• Constant growth period. Value at time 2

• Discount to time 0 and add to Ps

38
What About Stocks That Pay No Dividends?

• If investors value dividends, how much is a stock
  that pays no dividends worth?
• A stock that will literally never pay dividends
  in any form, has a value of zero.
• In actuality, a company that has not paid
  dividends to date can be worth a lot, if the
  company has good investment projects or it has
  assets that can be liquidated.
• McDonalds started in the 1950's but paid its
  first dividend in 1975. The market value of
  McDonalds stock was in excess of 1 billion
  prior to 1975.
• Microsoft has never paid a dividend

39
What About Stocks That Pay No Dividends?

• Microsoft Dividends

40
Valuing Operations Instead of Dividends

• Stocks can be(and often are) valued based on
  earnings and/or operating cash flows instead of
  dividends. Let OCF denote operating cash flow
  (after taxes and after all working capital
  corrections).
• Let F denote the net cash flow to the firm from
  financings (new debt and equity issues less any
  debt repaid or equity repurchased).
• Let I denote net new capital investment taken by
  the firm (count increases in the cash balance as
  capital investment).
• Then, using the cash flow identity, dividends can
  be stated as
• Dt OCF t F t - I t..
• So, we can value the firm by discounting future
  operating cash flows, financing flows, and
  requisite capital investments instead of
  dividends.

41
Valuing Operations Instead of Dividends (Cont.)

• Let NPVGO represent the net present value of the
  firms future investments. This is the present
  value of the operating cash flows those
  investments will create less the present value of
  the capital outflows that will be required.
• Let NPVF represent the net present value of the
  firms future financing transactions. This is
  the present value of the proceeds from financings
  less the present value of the resulting
  obligations --- interest and principal for debt,
  dividend dilution for equity (a good starting
  point is NPVF0).
• Let PVA denote the present value of the future
  cash flows from the firms existing assets.
• Let PVL denote the present value of the future
  cash flows associated with the firms existing
  liabilities.
• These should each be stated on a per share basis
  if we want the price per share.

42
Valuing Operations Instead of Dividends (Cont.)

• The following valuation approach is equivalent to
  the discounted dividend approach
• P0 PVA - PVL NPVGO NPVF
• Even though it does not directly involve dividend
  projections at all!
• Observations regarding RWJs Chapter 5
  discussion
• They assume no future financings. (More
  generally, NPVF 0 is probably a good first
  approximation).
• They assume no existing debt, so PVL 0.
• They assume that existing assets pay a perpetuity
  in the amount of EPS per period. So, PVA
  EPS/rs.
• So, with their special restrictions, we have
• P0 EPS/rs NPVGO.

43
XCORP EXAMPLE

• Suppose that Xcorps current assets produce net
  cash flows of 1 million per year in perpetuity.
  The discount rate for Xcorp is 15.
• What is the market value of Xcorp?

44
XCORP EXAMPLE (continued)

• Now suppose that Xcorp has an RD project that
  will require cash infusions of 1 million in each
  of the next three years. Subsequently, the
  project will generate additional cash flow of
  0.75 million per year in perpetuity. Xcorps net
  cash flow with the project is shown below.

• What is the market value of Xcorp with the
  project?

45
XCORP EXAMPLE (continued)

• Xcorps cash flow can be divided up into two
  pieces
• The cash flow from current assets

• Plus the cash flows from the new project

46
XCORP EXAMPLE (continued)

• The NPV of the project at time 0 is

• Xcorps Value with the project is

47
Price-Earnings (P/E) Ratios

• The investment community relies heavily on P/E
  ratios.
• P/Es are one of the items reported for every
  NYSE and NASDAQ stock in daily newspapers.
• Some analysts do simple valuation by obtaining
  the product of earnings per share and the p/e
  multiplier.
• Using the RWJ Chapter 5 framework,
• P0 EPS/rs NPVGO,
• so the ratio of price to earnings per share
  is
• P0 /EPS 1/rs NPVGO/EPS

48
Price-Earnings (P/E) Ratio Example

• If NPVGO 0 and r .15, then P/E 1/.15 6.67
• If NPVGO 0 and r .08, then P/E 1/.08
  12.50.
• If the Net Present Value of Future Investments is
  five times as large as current EPS and r .08,
  then P/E 1/.08 5 17.50
• So, high P/Es require either low discount rates
  or lots of good future investments (relative to
  current earnings), i.e. earnings growth. Note,
  though, that earnings growth obtained through
  negative NPV investment wont help.

49
Valuation Techniques Summary

• Financial Assets (and some real assets) can be
  valued by discounted cash flow techniques
  compute the present value of the future cash
  flows to be given off by the asset.
• For Bonds, this is mainly a matter of time value
  mechanics and the selection of the appropriate
  discount rate.
• For stocks, DCF techniques can be implemented
  either by discounting the forecasted dividend
  stream, or by discounting future flows to equity.
  The important issues are the inherent ability to
  generate cash flows and the riskiness of the cash
  flows than the details of the dividend payments.