As a general note, it is easy to get lost by focusing on the calculation of ratios. The students probably need more help in interpretation of ratios. Instruction should include both help with calculations and guidance in interpretation.
Valuation is critical to investment, mergers and acquisitions. It provides a benchmark for categorizing under valuation and overvaluation. We will consider stock valuation. Depending on the circumstances, we will use discounted dividend models, discounted cash flow models and market multiple models. Students will have the opportunity to try each method on real companies in the homework. Finally, they will have the opportunity to trade in the IEM based on their analysis.
While intrinsic value is the major focus o this module, we should be aware of other measures of value. Book value per share is the total common stockholders’ equity divided by the number of shares outstanding. Liquidation value is the break-up value of assets in the case of bankruptcy. It should form a floor for value. Market value is the market determined price per share. The intrinsic value of a financial assets is the present value of its future cash flows discounted according to the riskiness of the cash flows. In an efficient market, market values and intrinsic values should converge.
For common stock, the investors’ required rate of returns, k, can be obtained from CAPM. According to CAPM, the higher the systematic risk (beta), the higher the required rate of return.
Beta measures the sensitivity of a stock’s return to the return on the market. The market has a beta of 1. The 3-month treasury bill rate is a proxy for the risk-free rate. The risk premium is the excess return that is awarded for investments in risky assets. A historical average risk premium is used to estimate its value. NOTE: it is important to be consistent. Use a risk premium estimated relative to 3-month Treasuries if you use a 3-month Treasury as the risk free rate. Use a risk premium estimated relative to 10-year Treasuries if you use a 10-year Treasury as the risk free rate, etc. We will stick to a 3-month rate here.
Students can get all this information from the web. You might want to do another example in class. Go to the MSN MoneyCentral website (MoneyCentral.msn.com) and enter ticker symbol of the company you wish to consider. The “company report” lists beta at the bottom right. For the current 3-month treasury rate, enter TB3M as the ticker symbol.
NOTE: All three factors increase the cost of borrowing. A 0.05 increase represents a 5% increment to the risk free rate and the risk premium. A 0.05 increase represents a 0.5 unit change in beta. The discount rate will be more sensitive to the risk free rate than the risk premium if beta1.
As owners of the firm, shareholders have claims to dividends and retained earnings. The growth in dividends parallels the fortunes of the firm, while retained earnings provide the impetus for capital gains. The required rate of return is a combination of the dividend yield and the capital gains yield. The retention ratio, which is equal to 1-payout ratio, is a determinant of the apportionment of return between dividend yield and capital gains yield. The sustainable growth rate g, is the product of the retention ratio and the return on equity. Firms that have several investment options will payout less (or nothing) in dividends. Whereas firms in mature industries will have low or zero retention ratios. Shareholders own cash flows and and have a keen interest in the projections of future cash flows. The valuation of the financial asset, common stock, is equal to the present value of discounted future dividends. The value is directly related to the growth rate in dividends and inversely related to the discount rate. The discount rate is influenced by the riskiness of future dividends.
The zero growth discounted dividend model assumes that the expected level if dividends is constant forever. It is important to distinguish the difference between dividends that are constant in expectation and those that are actually constant. All that is required here is constant in expectation. This is also the valuation model for a perpetuity or preferred stock with a fixed dividend. In these cases, the dividend is actually constant.
A lively discussion should ensue here! Why is the estimated price so low? Try changing the dividend…within reasonable bounds, it doesn’t come any where near $52.83. Try changing the discount rate…within reasonable bounds, it doesn’t come anywhere near $52.83. What is going on? Obviously, we’re missing growth. The zero growth model assumes that the firm has a zero retention rate and, hence, a zero growth rate. For firms such as Wal-Mart, that plowback a significant amount of their earnings, this model will grossly understate the value as this example shows. Hence, the need for models of stock pricing that incorporate growth.
Obviously, increasing dividends increases value…but not by much relative to the effect of growth, which we will see later. Similarly, decreasing the discount rate increases value…but, again, not by much relative to growth. You might want to begin discussing the consistent inverse relationship between the discount rate and value here.
Firms increase dividends as earnings grow along with future prospects for growth. Competitive advantages, const containment, leverage, surging demand, increases in high-end or high-margin sales, etc., are all reasons that earnings and dividends grow. A wider choice of positive NPV projects will enable firms to re-invest a larger portion of their earnings. This will further accelerate earnings. Even at a constant payout ratio, increased earnings will lead to growing dividends.
The constant growth model assumes that dividends are expected to grow a a constant rate forever. (Again, this is an expectation, not an ex-post realization.) the formula for valuation under this scenario has a major requirement: that the required rate of return must exceed the growth rate in dividends. The model will not work if exceptionally high growth is anticipated forever. However, such growth rates are unrealistic in most situations. Why? The growth rate is forever…not for just a few years. Sure, a company can grow exponentially for a time, but eventually, the must slow as their market matures, as they become a large share of their market, etc. Otherwise, they would outstrip the growth in the economy as a whole! The trouble is that most forecasts of growth are for short periods. Even the “long run” growth reported by analysts on the internet are only for the next 5 years. It’s easy to grow at, say, 10% for five year…you’ll less than double in size. But, you have to double in size every 7 years to continue at this rate forever. Since the economy doesn’t grow that fast, no company would be able to sustain it for ever. It is important to emphasize realistic expectations for long run growth.
The growth rate, g, is an important input in the discounted dividend model. The estimate of g is critical to the value derived. Sensitivity analysis is useful in analyzing the range of values for different estimates of g. The growth rate can be estimated using a historical average or the average of analysts’ forecasts. (But, keep in mind, analysts’ “long run” forecasts are only for 5 years!) The sustainable growth rate is given by retention ratio times ROE. But, the market may not support this much growth. Finally, a market based estimate of the growth rate can be determined by subtracting the dividend yield from the required rate of return.
While estimating the growth rate, using various methods, the choice of g must be based on reasonable LONG RUN expectations and the requirement that g<k. The required return minus the dividend yield gives a market based forecast.
The value of common stock is very sensitive to the estimate of g. As g approaches k, the price increase exponentially…as the following sensitivity analysis shows. Note: It is not particularly surprising here that the price is close to the market price because we chose a growth rate that is close to the 11.3% implied by the market. You might want to see if your students can figure this out in discussion.
Dividends matter…sure. But not nearly as much as increasing long run growth and decreasing the discount rate. Really, it is the difference between the two that matters. As k-g 0, the price increases without bound…and it becomes very volatile. This forms the basis for a good discussion on the sky-high valuations of internet stocks and their extreme sensitivity to interest rates and (largely unfulfilled) growth expectations.
The dividend discount models are appropriate for valuing companies that generate dividends at a steady growth rate or, in the extreme, zero growth rate. This present difficulties when valuing companies which are growing at a fast pace (g>k) and, moreover, cannot be sustained indefinitely. Companies who do not pay dividends can be valued by using earnings as a proxy for dividends or discounting future cash flows available to the shareholders. In the case of companies that have not generated earnings yet, the price to sales ratio can be used instead of price to earnings.
Discounted dividend models are useful in valuing companies that pay dividends. In the case of companies that do not pay dividend, valuation methods using cash flows can be used.
Cash flow is commonly stated as net income plus depreciation – preferred stock dividends. This cash flow can be paid out as dividends or re-invested. The returns demanded by bondholders and preferred stockholders have already been accounted for. Hence, it forms the returns to common stock investors.
The discount rate is an important factor in valuation. The higher the discount rate, the lower the value. In equity valuation, k can be calculated using CAPM. The higher the systematic risk, beta, the higher the required rate of return and, hence, the lower the value of the stock. In the case of cash flows that include payments to bondholders and preferred stockholders, the proper discount rate is the WACC.
CAPM provides a simple way to calculate the required rate of return. The risk-free rate is measured by the 3-moth Treasury bill rate, the historical average risk premium relative to this risk free rate is used along with the beta. You might want to do another example here. From MoneyCentral (MoneyCentral.msn.com), the beta for a company can be found after entering its ticker symbol under “company report” in the lower right. The current 3-month Treasury rate can be found by entering the ticker symbol: TB3M.
To estimate the growth rate, g, in cash flows, earnings or sales growth can be used as a proxy. Expenses and re-investment rates need to be relatively constant percentage of sales for this to “work.”
Again, you may want to work up another example. All of the information is form MoneyCentral under “Financial Results—Statements—Income Statement.” Be aware: Cash flow growth is often extremely volatile. As in the case of g for the discounted dividend model, the growth rate can be estimated from different sources. The proper rate will depend on the circumstances. For K-Mart, the 5 year historical sales growth was 2.35%, the 5 year historical cash flow growth was 8.37%. Analysts were forecasting earnings growth of 10.3% for the next 5 years. The market implies a NEGATIVE growth rate for K-Mart..as we’ll see next.
This should spark a lively discussion. The zero growth rate gives a value well above the current market price! Apparently, the market thinks that K-mart is expecting negative growth! Can your students figure this out?
The sensitivities are the same as for the constant growth discounted dividend model…for the same reasons! Again, growth relative to the cost of borrowing are the real value drivers.
Shareholders own cash flows. Part are paid out in dividends the rest of re-invested on the shareholders’ behalf. Since the cash flows are derived from net income minus preferred stock dividends, after-tax interest expense and the returns given to preferred stockholders are excluded from cash flows. Because of this, the discount rate only needs to reflect the equity risk. So, using CAPM, we can derive the discount rate for the cash flows.
In the case of companies that do not fit the discounted dividend model profile, price per share can be estimated by forecasting earnings, sales or cash flows based on historical averages or analysts’ projections and applying the company’s historical P/E, P/S or P/CF ratio. As an alternative, the industry average ratios may be used. The market multiples are good indicators of market sentiment on a stock’s future prospects. Shareholders are interested in this information as they justify holding or selling the shares.
Thus, the P/E ratio reflects two things: The required return for the company and The value of growth opportunities relative to current company earnings
Sales, earnings and cash flows are the drivers of profits, growth and value. Price to sales, price to earnings and price to cash flows measure the relationship between market price and these value drivers. If, there is considerable homogeneity in the sale, profit and cash flow patterns, it is reasonable to value a firm based on it’s sales, earnings or cash flows times the respective industry ratios.
Timing is tricky here. You can also us the industry average to predict future prices if you put future cash flows in.
Again, discuss the differences in the prices derived from this valuation and the actual price.
As earnings or the P/E ratio rise…so does price. The 0.50 change on the scale represents a 5 unit change in P/E.
Price to sales is a useful proxy for P/E when a company has not reported any earnings. This became increasingly popular with the rise of internet companies!
Amazon is a company that has not reported any earnings as of this date. The disparity between Amazon's current stock price the the calculated price should spark discussion! The calculated price comes from the industry “ Internet Software & Services,” but is this the right comparison industry for Amazon? Maybe they should be compared to the “bricks and mortar” retailers like Barnes and Noble. The industry (Specialty Retail, Other) P/S ratio for this industry is: 0.42. This would result in a MUCH lower price for Amazon!
Same as before…
Price to cash flow is another method for valuing companies that do not pay dividends.
Again, it’s a discussion opportunity! K-Mart’s CF/Share of $2.50 multiplied by the industry average P/CF of 21.3 give s price MUCH higher than the current price. Why? Is it undervalued? Does the market know that it’s in serious trouble? What do you students think? Again, you can use your own example from Money Central. The number of shares can be found on the balance sheet under “financial results—statements.”
Same as before!
The valuations provided by historical ratios and the industry average ratios provide useful benchmarks for valuing the shares of a firm. They incorporate analysts’ projections, historical information and current market prices.
Sensitivity analysis is very useful in assessing forecasting risk. Stock valuation is sensitive to estimates of growth rates, the discount rate, the risk free rate, the risk premium and beta. Of these factors, the financial manager probably has the most influence over long run growth! Therefore, it should command his or her attention. The assignments provide a means for applying the techniques for valuation discussed in this module as well as familiarizing students with information sources on the internet and the Iowa Electronic Markets.
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Valuation Curriculum designed for use with the Iowa Electronic Markets by Roger Ignatius Thomas A. Rietz