Intrinsic Value versus Market Price

Scenario Assumptions:

• Stock G has the following:
  • Expected dividend per share (E(D1) = 4 pesos.
  • Current price of the stock (P0) = 48 pesos.
  • Expected price at the end of 1 year (E(P1​)) = 52 pesos.

Formula for Expected Holding-Period Return (HPR):

HPR= E(D1)+[E(P1)−P0]P0HPR=P0​E(D1​)+[E(P1​)−P0​]​

Where:

• E(D1) is the expected dividend per share.
• E(P1) is the expected stock price after 1 year.
• P0 is the current stock price.

Substitute values into the formula:

HPR=4+(52−48)48=4+48=16.7%

HPR=48+(52−48)​=48+4​=16.7

Explanation:
This means that the investor expects to earn a 16.7% return from the stock over 1 year, which includes:

• Dividend Yield: The dividend (E(D1)) relative to the current price (P0​)
• = 4 divide 48 =8.3%

• Capital Gains Yield: The increase in the stock price (E(P1)−P0E(P1​)−P0​) relative to the current price (P0)
• = E(P1)−P0 divide P0
• = 52−48 divide 48 = 8.3%P0​

Thus, the total expected return (HPR) is 16.7%.

Capital Asset Pricing Model (CAPM)

CAPM is used to calculate the required return for a stock, considering its risk in comparison to the market.

CAPM Formula:

k=rf+β⋅[E(rm)−rf]k=rf​+β⋅[E(rm​)−rf​]

Where:

• kk = Required rate of return (the return an investor expects to earn).
• rf​ = Risk-free rate (the return from a risk-free investment, like government bonds).
• E(rm​) = Expected market return (the average return from investing in the market).
• β = Beta, which measures the stock's risk relative to the market:
  • If β>1, the stock is riskier than the market.
  • If β<1, the stock is less risky than the market.

Example Values:

• rf=6%rf​=6% (Risk-free rate).
• E(rm)−rf=5% (Market risk premium, the extra return the market offers over the risk-free rate).
• β=1.2 (This stock is 20% riskier than the market).

Substitute values into the CAPM formula:

k=6% + 1.2 x 5% = 6% + 6% = 12%

Explanation:

• The required rate of return (kk) for this stock, considering its risk, is 12%.
• This means the investor expects to earn at least 12% from this stock, given its level of risk.

Comparing Expected Return vs. Required Return

Now, let's compare the expected return with the required return:

• From the previous calculation, the expected return (HPR) is 16.7%.
• From the CAPM formula, the required return is 12%.

Difference:

E(r)−k=16.7%−12%=4.7%E(r)−k=16.7%−12%=4.7%

Interpretation:

• Since the expected return (16.7%) is higher than the required return (12%), this stock provides a better return than what the investor would require, considering its risk.
• This makes the stock a good investment because it offers a return higher than expected from its level of risk.

Intrinsic Value of a Stock

The intrinsic value (V0V0​) of a stock is an estimate of its true worth, based on the present value of future cash flows (dividends and expected price), discounted at the required rate of return.

Intrinsic Value Formula:

V0=E(D1)+E(P1)1+kV0​=1+kE(D1​)+E(P1​)​

Where:

• E(D1)E(D1​) is the expected dividend.
• E(P1)E(P1​) is the expected price after 1 year.
• kk is the required return (calculated by CAPM).

Example Values:

• E(D1)=4E(D1​)=4 pesos.
• E(P1)=52E(P1​)=52 pesos.
• k=12%k=12% (Required return from CAPM).

Substitute values into the intrinsic value formula:

V0=4+521.12=561.12=50V0​=1.124+52​=1.1256​=50

Interpretation:
The intrinsic value of the stock is 50 pesos, meaning this is what the stock is truly worth based on the expected dividends and price.

Comparing Intrinsic Value vs. Market Price

Now, compare the intrinsic value (V0​) to the market price (P0​):

• Intrinsic value (V0​) = 50 pesos.
• Market price (P0) = 48 pesos.

Conclusion:

• Since V0>P0​ (50 pesos > 48 pesos), the stock is undervalued.
• This means the stock is priced below its true worth, so it might be a good investment opportunity.

Dividends Discount Model

• The price or value of a stock is equal to the present value of its future dividends, whose values are uncertain.
• It requires an infinite number of future dividend values to be estimated.
• So, assumption are made for the expected pattern of the uncertain flow of dividends over the life of the stock.
• The commonly used assumptions are Zero growth in dividends over the infinite life of stock,
• constant growth rate in dividends over the infinite life of the stock,
• non-constant growth in dividends over the infinite life of the stock.

• Financial analysts take much care in forecasting future earnings, specifically, dividends.
• Investors rely on some form of a discounted cash flow (DCF) analysis for estimating the intrinsic value of stock investment.
• This is simply present value model, where the intrinsic value of an asset at time zero, V₀, is determined by the stream of cash flows it generates for the investor.
• Such value is also called justified value since it is the value that is justified by the forecasted cash flows.

• In a Dividend Discount Model (DDM), the stock market price is set equal to the stream of forecasted dividends (D) discounted at the required rate of return (r).
• The intrinsic value of the share is the present value of the dividend to be received at the end of the first year,
• D₁ and the expected sales price, P₁.
• The future prices and dividends are unknown, and we are dealing with expected values not certain values.

Constant-Growth Dividend Discount Model

• Valuing a stock requires dividend forecasts for every year into indefinite future.
• To make the DDM practical we have to introduce assumptions.

• Assuming that dividends are trending upward at a stable growth rate, g.
• The if g = .05, and the
• most recently paid dividend was D₀ = 3.81,
• expected future dividends are

D₁ = D₀ (1 + g) = 3.81 x 1.05 = 4.00

D₂ = D₀ (1 + g) = 3.81 x (1.05)² = 4.20

D₃ = D₀ (1 + g) = 3.81 x (1.05)³ = 4.41 and so on ….

Using the dividend forecast, the intrinsic value will be

V₀ = D₀ + (1 + g) / 1 + k + D₀ + (1 + g)² / (1 + k)² + D₀ + (1 + g)³ / (1 + k)³

Simplifying the equation we have

V₀ = D₀ + (1 + g) / k – g = D₁ / k - g

Assuming the market capitalization rate for ABC stock is 12%, then the intrinsic value of ABC stock is

• 4.00 / .12 - .05 = 57.14

• The constant-growth DDM is valid only when g (growth rate) is less than k (required rate of return).
• If dividends were expected to grow forever at a rate faster than k,
• the value of the stock would be infinite .

• If the analyst derives an estimate of g that is greater than k, that growth rate must be unsustainable in the long run.
• The appropriate valuation model to use in this case is a multistage DDM.

The constant growth rate DDM implies that a stock’s value will be greater:

1. The larger its expected dividend per share.
2. The lower the market capitalization rate (consensus value of required rate of return).
3. The higher the expected growth rate of dividends.

Another implication of the constant-growth model is that the stock price is expected to grow at the same rate as dividends.

Stock prices and Investment opportunities

Scenario:

• Cash Cow Company and Growth Prospects Company expected a 5/share in the coming year.
• Both of them pay out all of their earnings as dividends, maintaining a perpetual dividend flow of 5/share.
• The market capitalization rate (required rate of return-consensus) k=12.5%.
• Both companies valued at 40/share = D₁ / k = 5/.125 = 40.

The growth rate of dividends is g= ROE X b = .15 x .60 = .09 or 9 %

If the stock is equals its intrinsic value, and this growth rate can be sustained (if the ROE and payout ratios are consistent with the long-run capabilities of the firm), then the stock should sell at

P₀ = D₁ / k – g = 2 / .125 - .09 = 57.14

Therefore, when Growth prospects Co. reduced its current dividends and reinvest some of its earnings in new investments, its stock price increased. That means expected return (E₁) is greater than required rate of return (k), the investment opportunities have a positive net present value called present value of growth opportunities (PVGO).

The value of firm then is the sum of the value of assets already in place, or the no-growth value of the firm, plus the net present value of the future investments the firm will make, which is PVGO. Growth Prospects firm has PVGO= 17.14 per share (57.14 – 40 = 17.14)

P₀ = E₁ / k + PVGO = 57.14 = 40 + 17.14

• Suppose Growth Prospects Company engages in projects that generates 15% return on investments (ROE) of 15% which is greater that the required rate of return, k=12.5%.
• Suppose Growth Prospects Co. choose to lower dividend pay out ratio, reducing it from 100% to 40% and maitaining a plow back ratio (fraction of earnings reinvested in the firm) or earnings retention ratio of 60%.
• The dividend now is 40% of 5/share earnings = 2/share instead of 5/share.
• Assuming Growth Prospect invested in a equipment of 100 million which is all-equity-financed. With investment or equity return of 15%, then ROE X 100 million = 15 million return.
• There are 3 million shares of stock outstanding. If 60% of the 15 million is reinvested this year, then the value of the capital stock is .60 X 15 million = 9 million or 9%.
• The precentage increase in the capital stock is the rate at which income was generated (ROE) times the plowback ratio ( the fraction of earnings reinvested in more capital) which is denote as b.
• The growth rate of dividends is g= ROE X b = .15 x .60 = .09 or 9 %

• If the stock is equals its intrinsic value, and this growth rate can be sustained ( if the ROE and payout ratios are consistent with the long-run capabilities of the firm), then the stock should sell at

P₀ = D₁ / k – g = 2 / .125 - .09 = 57.14

• Therefore, when Growth prospects Co. reduced its current dividends and reinvest some of its earnings in new investments, its stock price increased.
• That means expected return (E₁) is greater than required rate of return (k),
• the investment opportunities have a positive net present value called present value of growth opportunities (PVGO).

• The value of firm then is the sum of the value of assets already in place, or the no-growth value of the firm, plus the net present value of the future investments the firm will make, which is PVGO.
• Growth Prospects firm has PVGO= 17.14 per share (57.14 – 40 = 17.14)

P₀ = E₁ / k + PVGO = 57.14 = 40 + 17.14