ACST1001 Finance Fundamentals - Week 7: Valuation of Financial Assets: Shares

Share Basics

• Ordinary Shares: Represent ownership in a firm, entitling the owner to ordinary dividends and voting rights in director elections and major events like mergers.

  • Dividends are not guaranteed and depend on the company's profitability and management's decision to distribute earnings or reinvest for growth.

  • Dividends vary with profitability and growth stage.

  • In liquidation, ordinary shareholders have the lowest priority claim on assets, receiving what remains after creditors and preference shareholders are paid.

• Preference Shares: Also represent ownership but have preferential treatment over ordinary shares.

  • Dividend payments are fixed obligations, similar to interest on bonds.

  • Preference shareholders have priority in dividend payments and liquidation proceeds over ordinary shareholders.

  • Preference shareholders typically do not have voting privileges.

  • Legally considered equity but can resemble debt.

The Dividend-Discount Model

• Introduction: An ordinary share's value equals the present value of all future cash flows expected from owning the share.

  • Unlike bonds, shares don't promise fixed interest or maturity payments.

  • The required rate of return on shares isn't directly observable like the yield to maturity on bonds.

• Three-Step Procedure for Valuing Ordinary Shares:

  1. Estimate the amount and timing of future cash flows (dividends) the share is expected to provide.

  2. Evaluate the risk of the share's future dividends to determine the required rate of return $r_E$, also known as the equity cost of capital.

  3. Calculate the present value of expected dividends by discounting them at the share's required rate of return.

• Basic Concept of the Share Valuation Model: The value of a stock today $P_0$ is the present value of the future dividends and selling price.

  • If holding a share for one year with an expected dividend of $1.75 and a selling price of $50, with a required return of 15%:
    P_0 = \frac{1.75 + 50}{1.15} = $45

  • If holding the share for two years with annual dividends of $1.75 and a selling price of $55.75:
    P_0 = \frac{1.75}{1.15} + \frac{1.75 + 55.75}{1.15^2} = $45

  • The selling price at the end of year one is the present value of the dividend for year two and the price at the end of year two discounted back:
    P_1 = \frac{1.75 + 55.75}{1.15} = $50

  • The value of an ordinary share is the present value of future dividends over an infinite number of years:
    $P<em>0 = \frac{Div</em>1}{1 + r<em>E} + \frac{Div</em>2}{(1 + r<em>E)^2} + \frac{Div</em>3}{(1 + r_E)^3} + \cdots$

Estimating Dividends in the Dividend-Discount Model

• Constant Dividend Growth: Assumes dividends grow at a constant rate $g$ forever.

  • The value of the firm depends on next year's dividend level divided by the equity cost of capital, adjusted by the growth rate:
    $P<em>0 = \frac{Div</em>1}{r_E - g}$

• Constant Dividend Growth: Lecture Example 1:

  • ABC Limited will pay a dividend next year of $3.20 and expects that to grow indefinitely at 8% per year. If the equity cost of capital is 18% per year, what is the value of ABC shares?
    P0 = \frac{Div1}{r_E - g} = \frac{3.20}{0.18 - 0.08} = \frac{3.20}{0.10} = $32.00

• Constant Dividend Growth: Lecture Example 2:

  • ABC Limited just paid a dividend of $3.20 and expects that to grow indefinitely at 8% per year. If the equity cost of capital is 18% per year, what is the value of ABC shares?
    $P<em>0 = \frac{Div</em>1}{r_E - g} =?$

• $Div<em>1$ Versus $Div</em>0$: The timing of dividends is important as the perpetuity value is 'anchored' on the first dividend.

  • If given $Div<em>0$ rather than $Div</em>1$, estimate $Div<em>1$ before applying the growing perpetuity formula: $P</em>0 = \frac{Div<em>1}{r</em>E - g} = \frac{Div<em>0 (1 + g)}{r</em>E - g}$

• Constant Dividend Growth: Lecture Example 2 (Again):

  • ABC Limited just paid a dividend of $3.20 and expects that to grow indefinitely at 8% per year. If the equity cost of capital is 18% per year, what is the value of ABC shares?
    P0 = \frac{Div1}{r_E - g} = \frac{3.20 \times 1.08}{0.18 - 0.08} = $34.56

• Constant Dividend Growth: The Relationship between $r_E$ and $g$: The model yields solutions that are invalid whenever the dividend growth rate equals or exceeds the equity cost of capital.

  • If $g > r_E$, the present value of dividends is negative, which is not realistic, as negative share prices don't occur. Such a large growth rate would imply that a company is growing at a very fast rate forever.

• Estimating $r<em>E$: The value of a share depends upon the equity cost of capital, $r</em>E$, and its growth rate, $g$.

• Where does $r_E$ come from?

  • The equity cost of capital is often estimated by the Capital Asset Pricing Model (CAPM).

• Estimating $r_E$:

  • Starting with $P<em>0 = \frac{Div</em>1}{r_E - g}$

  • Rearrange and solve for $r<em>E$: $r</em>E = \frac{Div<em>1}{P</em>0} + g$

  • $\frac{Div<em>1}{P</em>0}$ is the dividend yield.

  • $g$ can be interpreted as the capital gain rate.

  • With constant expected dividend growth, the expected growth rate of the share price matches the growth rate of the dividends.

Dividends Versus Investment and Growth

• A simple model of growth:

  • The dividend each year equals the firm’s earnings per share (EPS) multiplied by its dividend payout rate.
    $Div<em>t = \frac{Earnings</em>t}{Shares \space outstanding<em>t} \times Dividend \space payout \space rate</em>t$
    Where:
    $\frac{Earnings<em>t}{Shares \space outstanding</em>t} = EPS<em>t$ $Dividend \space payout \space rate</em>t$ = fraction of the firm's earnings paid out as dividends.

• The firm can increase its dividend in three ways:

  1. Increase its earnings.

  2. Increase its dividend payout rate.

  3. Decrease its number of shares outstanding.

• Let's examine the trade-off between options 1) and 2).

  • A firm can do one of two things with its earnings: it can pay them out to investors, or it can retain and reinvest them.

  • By investing cash today, a firm can increase its future dividends.

• If all increases in future earnings result exclusively from new investments made with retained earnings, then:

  • Change in earnings = New investment × Return on new investment (equation 1)

  • New investment equals the firm’s earnings multiplied by its retention rate or the fraction of current earnings that the firm retains $1 - Dividend \space payout \space rate$:
    New investment = Earnings × Retention rate (equation 2)

• Substituting equation 1 into equation 2 and dividing by earnings gives an expression for the growth rate of earnings:

  • $Earnings \space growth \space rate = \frac{Change \space in \space earnings}{Earnings} = Retention \space rate \times Return \space on \space new \space investment$

• If the firm chooses to keep its dividend payout rate constant, then the growth in its dividends will equal the growth in its earnings:

  • $g = Retention \space rate \times Return \space on \space new \space investment$

• Key takeaway:

  • A firm can increase its growth rate by retaining more of its earnings.

  • But if the firm retains more earnings and, as a result, pays out a smaller fraction of those earnings as dividends, then the firm may have to cut its dividend in the short run.

  • So, if a firm wants to increase its share price, should it cut its dividend and invest more, or should it cut its investments and increase its dividend?

  • The answer to this question will depend on the profitability of the firm's investments.

• Thus, our valuation model is:

  • $P_0 = PV \space Changing \space dividend \space growth + PV \space Constant \space dividend \space growth$

  • $P<em>0 = \frac{Div</em>1}{1 + r<em>E} + \frac{Div</em>2}{(1 + r<em>E)^2} + \cdots + \frac{Div</em>n}{(1 + r<em>E)^n} + \frac{P</em>n}{(1 + r<em>E)^n}$ Where: $P</em>n = \frac{Div<em>{n+1}}{r</em>E - g} = \frac{Div<em>n (1 + g)}{r</em>E - g}$

• Harris Mushroom Farms Limited expects to pay a dividend of $3 per share next year. After that, the dividend is forecast to grow at 10% per year for 2 years. From year three onwards, dividends are expected to grow by 3% per year indefinitely. If the equity cost of capital is 12% per year, what is the share price?

  • We will use the following model to calculate the share price:
    $P<em>0 = \frac{Div</em>1}{1 + r<em>E} + \frac{Div</em>2}{(1 + r<em>E)^2} + \frac{Div</em>3}{(1 + r<em>E)^3} + \frac{P</em>3}{(1 + r_E)^3}$

• Our inputs are:

  • $Div<em>1 =$3.00; Div2 = 3.00 \times 1.1 = 3.30; Div3 = 3.30 \times 1.1 = $3.63; and P3 = \frac{3.63 \times 1.03}{0.12 - 0.03} = $41.54

• The share price is, therefore:

  • P_0 = \frac{3.00}{1.12} + \frac{3.30}{1.12^2} + \frac{3.63}{1.12^3} + \frac{41.54}{1.12^3} = $37.46

• When we think about how valuable a firm is, we usually focus on how profitable it is now and how that profitability will grow or decline in the future, along with the risk of investing in the firm.

  • Where are these measures captured in the dividend-discount model?

    • Profitability determines the firm's ability to pay dividends so, implicitly, in the forecasted dividend stream, we are forecasting the firm's profitability.

    • Risk is captured in the equity cost of capital we use to discount those forecasted dividends. Riskier investments require higher expected returns, which enter the dividend-discount model as higher equity cost of capital.

Limitations of the Dividend-Discount Model

• Uncertain Dividend Forecasts: The dividend-discount model values a share based on a forecast of the future dividends paid to shareholders.

  • However, unlike a Treasury bond, for which the cash flows are known with virtual certainty, a firm's future dividends carry tremendous uncertainty.

  • Small changes in the assumed dividend growth rate can lead to large changes in the estimated share price.

• Non-Dividend Paying Shares: Many firms do not pay dividends

  • In the U.S., Facebook (Meta Platforms Inc), Google (Alphabet Inc) and Amazon.com Inc are just a few examples of firms that have not yet paid dividends.

  • These technology firms reinvest all their earnings to grow their businesses rather than paying dividends.

  • How, then, do we value those shares?

    • To apply the dividend-discount model, you would have to assume that these firms will eventually pay dividends – but how do you estimate when?

    • A preferable technique is to value the free cash flows generated by the firm, which is known as the discounted free cash flow model. Students doing AFIN1002 will apply this model to value a company listed on the ASX.

Putting It All Together

• How would an investor decide whether to buy or sell a share?

  • They would value the share using their own expectations.

  • If their expectations differed substantially from others, they might conclude that the share was over- or under-priced.

  • Based on that conclusion, they would buy or sell the share.

• How could a share suddenly be worth more or less after an earnings announcement?

  • As investors digest the news, they update their expectations and buying or selling pressure would then drive the share price up or down until the buys and sells come into balance.

• What should managers do to raise the share price?

  • The only way to raise the share price is to make value-increasing investment decisions.

Summary

• Share basics

  • Ordinary versus preference shares

• The dividend-discount model

  • The value of an ordinary share is equal to the present value of all future cash flows the shareholder expects to receive from owning the share

• Estimating dividends in the dividend-discount model

  • Constant growth, changing growth, dividends versus investment and growth

• Limitations of the dividend-discount model

  • Uncertain dividend forecasts, non-dividend paying shares

Formula Summary

• Value of a share = PV of expected dividends: $P<em>0 = \frac{Div</em>1}{1 + r<em>E} + \frac{Div</em>2}{(1 + r<em>E)^2} + \frac{Div</em>3}{(1 + r_E)^3} + \cdots$

• Constant growth model: $P<em>0 = \frac{Div</em>1}{r<em>E-g}$; where $Div</em>1 = Div_0 (1 + g)$

• Equity cost of capital estimated from the DDM model: $r<em>E = \frac{Div</em>1}{P_0} + g$

• Growth rate in dividends: $g = Retention \space rate \times Return \space on \space new \space investment$

• Changing dividend growth:

  • $P<em>0 = \frac{Div</em>1}{1 + r<em>E} + \frac{Div</em>2}{(1 + r<em>E)^2} + \cdots + \frac{Div</em>n}{(1 + r<em>E)^n} + \frac{P</em>n}{(1 + r_E)^n}$

  • where: $P<em>n = \frac{Div</em>{n+1}}{r<em>E - g} = \frac{Div</em>n (1 + g)}{r_E - g}$