In chapter 9 we learned how to value a project. The same principles are applicable to financial assets such as stocks and bonds. It is the expected cash flow we receive, discounted at a risk-adjusted rate, that returns the correct value of any assets. There are some differences after tax, however, as depreciation in projects is tax deductible, as shown in chapter 9.
When we invest in stocks, the cash flows that we receive are the dividends, and, if you decide to sell, the cash flow from the sale. A stock represents a right of ownership of the equity in a company. The ownership has limited liability, implying that you cannot lose more than what you paid for the equity. When valuing a company we look at the cash flow to shareholders, which implies all future dividends and/or share buy-backs.
Financial analysts and investors use a number of models in order to gauge the value of a stock. The role of financial analysis is to find a value that differs from the current share price. If the estimated value is above the current price, you should buy it. If it is below, you should avoid owning it or short it. Below we look at some techniques that are used for valuing stocks.
We start with the simple dividend model. The cash flows to the shareholders are the dividends paid in eternity. In order to find the present value of all future dividends, we use the dividend discount model, also known as the Gordon Model, named after its inventor Myron Gordon. The value of a share is therefore the net present value of all future anticipated dividends discounted at the appropriate risk-adjusted cost of equity. Future dividends are expected to grow at a constant rate g.
where
DIV |
is the next year’s dividend |
g |
is the growth rate in dividend |
r |
is the cost of capital. |
If you decide to sell the stock in year T at price PT, the NPV becomes:
Equations 12.1 and 12.2 will yield the same value, as PT also is the present value of all cash flows from year T to infinity. It can be shown mathematically (beyond the scope of this book) that the expression in equation 12.1 converges to the much simpler formula:
when T goes to infinity.
But what if the value we have found is similar to the current stock price? Does this imply that we can expect no return from owning the stock? No! It means that we get the same return as the cost of capital. When the expected return equals the cost of capital, the investment has a net present value of 0. The net present value is the present value of all future cash flows minus the initial investment (here, the stock price). When a stock is correctly priced, its expected r equals the internal rate of return, which in turn is the stock’s cost of capital.
A stock is bought at the start of the year for P0 = 350. For the next five years it pays out an annual dividend of 30. The first dividend is paid out after year 1. In year 5 the stock is sold for 410. What is the return from the stock investment?
Cash flows are shown in cells B4:G4 in the spreadsheet in figure 12.1. At the end of year 5, we get a cash flow that comprises the dividend and the proceeds from the stock sale; 30 + 410 = 440. We can then use the Excel IRR function in cell B6, which yields an internal rate of return of 11.31 per cent.
Figure 12.1 Return from stock investment.
If this return, 11.31 per cent, is higher than for similar investments (its cost of capital), demand for the stock will increase and move the share price, P0, towards its “fair value”, an analyst’s jargon for an investment with a net present value of nil.
When the stock price rises, future return will fall towards the cost of capital. Similarly, an expected return that is below the cost of capital will lower the demand for the stock and drive the price downwards. In efficient markets prices for assets with the same risk will therefore converge to equilibrium where all assets will have the same risk-adjusted expected return. If not, there is a possibility of arbitrage. Arbitrage occurs when you can simultaneously sell one asset and buy a similar asset and pocket a risk-free profit.
As mentioned above, equations 12.1 and 12.2 represent similar formulas for valuing stocks. What assumptions do we have to make for the dividends; DIV1, DIV2 …? We have three possibilities, as follows.
1. Constant dividend
If we assume that the dividend (DIV) will be the same for ever, equation 12.1 becomes very simple. The term (1 + g) will be 1 for all years since g = 0. We just divide the dividend by the cost of capital, r:
This could be a preferred stock that promises to pay a fixed dividend for ever.
How do we find the cost of equity, r? We have two possibilities:
1) using the Capital Asset Pricing Model: r = rf + β[E(Rm) – rf] (equation 8.41)
2) using the Gordon Model (equation 12.3).
In equilibrium the cost of equity must equal the expected return of a stock at the given stock price. We can then rearrange Gordon’s formula in equation 12.3 to:
Since g = 0 here, we get
2. Dividends with constant growth
If we assume that the dividend will grow at a constant factor, g, equation 12.1 becomes an infinite geometrical series:
The return on equity, r, consists of return from dividends (DIV/P0) and yearly growth, g, in the dividend. The factor g is a constant yearly growth that can be the level of expected inflation or some other company-specific cause.
3. Erratic dividend
Things get more complicated once dividends vary unsystematically. We can then no longer use the simple formulas above. This is more realistic and we have to do some more tedious calculus.
For companies that grow rapidly, we usually assume that all earnings are retained for financing for a number of years. We can still use the dividend discount model though, but we have to adjust the dividend/pay-out ratio to reflect changes in the growth rate. When growth slows, we can estimate when dividends are expected to be paid out. For non-dividend-paying stocks it is more common to use discounted cash flow models.
Below we shall use the dividend discount model for valuing a company that has erratic dividends. We look at a company that at first has a constant dividend for a period, then some higher growth in dividend for some years and then a stable dividend growth for ever. This will then be a three-stage dividend discount model.
A stock is expected to pay out a constant dividend of 50 for the next six years. From year 7 to year 15, the dividend is expected to grow by 8 per cent per annum. From year 16 and forward, dividend is expected to grow annually at a rate of 5 per cent for ever. What should the stock be worth when the cost of capital is 14 per cent? What return will an investor get from buying the stock at 400?
The price should equal the net present value of the dividends, where g1 = 0.08 (years 7–15) and g2 = 0.05 (from year 16 onwards).
This calculation is also shown in cell B12 in the spreadsheet in figure 12.2. Here we have calculated the brackets separately in cells B11:D11. For instance, in cell B11 we find the formula “=B3*(((1+B14)^5)–1)/(B14*(1+B14)^5)” (figure 12.3).
Figure 12.2 Finding the stock price with different growth rates.
Figure 12.3 Formulas used to find the return with respect to the internal rate of return.
Now we will find the return if the stock is bought at a price of 400. This will be the same as finding the internal rate of return (IRR):
This equation is quite tedious to solve! Fortunately, we have the Goal Seek function in Excel. In the spreadsheet in figure 12.4, we have found IRR to be 16.5 per cent by using the Goal Seek function. (In the main tabs menu: Data, What-If Analysis, Goal Seek.) In cell B15 we have the function “=SUM(A11:D11)” and the formulas in cell B11:D11 point to cell B14.
The dividend discount model is very sensitive to the choice of growth rates and discount rates. In its simplest version (Gordon’s formula), the stock price moves exponentially with both variables.
Figure 12.4 Finding the return when the stock is bought for 400 using the Goal Seek function.
Some companies prefer to return capital to the owners through repurchases of shares. This must be added to any dividend payments as they also are cash flows to the owners. The relevant numbers to use are therefore dividends plus the amount of money that is used for repurchasing of the company’s own stock. The total is known as equity pay-out.
12.2 Discounted cash flow model (DCF)
The most common method among financial analysts for valuing a stock is probably the discounted cash flow method (DCF). When trying to gauge the expected future cash flows, analysts most often use the company’s financial statement. The dividend discount model in section 12.1 is based on the notion that only dividends received by shareholders have any value for investors. In a DCF analysis, analysts look at either
• the free cash flow to equity or
• the free cash flow to firm.
The methods will return the same answer as long as we use the appropriate discount rate; the cost of equity and the weighted average cost of capital respectively. Let us start with the free cash flow to equity.
Free cash flow to equity
The free cash flow to equity (FCFE) method is very similar to the dividend discount model (DDM), but will most often return different estimates of value. Only in two special cases will the two models return the same value:
• Dividends = free cash flow to equity
• Dividends < free cash flow to equity, but the residual (FCFE minus dividends) is reinvested at NPV = 0.
The main difference is therefore what you think about the cash flow to equity that is not paid out as dividends. Does the rate of return of the retained earnings exceed the cost of equity? If so, the DCF approach will return a higher value than DDM. Which is the method to use? For companies where shareholders have little influence on management, investments or pay-out ratio, DDM is the more appropriate model to use.
While DDM uses the strict definition of cash flow to equity as dividends only, the FCFE model uses an expanded definition: the residual cash flow after meeting all financial obligations, capital expenditure and working capital needs, or
We can now use the same procedure as in section 12.1, but substitute dividend with FCFE:
where
P0 |
is the value of the stock today |
FCFE1 |
is the expected free cash flow to equity next year |
r |
is the cost of equity |
gn |
is the expected growth in free cash flow to equity. |
Similarly, we can use a multiple stage model as shown in example 12.2. Remember how we compute the cost of equity, r:
a) the Capital Asset Pricing Model or
b) Gordon’s formula.
The Capital Asset Pricing Model
As shown earlier, the cost of capital can be estimated using the Capital Asset Pricing Model (CAPM). The model states that the expected return for stock i is:
where
rf |
is the risk-free rate |
[E(rm)–rf] |
is the risk premium in the equity market (expected excess return over the risk free rate) |
βi |
is the stock’s beta. |
Since all stocks actually represent the equity in the company, we can regard the stock’s expected return as the expected return for the entire equity. In equilibrium, the expected return on a stock must equal the cost of equity. Hence, we use the CAPM to find the cost of equity.
Assume that the risk-free rate is 5 per cent before tax and the equity risk premium is 7 per cent after tax. If the tax rate is 28 per cent and the stock’s beta is 1.5, we can derive the after-tax cost of equity:
rE = 5 per cent(1 – 0.28) + 1.5 · 7 per cent = 14.1 per cent
This capital cost mirrors the company’s risk. If a company undertakes a project that has a different risk than for the company, one should use a cost of capital that is appropriate for that project. If not, it could, for instance, seem more profitable for a low-risk pharmaceutical company to undertake oil drilling in harsh water than for an oil company to do so.
Figure 12.5 shows some mock data from 1981–2010 for the equity market (the market portfolio) and risk-free government bonds. All data are pre-tax. Estimate the return on equity as of 31 December 2010 for a stock that has a beta of 1.35.
Figure 12.5 Mock data for stock market return and risk-free return (government bonds).
In the spreadsheet in figure 12.6 we calculate the risk premium, E(rm) – rf, for all individual years. More correctly, we are computing the historical excess return (return above risk-free rate) as an estimate of the risk premium. We take the arithmetic average of all the years, as shown in cell D16. Remember that we use the arithmetic average as the expected value and geometric average as the realized or actual return. Note that we cannot know the “true” risk premium (because it is ex ante). It is quite common, however, to use the long-term arithmetic average as an estimate (ex post). We use the latest rate of expected return (“yield to maturity”) on a risk-free government bond as the risk-free rate (8.0 per cent). Then the cost of capital becomes:
Figure 12.6 Estimating the expected return from historical average (arithmetical).
Gordon’s formula
Instead of CAPM we can use Gordon’s formula in equation 12.3. This is most suitable for companies with stable growth. This growth cannot be too high, though, as g cannot exceed the growth rate of the overall economy. (Otherwise, the company eventually will become bigger than the whole economy!)
Gordon’s formula states that the value of a stock is the present value of all future dividends. If we assume that the stock pays out a dividend (DIV) that grows at a constant factor of g for ever, we can use the formula for an infinite geometrical series that converges to a simple expression:
Here we use the cost of equity, rE, since the market value of the shares in equilibrium should equal the value of the equity. Then, from equation 12.4, the cost of capital becomes
This model involves some circular reasoning. Using the current share price in equation 12.4 above, we get the cost of equity, but using this same cost of equity to find the share price in equation 12.5, we will (of course) find the same price.
A company is expected to pay a dividend of 5 for next year (DIV1), and the dividend is expected to grow at an annual rate of 5 per cent. Its stock trades at 50. Find the cost of equity.
Using the rearranged Gordon’s formula in equation 12.5, we find the cost of equity as:
We now use this cost of equity in equation 12.4 to find the value of the stock:
Hence, the stock is fairly valued at the cost of capital that is derived from the current stock price!
The DDM model assumes that the company is in a steady state, which implies that capital expenditure should be in line with depreciation and that the company is of average risk. But the cost of equity is very sensitive to a company’s use of debt. Many analysts therefore prefer to value a company from the perspective of free cash flow to the company instead.
Free cash flow to firm (FCFF)
Free cash flow to equity is very much dependent on the management’s decisions about payout ratio and stock repurchase. If we cannot change or influence the management’s decisions about pay-out and stock repurchases, it is better to look at the total free cash flow. If we look at the free cash flow to the firm, we can disregard elements such as dividend and leverage and instead focus on the company’s operating activities: sales, labour costs, investments etc.
Free cash flow is the sum of cash flows to all claim holders in the company: shareholders, bondholders and any holders of preferred shares. We can find the free cash flow to firm from two accounting perspectives.
Net profit after taxes |
Operating profit (EBIT) minus tax |
+ Depreciation |
+ Depreciation |
+ After-tax interest payments |
– Increase in current assets |
– Increase in current assets |
+ Increase in current liabilities |
+ Increase in current liabilities |
– Increase in fixed assets at cost |
– Increase in fixed assets at cost |
|
= FCFF |
= FCFF |
To demonstrate the difference between FCFF and FCFE more clearly, we can show this relationship: FCFF = FCFE + interest expense (1 – tax rate) + principal payments – new debt + preferred dividend. As we can see from the right-hand side of this equation, we have to add all cash flow to debtholders or holders of preferred stocks. The widely used accounting term “earnings before interest and taxes” (EBIT) is related to FCFF through this entity:
Here we see that FCFF is derived by adding or subtracting cash elements from the post-tax operating profit. FCFF can therefore remind one of another widely used valuation variable: earnings before interest, taxes, depreciation and amortization (EBITDA). A lot of analysts do indeed, wrongly, use the two interchangeably. FCFF includes potential tax liabilities from earnings and investments in fixed assets and working capital and is not similar to EBITDA.
When we use FCFF we have to relate this to the overall value of the company, also known as enterprise value (EV). We then have to use the company’s total cost of capital, not only the cost of equity, as with the FCFE method.
A company can finance itself by issuing shares (equity) or by borrowing (debt). Most companies do both. The cost of capital will therefore be the average of the cost of equity and the cost of debt. Unless the mix is exactly 50/50, we have to take the weighted average of debt (D) and equity (E). We therefore denote this weighted average cost of capital, WACC:
This cost can be before or after tax. We just have to make sure we don’t mix after-tax WACC and before-tax cash flows.
Imagine a company with 2 million in debt and 6 million in equity. If the after-tax cost of equity is 12 per cent and the after-tax cost of debt is 4 per cent, we get this cost of capital for the company:
If we substitute dividends with free cash flow to firm and use the WACC instead of the cost of equity, we can find the value of the company including debt, also known as the enterprise value (EV), in the same way as we found the value of the equity:
which is an infinite geometrical series that converges to:
Consider a company that has a free cash flow to firm of 1,000,000. This cash flow is expected to grow by an annual rate of 6 per cent. The cost of capital is calculated as the WACC shown above (10 per cent). The company has debt of 5,000,000 and cash and cash equivalents of 500,000. There are 1 million shares outstanding. What is the enterprise value and equity value of the company?
Using equation 12.6 we get:
The value of the enterprise is 26,500,000, but in order to find the value of the equity, we have to deduct the debt and add any cash:
Equity = EV – debt + cash = 26,500,000 – 5,000,000 + 500,000 = 22,000,000
With 1 million shares outstanding, the value per share is:
This is shown in the spreadsheet in figure 12.7.
Figure 12.7 Value of stock using the free cash flow to firm method.
The idea behind the DCF method is the separation theorem, i.e. a separate valuation of a company’s assets and debts also known as the Miller–Modigliani theorem (MM). The theorem states that the value of a company is independent of how the company finances itself, i.e. what the capital structure is. However, if equity and debt are taxed differently, which very often is the case in real life, this theorem does not hold.
The crux in MM is that when debt replaces equity, the equity risk will increase. A higher equity risk must be accompanied with higher expected return. Any cheaper financing from use of more debt will command a higher cost of equity, hence the company’s total capital cost (WACC) will not change.
Although taxes distort the MM proposition, we still may prefer the FCFF as the best valuation model. The main benefit of the FCFF model is that we don’t have to take account of the cash flows related to debt (but we do need to know the level of debt in order to calculate the WACC).
Second, dividends and repurchases of stocks can very much be influenced by management’s decisions. Using FCFF we can concentrate on the company’s business (sales, operating costs, capital expenditure, etc.), which in fact might be more easily estimated than cash flow to equity (dividends and repurchase of stocks). Last, cost of equity is responsive to the capital structure.
Using pro forma statements in valuation
We shall now show how you, as an analyst, can make predictions about future cash flows to the firm. This is usually done by looking at a company’s financial statements. Although the financial statement only shows historical numbers, they are very useful when it comes to understanding a company’s operational and financial characteristics.
Analysts use the financial statements as the source for making pro forma models of the company. These models are used for valuation of stocks, bonds and possible loans to companies. By plugging in the past five or 10 years of financial history, the analyst gets an understanding of the company’s financials, and is better suited for making cash flow projections. The beauty of these models is that we only have to enter some growth projections for sales, operational costs, investments, etc. and the model will return projected cash flows. (Note: not all companies experience a linear growth for ever – the so-called “hockey-stick” growth. Some volatility in the earnings is more realistic, albeit more difficult to project.) By discounting the cash flows, we can get the present value of all the cash flows, which then becomes the fair value of the company. By dividing the total value by the number of shares, we get the correct share price.
Usually, the most crucial input variable is sales. Most other variables are, in one way or another, related to sales; cost of sales, operating expenses and to some degree sales and marketing expenses. Let us look at a simple case.
In figure 12.8 we have the profit and loss statement and the balance sheet for a financial statement from an imaginary company.
The company is using the declining balance method for depreciation, with an annual rate of 8 per cent. The tax rate is 28 per cent. Interest on interest-bearing debt is 5.2 per cent, while the interest on cash deposits is 3.7 per cent. The company expects to keep its long-term debt fixed, and aims at 10 per cent pay-out ratio of its annual net profit. How much is the company worth?
Figure 12.8 Balance and profit and loss statement for a company.
First we have to make a number of assumptions. All these assumptions are shown in figure 12.9.
Figure 12.9 Assumptions for pro forma model.
We make the quite common assumption that variables such as operating costs, accounts receivable, long-term assets and short-term debt increase in line with sales growth. If we regard 2012 as a fairly normal year for the company, we can derive some ratios to sales from the profit and loss statement for 2012. We calculate different ratios that we assume will be constant going forward. For instance, cost of goods sold as a percentage of sales is 19,388/53,368 = 0.36 = 36 per cent. When the company’s sales grow, we expect the cost of sales to grow at the same rate, thus keeping the ratio constant. This is done with other ratios as well, and we can estimate next year’s income as shown in figure 12.10.
Figure 12.10 Pro forma model.
In the spreadsheet we have estimated next year’s income (2013). In cell C18 we have estimated the sales as previous year’s sales multiplied by the growth rate (5 per cent). Cost of goods sold, labour costs and other operating expenses are derived by a ratio of sales (B4, B5 and B7). For instance, cost of goods sold is 36 per cent of sales “=$B$4*C18”, which is –0.36 · 56,036 = –20,173. Depreciation in cell C21 is estimated using the declining balance method and a rate of 8 per cent (cell B33). We make the plausible assumption that new investments are larger than depreciation, so the balance items of fixed assets increase in line with sales.
Interest income in cell C24 is 3.7 per cent of average bank deposit during 2013, and becomes 0.037 · (1,972 + 5,906)/2 = 145. Interest expense is calculated in cell C25 as 5.2 per cent of long-term debt. (We assume steady debt so there is no need to use the average.) In cell C27 the tax cost is shown as 28 per cent of pre-tax profit, and dividend is 10 per cent of net profit. What if net profit turned into a net loss? Then we can transfer the loss to next year and deduct it from the profit. We should therefore ideally use the function IF in cell C27, with the condition that cell C26 is zero or more. Here, earnings are positive, though.
The retained profit (5,586) in cell C30 is added to the equity, so that the equity increases to 16,635 + 5,586 = 22,221 by the end of 2013. Short-term debt is found as 26 per cent of sales, while property, plant and equipment, inventory and accounts receivable are calculated in cells C33 to C35 as 56 per cent, 11 per cent and 19 per cent of sales respectively.
In order for the balance sheet to add up, cash and cash equivalents in cell C36 are the residual of equity + debt – (property, plant and equipment + inventory + accounts receivable) = 22,221 + 17,307 + 14,569 – (31,380 + 6,164 + 10,646) = 5,906.
In the model, cash and cash equivalents are residuals. Alternatively, we could have used short-term or long-term debt as the residual by paying down debt instead of increasing cash balance.
In the example we compute the interest income in cell C24 from the cash and cash equivalents in cell C36. Simultaneously we compute the cash and cash equivalents in cell C36 from the interest income in cell C24. This creates a circular reference, so we have to activate an iterative calculation as described in section 2.1.
In order to find the value of the company, we have to estimate pro forma statements for a number of years ahead. We use the C column (with $-sign in the proper cell addresses) to copy the formulas and estimate profit figures for as many years as we like. In the spreadsheet in figure 12.11 we have done this to year 2017.
Figure 12.11 Estimating cash flow from earnings.
From the pro forma statements we will now derive cash flows from operating activities until 2017. We also show the formulas that are used. These cash flows are different from ordinary cash flow analysis. In order to get the cash flows from operations, we have to adjust the accounting numbers. In cells C44:G44 we have the net profits for years 2013–2017. Depreciation is a non-cash expense, so we have to add this (cells C45:G45) to get the net profit without depreciation.
We also have to correct for changes in net working capital. This is not part of the net profit, but will affect the size and timing of the cash flows. Any increase in inventory, accounts receivable and fixed assets will imply cash outflows and is consequently deducted from cells C46:G46, C47:G47 and C49:G49. For short-term debt, the situation is the opposite. The increase in short-term debt is a cash inflow in cells C48:G48.
We assume that this is a non-financial company and that interest income and interest costs are outside the company’s ordinary operations. As this is part of the net profit, we should correct for these items as well. But both interest income and interest costs will have an effect on tax, so we have to correct cells C50:G51 to after-tax numbers.
What about cash flows after 2017? The usual approach is to assume that the company has a terminal value at the end of the forecast period. This can be looked upon as the value of the company if it is sold in year 2017. It is both tedious and somewhat unrealistic to try to estimate cash flows far into the future. Instead we assume that the company at one stage enters a steady state situation in which cash flows will grow at a constant rate. Then we can use the dividend discount model shown in equation 12.3. Using Gordon’s formula from the end of 2017, we enter the cash flow in 2017 times the growth rate of 5 per cent (i.e. next year’s cash flow). The cost of capital is 17 per cent (cell B57).
This market price is calculated in cell G53 and should be added to the cash flow in 2017 as if we sold the company at this price and received cash at the end of the year. Now we have all necessary cash flows in cells C54:G54. We have to discount all the cash flows to today’s value, i.e. find the present value of all cash flows. This will then be the total value of the company. The company’s weighed cost of capital is 17 per cent.
Figure 12.12 Value of equity.
The present value of the cash flows is computed in cell B59. We then have to subtract the debt to find the value of the equity (cell B61). The company’s equity is worth 31,541,000.
12.3 Multiples/comparables
Instead of spending time estimating future cash flows, some analysts use different ratios to gauge the value of a company. The idea is that similar companies should trade at the same ratios. We then make an implicit assumption that the market provides us with the correct valuation for an industry, but that some companies will trade out of line and that their valuations eventually will converge to the industry’s average. As we shall see, comparing different companies’ multiples is a very crude and often a misleading approach. Some of the multiples do not adjust for differences in leverage or growth prospects. The method works only as long as the companies are truly comparable. It is also somewhat dubious to assume that all securities, except the one in question, are correctly priced. We shall look at the most usual multiples, from both the equity perspective and the enterprise value perspective.
Price/earnings – EV/EBITDA
The price–earnings multiple (P/E) is probably the most widely used ratio for comparing companies, probably due to its simplicity and readily available input variables. The price earnings ratio is the ratio of the company’s stock price to its earnings per share:
Here, we don’t have to make any predictions about growth, investments, dividends or risk as we do in a DCF analysis. Still, these same variables indeed determine the stock price. Furthermore, P/E ratios are influenced by differences in accounting rules across countries, especially when it comes to depreciations and write-downs.
Finally, P/E can be a misleading ratio when comparing companies with different capital structure (leverage) as shown below.
Consider four companies that are identical except for their capital structures. Company A is unleveraged, while Company D is heavily leveraged. In the spreadsheet in figure 12.13 we have computed the price/earnings ratios for different levels of leverage. As seen in line 20, the P/E ratio falls as leverage increases. If we compare companies that are similar, but with very different financial risk, we might conclude that the more risky company is undervalued.
Figure 12.13 Companies with same operating profit, but different price-earnings ratios.
If most similar companies trade at a P/E of 12, a P/E of 8 may signal an undervalued stock. There are several caveats here. Company D looks cheaper than company A, although the two companies are identical except for their capital structure. This would suggest that we can add value to the equity by just taking on more debt? That is not the case. A company’s equity does not become more valuable solely because of use of more debt (disregard the effect of tax shield here).
Here is what happens if we use P/E straightforwardly: If we use the same P/E-multiple on companies with different leverage, we will overstate the enterprise value (figure 12.14).
Figure 12.14 Overstating value by using the price–earnings ratio inappropriately.
The difference between Company A’s and Company C’s P/E ratios is a function of interest costs and the different capital structures. Company C has financed its assets partly with debt. If the interest rate jumps to 10 per cent, then C’s net profit will fall to 108 and its P/E jump to 14, the same as the unleveraged company A. This is no coincidence. If Company C’s debt costs the same as its pre-interest earnings yield, the P/E will be identical to an unleveraged P/E (company A) whatever debt level, or at least until it becomes so high that the cost of financial distress might become an issue. On the other hand, if the interest rate drops to 2 per cent, the P/E will fall to 11.
Using the P/E multiple as a method for comparing values of different companies is very common, but it can be very misleading if the companies are different with respect to return on assets, capital structure and so forth. In order to neutralize the effect of leverage, another multiple has been introduced:
Here we compare the market price of debt and equity to the earnings before interest and taxes. Note that EV/EBIT is a pre-tax multiple and should therefore yield a lower number than P/E (because EBIT > earnings), which is after tax.
While helpful, the method is crude. Different asset mixes and hence different depreciation levels will also limit the use of multiple comparables as a valuation method. Yet another remedy has therefore been proposed:
EBITDA is very closely related to cash flow, but as we have seen earlier, it neglects capital expenditures and changes in (net) working capital. Since EBITDA > EBIT, this multiple will usually be even lower than EV/EBIT. An EV/EBITDA multiple of 7 might seem attractive, but if the business requires high capital expenditures and increased working capital, an apparently low multiple might be deceptive.
Price/Book – EV/book value
Another popular valuation method is to look at the relationship between the market value of a company’s equity and its book value of equity. We find the book value of equity as the difference between the book value of the assets and the book value of the liabilities. This implies, for instance, that the book value of assets decreases in line with depreciations if investments do not keep up with the depreciations.
If the market value of the equity is below the book value of the equity, the stock might seem undervalued. However, using Price/Book on a single company is not very helpful. In some industries, typically where strong brand names or intellectual (human) capital dominates, book value will usually count much less than in capital-intensive industries where tangible assets play a more important role.
Actually, there is a link between the value in the Gordon’s formula and price/book-ratio. Let us revisit Gordon’s formula (equation 12.3):
We know that the dividend is the residual of the profit minus retained earnings (1 – the retention rate = pay-out ratio). We can therefore substitute the DIV1 with [EPS0 · (pay-out ratio) · (1 + g)]. Introducing return on equity (ROE)as EPS0/book value of equity (BV) per share, we can write:
Value of equity then becomes:
To find the price to book ratio, we divide by BV:
To simplify, assume ROE is calculated from next year’s earning. Then we can skip (1 + g) in the equation.
The growth rate can be found as the return on the retained earnings:
g = (1 – pay-out ratio) · ROE
Using this entity gives:
Inserting g = (1– pay-out ratio) ROE again gives:
The return on equity and price to book value are thus related. The expected growth rate can be derived from the retention rate and return on equity:
g = retention rate · return on equity = (1 – pay-out ratio) · return on equity
The higher the return on equity, the higher P/BV will be. A higher growth rate will also increase the P/BV ratio.
Generally, we can state that for stable companies (with low or moderate growth) the following should be observed:
• If return on equity > cost of equity ⇒ Price/Book > 1
• If return on equity = cost of equity ⇒ Price/Book = 1
• If return on equity < cost of equity ⇒ Price/Book < 1
Price/Sales – EV/sales
Some analysts also look at sales figures for valuation. While sales per se do not tell us anything about value, it may give us some hints about reasonable valuation, especially when comparing companies. Some variables, such as sales, are more stable than earnings and less sensitive to different accounting rules. It may also reveal a potential upside in valuation if sales margins increase or revert to some industry mean. Let us see how the margin is related to valuation. Remember the value of a stock:
Here P = value of stock (equity value), DIV1 = next year’s expected dividend, r = cost of equity, and g = growth rate in dividends for ever.
DIV1 is equal to the pay-out ratio times the earnings per share (EPS) times the growth rate:
DIV1 = EPS0 · pay-out ratio · (1 + g)
Profit margin is the ratio between earnings and sales (margin = EPS0/sales per share), so we can write:
In order to get the price/sales ratio, we divide by sales per share (S = Sales0)
When profit margin is next year’s expected earnings, we can further simplify:
Company A and B are in the same industry and their financial statements are shown in the spreadsheet in figure 12.15. Calculate the various multiples shown in this chapter and compare the two companies. Which of the stocks seem more attractively priced? We first have to find some market values.
Figure 12.15 Data for two companies.
Figure 12.16 Estimating enterprise value.
Then we can compute the different ratios.
Figure 12.17 Comparing different valuation methods.
Using the traditional price/earnings multiple, the two companies are priced similarly. The EV/EBIDTA multiple suggests Company B is cheaper. However, as we do not know the size of depreciations or investment needs in the two companies, we should be careful about making any decision based on this multiple. Furthermore, Company B is more leveraged than A and should therefore have a lower P/E than A.
The price of Company B’s book equity is higher than A’s (7.5 vs 5.0). This could be due to different return on equity (ROE). For company A the ROE is earnings per share/book value per share = 5/10 = 50 per cent. For company B it is 10/13.33 = 75 per cent. The higher ROE, the higher P/BV will be.
On sales multiple, Company A looks more expensive. This is related to the higher profit margin of 15 per cent versus 8 per cent for company B.
Multiple |
More highly valued |
Earnings |
The same |
Book value |
Company B |
Sales |
Company A |
To sum up: We cannot conclude which company is the cheaper solely based on multiples. We need information about growth prospects. Furthermore, a financial statement for one single year might be misleading. Company A might have experienced an extraordinary good year, while the opposite might have been the case for Company B.
The best solution is to make cash flow projections and discount the cash flows at the appropriate discount rate and then compare the net present value to today’s market price.
Problems
12-1. A company has paid dividends, bought back own shares and issued new shares according to the table below. At the end of year 15, the company has 23,812 shares and the market price per share is 35. Find an appropriate cost of equity (pre-tax).
12-2. Billy’s car wash company will pay an annual dividend of 80 per share the next five years. From year 6 and onwards, the dividend is expected to increase by 4 per cent annually for ever. What should be the market price for the stock when stocks with similar risk have an expected return of 13 per cent? What will be the expected return if you buy the stock for 600?
12-3. A stock is expected to pay out a dividend of 250 the next three years. From year 4 to year 7 the dividend is expected to increase by 7 per cent annually, and then by 5 per cent for all subsequent years. What should be the fair value of the stock when alternative and equally risky investments have an expected return of 15 per cent? What will be the expected return if you buy the stock for 2,200?
12-4. StockOut Inc. is expected to pay a dividend of 2 per share at the end of the year and the dividends are expected to grow at a constant, annual rate of 4 per cent in perpetuity. Current share price is 20. Find the expected return (cost of equity) for the firm.
12-5. Below you will find the balance and profit and loss statements for Marki Ltd. Its assets are depreciated by 20 per cent using the declining balance method. Tax rate is 28 per cent. Long-term interest rate is 8.5 per cent, while the deposit rate is 4.5 per cent. Every year the company pays out all the profit as dividend. Yearly sales growth is expected to be 10 per cent annually. Produce a pro forma statement where you assume that the various ratios (for instance cost of goods/sales) are constant. Use a cost of equity of 15 per cent to compute the fair value of the equity.
12-6. Hit&Run music company has a return on equity of 12 per cent and retains two-thirds of its earnings each year. This year’s earnings were 4. Expected return of the overall market is expected to be 14 per cent, while the risk-free rate is 6 per cent. Hit&Run’s stock beta is 1.25. Find the fair value of the stock and its price/earnings ratio. What happens to the stock price if the company increases its dividend to two-thirds of earnings? Why do we observe this change?
12-7. Cinema Corp. has a stock beta of 1.1 and the market price of its stock is 35. The risk-free rate is 4.0 per cent and the expected return on the market portfolio is 12 per cent. Find the required rate of return (cost of equity) from the Capital Asset Pricing Model. The company’s dividend is expected to grow by 10 per cent the first three years and 7 per cent thereafter. Current dividend is 1.5. Is the fair (intrinsic) value of the stock different from today’s market price of 35? Use the two-stage (erratic) dividend model to find the fair value. Should you buy or short Cinema Corp.?
12-8. Divi-End Corp. paid out half of its earnings of 6 per share last year (dividend of 3). The book value per share is 50. Earnings are expected to grow at 5 per cent for ever. The stock has a beta of 0.9, the expected return on the market portfolio is 11 per cent, and the current share price in the market is 75. We use the long-term government bond rate of 6 per cent as the risk-free rate. What is the price/book ratio, and what return on equity does the current market value of equity warrant?
12-9. Sell-IT-Now Corp. has sales of 100 per share, of which it reported earnings per share of 2.50. Of this, it paid out 1.25 in dividend. The company is expected to grow at a rate of 6 per cent annually. Its stock beta is 0.95. The risk-free rate is 5 per cent. Find the Price/Sales ratio. The stock trades in the stock market at 50. If the estimated growth is correct, what profit margin is required to defend current market price?
12-10. ABC Company has just paid a dividend 3 per share out of earnings of 6 per share. If the book value per share is 40 and the market price is 60 per share, calculate the required rate of return on the stock.