Ch.8 Valuation and Rates of Return

• Goal:

1) Definitions of values

2) Intrinsic Value Calculation

3) Required rate of return

4) Stock valuation

1. What is Value?

1) Book Value: Price - Depreciation

2) Intrinsic Value:

Value determined by taking the present value of the future cash flows at the investor’s required rate of return.

3) Market value: Price determined in the market

• In finance, we assume that investors will buy until the market value rises to their intrinsic value and sell until the market value falls to their intrinsic value.

2. Fundamentals of Valuation

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• The more cash flows, the higher value

• The earlier cash flows, the higher value

3. Determining the Required Rate of Return

• Return offered by competing investment vehicles

• Risk of the investment

• Investors’ risk preference

3-1) Risk Preferences

• Risk Averse

• Risk Neutral

• Risk Lover

• Investors are assumed to be risk averse.

• They can have different risk preference

3-2) A Simple Risk Premium Model

• E(R) = Base Rate + Risk Premium

• Here, Base rate is the rate of return on a bench mark

• Problem: Too much subjective

3-3) CAPM

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• Kind of a simple premium model

• First part: risk free rate

• Second part: market risk premium

4. Valuing Common Stocks

• 1st Question: What are the expected cash flows? Dividends and sale price

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Ex) XYZ corporation recently paid a dividend of $2.4 and you expect that this dividend will continue to be paid into the foreseeable future. It is believed that you will be able to sell this stock in three years for $20 per share. If your required rate of return is 12% per year, what is the maximum amount that you should be willing to pay for a share of XYZ common stock?

• Depending on the assumptions for dividend payments, three types of stock valuation models are available:

1) Zero Growth- Preferred Stocks

2) Constant Growth

3) Non-constant Growth

4-1) Zero Growth Model

• It assumes constant dividends: Perpetuity• Ex)Preferred stock with $ 2 dividend. And assumed 12%

of return

4-2) Constant Growth Model

• Under this model, dividend payments are assumed to grow constantly by g%.

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Ex) Lets’ use the XYZ example. Here, we assume that the dividend is growing by 6% every year forever.

4-3) Non-constant Growth Model

• No pattern in dividend payments. Ex) you are supposed to purchase a share of the

common stock of the ABC corporation. ABC has not recently paid any dividends nor is it expected to for the next three years. However, ABC is expected to begin paying a dividend of 1.5 per share four years from now

In the future, that dividend is expected to grow at a rate of 7% per year. If your required return is 15% per year, what is the price of the stock?

5. Alternatives to dividend models

• 1) Earnings Model• 100% dividend payout ratio.• Dividend per share is the same as earnings

per share.• Zero growth rate• With zero growth, V=EPS1/K• With growth opportunities (PVGO),

V=EPS1/K+PVGO

g = b(retention ratio)*r(ROE)

PVGO=NPV1/(k-g)NPV1=(RE1*r/k) – RE1

(here RE stands for reinvested earnings)

PVGO=(RE1*r/k-RE1)/(k-g)

= RE1(r/k-1)/(k-g)

•Thus, V=EPS1/K+RE1(r/k-1)/(k-g). It considers ROE in the stock valuation model.

• Ex) Analysts expect that Aurora Foods will earn $1.40 per share in the coming year and pay a dividend of $0.49 per share. Historically, the firm’s ROE has been 15% and its required return on investments is 12%. What is the value of stock?

• RE1=EPS1-D1=0.91• Retention ratio = 0.91/1.40 =0.65• Growth rate (g) = 0.65*0.15=0.00975• V=1.40/0.12+0.91(0.15/0.12-1)/(0.12-

0.0975)=21.78

2) Free Cash Flow Model2-1) Free cash flows = operating cash flow – change

of operating assets.• Operating cash flow = NOPAT + Non-cash

expenses.(here, NOPAT = EBIT*(1-tax rate), Non-cash expenses are depreciation, amortization and other non-cash charge).

• Change of operating assets = change of NOWC + change of operating fixed assets.(here, NOWC = operating current asset – operating current liabilities).

• The value of the firm’s operating assets is the present value of the expected free cash flow, discounted at the firm’s weighted average cost of capital. But because non-operating assets (e.g. marketable securities) were omitted, it should be added back to calculate the value of entire firm.

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• Ex) Analysts project that Front Range Mountaineering Supplies will generate pre-tax operating profits (EBIT) of $160,000 in the coming year. The firm will have $40,000 in depreciation expenses and a tax rate of 30%. Management has told analysts that it expects to make net new investments of $30,000 in operating assets over the next year. It has $25,000 in marketable securities on the book and the market value of its debt is $450,000. The analysts believe that the WACC is 12% and that free cash flow can grow at about 7% per year. If the company has 350,000 common shares outstanding, what is the intrinsic value per share?

• 3) Relative Value Models• Valuation model without DCF• V = P/E ratio * EPS• (assumption: if the market is efficient, the

same price should be paid for dollars of earnings per share)

• Using a dividend model, we can see the impact of growth rate and the required rate of return on the P/E ratio.

• P/E = D/(k-g)/EPS

P=V=EPS1/K+PVGOif it is divided by EPS

6. Option Pricing

• 6-1) Two types of options

• - Call: option to buy stocks

• - Put: option to sell stocks

6-2) payoff of options.

• Call option:

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• S1=stock price at expiration

• S0=stock price today

• C1=value of call option on the expiration date

• C0=value of call option today

• E=exercise price/ striking price

6-2) Valuation• - replicating payoff of option: Buying call options and

investing in a risk free asset will generate the same payoff for having stocks

Ex) assumption• Current stock price:$100• Risk free rate is 20%• Stock price in one year is $110 or $130• Exercise price of call option is $105• Option value is $5 or $25• Invest the present value ($87.50 =105/(1+0.2)) of exercise

price in the risk free asset and purchase one call option

In one year, performance will be

Stock value = Risk free + Call value

• 110 = 105 + 5

• 130 = 105 + 25

Therefore

In terms of the initial position

Stock price = E/(1+risk free) +call value

Call value = stock price - E/(1+risk free)

• Key point: purchasing stocks and investing in risk free rates, we can replicate payoff of call option.

• Black & Shore’s option pricing model

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