FIN 340 Ch 8

IN 340 INTERMEDIATE FINANCIAL MANAGEMENT STOCK VALUATION

TOPIC OUTLINE

  1. The Present Value of Common Stocks

  2. Growth Rate Estimate

  3. Comparables

  4. Firm Valuation Examples

1. THE PRESENT VALUE OF COMMON STOCKS

The value of any asset is defined as the present value of its expected future cash flows. The intrinsic value can be expressed as the present value (PV) of expected future cash flows. It is essential to differentiate between market price and intrinsic value, which is also referred to as fundamental value. Stock ownership typically generates cash flows in two main forms: dividends and capital gains.

Valuation of Different Types of Stocks

  • Zero Growth: The stock value remains constant with no growth in dividends.

  • Constant Growth: The stock value reflects a consistent growth in dividends over time.

  • Differential Growth: The stock value varies as dividends grow at different rates at different stages.

Investors must assess how much they are willing to pay for an asset versus its worth according to valuation methods.

VALUING A STOCK WITH THE DIVIDEND DISCOUNT MODEL

The intrinsic value (I) of an asset can be represented by the equation that includes various notations:

  • $Div_t$: Dividend at time t

  • $EPS_t$: Earnings per share at time t

  • $d_t$: Dividend payout ratio

  • $R$: Discount rate

  • $P_t$: Price at time t

CASE 1: ZERO GROWTH

In the zero growth case, it is assumed that dividends will remain constant indefinitely. Therefore, the value of such a stock can be determined by the present value of a perpetuity:

P0=racDivRP_0 = rac{Div}{R}
This represents a fixed dividend that lasts forever.

ZERO GROWTH EXAMPLE

If Big D, Inc. just paid a dividend of $0.50 and it is expected to maintain that amount, and the market's required return is 15%, the stock should be valued as follows:

  1. Current stock price:
    P0=rac0.500.15=3.33P_0 = rac{0.50}{0.15} = 3.33

  2. Future stock price (in 3 years):
    P3=rac0.500.15=3.33P_3 = rac{0.50}{0.15} = 3.33

  3. To compute what you should pay for the stock today (buy now, sell in 3 years):
    P0=rac0.50(1+0.15)+rac0.50(1+0.15)2+rac0.50(1+0.15)3+rac3.33(1+0.15)3P_0 = rac{0.50}{(1 + 0.15)} + rac{0.50}{(1 + 0.15)^2} + rac{0.50}{(1 + 0.15)^3} + rac{3.33}{(1 + 0.15)^3}
    which also evaluates to $3.33.

CASE 2: CONSTANT GROWTH

The scenario of constant growth posits that future cash flows (dividends) will grow at a constant exponential rate, represented as $g$. In this context, the present value of a growing perpetuity will ascertain the stock value.

The formula used is:

P<em>0=racDiv</em>1R−gP<em>0 = rac{Div</em>1}{R - g}
where:

  • $Div_1$ = Dividend expected in year 1

  • $g$ = constant growth rate of dividends

CONSTANT GROWTH EXAMPLE

If Big D, Inc. maintains a $0.50 dividend, with an increase of 2% per year and a required market return of 15%:

  1. Calculate stock price:
    P0=rac0.50(1+0.02)(0.15−0.02)=3.92P_0 = rac{0.50(1 + 0.02)}{(0.15 - 0.02)} = 3.92

  2. Stock price three years from now:
    P3=rac0.50(1+0.02)4(0.15−0.02)=4.16P_3 = rac{0.50(1 + 0.02)^4}{(0.15 - 0.02)} = 4.16

  3. If it's known that EPS is $2.00 and the payout ratio is 40%, first calculate the dividend:
    Div<em>0=0.40imes2.00=0.80Div<em>0 = 0.40 imes 2.00 = 0.80 Then, P</em>0=rac0.80(1+0.02)(0.15−0.02)=6.28P</em>0 = rac{0.80(1 + 0.02)}{(0.15 - 0.02)} = 6.28

  4. If given a stock price of $3.50 without knowledge of the required rate of return, calculate it as:
    R=rac0.50(1+0.02)3.50+0.02=16.6 %R = rac{0.50(1 + 0.02)}{3.50} + 0.02 = 16.6\, \%

CASE 3: DIFFERENTIAL GROWTH

Differential growth refers to the scenario where dividends increase at varying rates initially and then settle into a constant growth. To evaluate a stock under this model, the following steps must be undertaken:

  1. Estimate future dividends during the initial growth phase.

  2. Determine the future stock price when it will transition into a constant growth dividend model.

  3. Compute the total present value (PV) of both anticipated dividends and the stock price assumed at the constant growth stage.

The growth rates are designated $g1$ for the initial period and $g2$ for the following.

Differential Growth Example

If a stock just paid a dividend of $2, growing at 8% for 3 years then at 4% perpetually:

  1. The price at Year 0 (through cash flows):
    Cash flows must be calculated over time.

  2. The growing perpetuity from Year 4 onward can be evaluated as:
    P=racDiv<em>N+1R−g</em>2P = rac{Div<em>{N+1}}{R - g</em>2} where $P_1$ equals the present value at Year 0.

2. GROWTH RATE ESTIMATE (INPUT IN STOCK VALUATION)

The growth rate $g$ in stock valuation can be estimated using the following relationship:

g=extRetentionratioimesextReturnonretainedearnings=(1−d)imesextROIg = ext{Retention ratio} imes ext{Return on retained earnings} = (1 - d) imes ext{ROI}
Where:

  • $d$ = Dividend payout ratio (calculated as $Div$ / $NI$)

  • $ROI$ = Return on investment, equating to ROE (Return on Equity).

Growth Rate Exercise

Given that Bennington Enterprises earned $34 million with a ROE of 16% and retained 80% of its earnings, the growth rate would be:

  • Calculate growth rate:
    G=0.16imes0.80=0.128=12.80 %G = 0.16 imes 0.80 = 0.128 = 12.80\, \%

  • Project next year's earnings:
    E=34,000,000(1+0.128)=38,352,000E = 34,000,000(1 + 0.128) = 38,352,000

3. COMPARABLES

Valuing businesses using comparables is grounded in the principle of price multiples to assess relative valuations against benchmark stocks. Key multiples include:

  • Price-to-Earnings (P/E) ratio

  • Enterprise Value Ratios

HOW DOES IT WORK?

  1. Establish benchmark stocks and their respective P/E multiples.

  2. Multiply the benchmark multiple by the projected earnings of the company.

PRICE-EARNINGS MULTIPLE

The computation of the price-earnings ratio reflects the current stock price divided by annual EPS (Earnings per Share):

extP/Eratio=racextPricepershareextEPSext{P/E ratio} = rac{ ext{Price per share}}{ ext{EPS}}
where:

  • Market cap = Total Earnings after Dividends.

EXAMPLE ON P/E MULTIPLE

Consider Hutchinson Tech, a private company with $250 million Net Income (NI) and a competitive industry average P/E of 6:

  • Compute market value:
    extMarketcap=extP/EratioimesextNI=6imes250=1,500 Mext{Market cap} = ext{P/E ratio} imes ext{NI} = 6 imes 250 = 1,500 \, M

  • Determine stock price per share:
    extPricepershare=rac1,500,000,000500,000,000=3$/shrext{Price per share} = rac{1,500,000,000}{500,000,000} = 3 \$/shr

P/E AND GROWTH

The P/E ratio resonates with growth potential, where high-tech stocks carry higher P/E due to anticipated growth. Conversely, more traditional sectors like utilities maintain lower multiples owing to lesser growth opportunities. A snapshot of P/E ratios includes:

  • Chubb (Insurance): 19

  • PepsiCo (Beverages): 25

  • Ford (Automotive): 6

  • Goldman Sachs (Financial Services): 32

  • Whirlpool (Home Appliances): 40

  • Facebook (Technology): 36

  • S&P 500 average: 23

ENTERPRISE VALUE RATIOS

The P/E ratio addresses equity alone, while enterprise value (EV) encompasses a fuller picture:

  • extEV=extMarketValueofEquity+extMarketvalueofDebt−extCashext{EV} = ext{Market Value of Equity} + ext{Market value of Debt} - ext{Cash}

  • The EV ratio is calculated as:
    extEnterpriseValueRatio=racextEVextEBITDAext{Enterprise Value Ratio} = rac{ ext{EV}}{ ext{EBITDA}}
    where EBITDA stands for Earnings Before Interest, Taxes, Depreciation, and Amortization, indicative of overall firm cash flow.

EV EXAMPLE AND EXERCISE

Given FFDP Corp with sales of $28 million, costs of $12 million, debts of $54 million, and cash of $18 million, find the enterprise value:

  1. Calculate EBITDA:
    extEBITDA=28,000,000−12,000,000=16,000,000ext{EBITDA} = 28,000,000 - 12,000,000 = 16,000,000

  2. Compute Enterprise Value:
    extEV=16,000,000imes7.5=120,000,000ext{EV} = 16,000,000 imes 7.5 = 120,000,000

  3. Derive equity value:
    extEquityValue=120,000,000−54,000,000+18,000,000=84,000,000ext{Equity Value} = 120,000,000 - 54,000,000 + 18,000,000 = 84,000,000

  4. Lastly, stock price = $84,000,000 / 950,000 = $88.42.

4. FIRM VALUATION EXAMPLES

Example (1) Valuing Stocks Using Free Cash Flows

  1. Sales Forecasts:

    • Year 1: $500 million

    • Year 2: $550 million

    • Year 3: $605 million

    • Year 4: $653.40 million

    • Year 5: $705.67 million

    • Constant growth thereafter at 6%.

  2. Free Cash Flows (FCF Calculation):

    • extFCFYear1=OCF−extNetInvestmentsext{FCF Year 1} = OCF - ext{Net Investments} where Total FCF values are kept proportional to sales (14% throughout).

  3. Present Value of Future Cash Flows:

    • Total PV of FCF during Years 1-5 and beyond.

    • The terminal value ($P5$) will be as follows: P</em>5=rac104.7220.16−0.06=1,047.22P</em>5 = rac{104.722}{0.16 - 0.06} = 1,047.22

  4. Calculating Total Value and Stock Price

    • Sum of present values yields:
      269.39+498.59=767.98 extmillion269.39 + 498.59 = 767.98 \, ext{million}

    • Hence, stock price per share becomes:
      rac{767.98}{12} = 64 \, ext{$/shr}.

Example (2) Discounting Cash Flows Vs. Comparables

Given net cash flow of $225 million, with expected growth of 4% perpetually, and a discount rate of 15%:

  1. Estimate firm value derived from cash flows:
    FirmValue=rac225imes(1+0.04)0.15−0.04=2,127 extmillionFirm Value = rac{225 imes (1 + 0.04)}{0.15 - 0.04} = 2,127 \, ext{million}

  2. If a PE multiple of 9 applies:
    FirmValue=225imes9=2,025 extmillionFirm Value = 225 imes 9 = 2,025 \, ext{million}
    In conclusion, both cash flow discounting and comparable methods hold merit, with the best approach subject to the quality of the benchmark chosen, or confidence in growth rate assumptions.