FIN 40153: Advanced Corporate Finance

Applications of Valuation to Bonds and Stocks

(BASED ON RWJ CHAPTERS 8 & 9)

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.

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

bond’s promised payments to its observed price.

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

Value of a semiannual coupon bond

1 2 N-1 N

C/2 C/2 C/2C/2 C/2C/2 C/2 C/2F

0

)r+(1

F

rrrC = P 2NN0

2/)2/1)(2/(

1

2/

12/

2

• 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.

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?

Bond Example (continued)

Annual coupon payment=0.0795*$1000=$79.50 Semiannual coupon payment=$39.75 Semiannual discount rate=0.0773/2=0.03865 Number of semiannual periods=28*2=56

06.1025$)03865.0(1

1000

)03865.01)(03865.0(1

03865.01

75.39 = P

56

560

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

Yield to Maturity The Yield To Maturity Is The Discount Rate That Equates

The Bond’s Current Price With Its Stream of Promised Future Cash Flows.

An ExampleAn Example

On 9/1/95, PG&E bonds with a maturity date of 3/01/25 On 9/1/95, PG&E bonds with a maturity date of 3/01/25 and a coupon rate of 7.25% were selling for 92.847% of 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?par, or $928.47 each. What is the YTM on these bonds?

Semiannual coupon payment=0.0725*$1000/2=$36.25Semiannual coupon payment=0.0725*$1000/2=$36.25 number of semiannual periods=30*2-1=59number of semiannual periods=30*2-1=59

Yield to Maturity Example (cont.)

)2/r+(1

1000

)2/r1)(2/r(

1

2/r

125.36$ = 47.928$ 5959

• 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/2=3.939%, or r=7.877%.• This is an effective annual rate of :

(1.03939)2 - 1 = 8.03%.

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Corporate Bond Credit Rating Symbols

Bond Ratings and Bond Yields

So on 3/1/2006 10 year AAA bonds pay 68 basis points higher than 10 year than Treasuries, 4.59% + 0.68% = 5.27%

High Yield Bond Quotes

Common Stock Valuation Techniques

Dividend Discount Model

Using Multiples

Free Cash Flow (skip this for now and come back to later in the semester)

Conceptually the value of a stock is a stream of dividends plus future sale

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

Common Stock Valuation: Dividend Discount Model

1t

ts

t0

)r+(1DP

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

Hs

HH3

s

32

s

2

s

10 )r1(

PD....

)r1(D

)r1(D

)r1(D

P

Date Div Date DivDec-96 $0.76 Mar-92 $0.69Oct-96 $0.75 Dec-91 $0.69Jul-96 $0.75 Sep-91 $0.60Apr-96 $0.75 Jun-91 $0.60Jan-96 $0.75 Apr-91 $0.60Oct-95 $0.74 Dec-90 $0.60Jul-95 $0.74 Oct-90 $0.53Apr-95 $0.74 Jun-90 $0.53Dec-94 $0.74 Apr-90 $0.53Oct-94 $0.73 Dec-89 $0.53Jun-94 $0.73 Sep-89 $0.50Mar-94 $0.73 Jun-89 $0.50Jan-94 $0.73 Apr-89 $0.50Sep-93 $0.72 Dec-88 $0.50Jun-93 $0.72 Oct-88 $0.42Mar-93 $0.72 Jun-88 $0.42Jan-93 $0.72 Mar-88 $0.42Sep-92 $0.69 Jan-88 $0.42Jun-92 $0.69

Bristol Myers Squibb Dividends

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-rD = Ps

10

g must be less than rs to use this formula

If g=0 then the formula reduces to the perpetuity formula

Geneva steel just paid a dividend of $2.10. Geneva’s 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

$37.10 = 0.06-0.12

$2.226 = P0

Example

Above 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 = 1.50*1.06 = 1.59

rs = 1.59/22 + .06 = .0723 + .06 = 13.23%

This method is often used in utility regulation.

Estimating the Required Return from the Price.

A starting point for estimating the growth rate is to assume: (1) The firm’s ROE is constant over time and

across projects. (2) The proportion of the firm’s 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 owner’s 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!

Back to Valuation. Estimating the growth rate.

As of early 1996,

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)

Common Stock Valuation Example: Sears

Example of Stock Valuation with Non Constant Growth

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, Batesco’s 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?

First, determine the dividends. D0=$1 g1=50%

D1=$1(1.50)=$1.50 g2=25%

D2=$1.50(1.25)=$1.875 g3=6%

D3=$1.875(1.06)=$1.9875

0 321 4

......

1.50 1.875 1.9875 2.107

g=50% g=25% g=6% g=6%

Example (continued)

Supernormal growth period:

796.2$ = )(1.13

1.875+

(1.13)1.50

= )r+(1

D+)r+(1

D = P 22s

2

s

1s

• Constant growth period. Value at time 2:

$28.393 = 0.06-0.13

1.9875 =

g-rD = P

3s

3c

• Discount to time 0 and add to Ps:

03.5$2 = )(1.13

28.393+796.2 =

)r+(1P+P = P 22

s

cs0

Example (continued)

What About Stocks That Pay No Dividends? 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.

Valuing Operations Instead of Dividends (Cont.)

Let NPVGO represent the net present value of the firm’s 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 firm’s 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 NPVF=0).

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 firm’s existing liabilities.

These should each be stated on a per share basis if we want the price per share.

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 RWJ’s Chapter 9 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.

Suppose that Xcorp’s 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?

0 321 4

......

1 million 1 million 1 million1 million

XCORP EXAMPLE

million67.6$15.0

million1r

CFPVA

s

1

0 321 4

......

0 million 0 million 1.75 million0 million

What is the market value of Xcorp with the project?

Now suppose that Xcorp has an R&D 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. Xcorp’s net cash flow with the project is shown below.

XCORP EXAMPLE (continued)

Xcorp’s cash flow can be divided up into two pieces:Xcorp’s cash flow can be divided up into two pieces: The cash flow from current assetsThe cash flow from current assets

0 321 4

......

1 million 1 million 1 million1 million

• Plus the cash flows from the new project

0 321 4

......

-1 million -1 million 0.75 million-1 million

XCORP EXAMPLE (continued)

The NPV of the project at time 0 is:The NPV of the project at time 0 is:

Xcorp’s Value with the project is:

XCORP EXAMPLE (continued)

million004.1$

15.075.0

)15.1(1

)15.1(1

)15.1(1

15.11

NPVGO 332

million671.7$004.1$667.6$

NPVGOPVAP0

PVGO Example It is sometimes interesting to see how much of

a company’s value is due to existing earnings and how much is from anticipated growth.

Company Stock Price EPS "r" EPS/r % of Price PVGO % of Price

Microsoft 103 1.32 0.13 10.15 9.9% 92.85 90.1%

Ford 58 5.75 0.11 52.27 90.1% 5.73 9.9%

Coca-Cola 85 1.67 0.125 13.36 15.7% 71.64 84.3%National

Steel 12 4.82 0.10 48.2 401.7% (36.2) (301.7)%Newmont

Gold 23 0.44 0.09 4.89 21.3% 18.11 78.7%

Valuation Using Multiples

Price-to-earnings (P/E) Price-to-earnings-before-interest-tax-

depreciation and amortization (P/EBITDA). Price-to-book (P/B) Price-to-sales (P/S) Price-to-cash flow (P/CF).

Determining Value

Value = Item x Multiplier

We illustrate this approach using the P/E method:

Value = EPS forecast x Predicted P/E multiple

Choosing the Level of the Multiplier

1)Examine historic P/E’s for the company. Pay special attention to trends.

2)Examine P/E’s and trends for several comparable companies.

3)Determine if the company has historically traded at a premium, at the same level, or a discount to its competitors. If at a premium, can it maintain that premium? Why? If a discount, can it move to the industry level? How?

4)Repeat (3) relative to the S&P index.

Example

We want to value an unlisted company in the automobile manufacturing sector.

Our pro forma estimates suggest earnings next year of $25 million.

Data on four comparables are given on the next slide (the comparables are chosen from the same industry and are about the same size as our company)

Example Data

Comparable P/E Comparable P/E

Arvin Industries 12.75 Arvin Industries 12.75

Detroit Diesel 15.72 Detroit Diesel 15.72

Donnely 16.86 Donnely 16.86

Excel 10.76 Excel 10.76

Lear Corp. 6.16 Lear Corp. 6.16

Average 14.45 Average 14.45

P/E Example

We believe our company has better growth prospects than the typical firm in the industry.

Therefore we assign it a P/E multiple of 17

Using this gives the following valuation:

Value = $25m x 17 = $425m

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.