Dr. P.V. Viswanath
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## Valuing Lifeway Foods, Inc.

### The Problem:

We are going to value the equity of Lifeway Foods, Inc. (LWAY) as of February 2004, using publicly available information. Here are the steps we need to follow:

First, we need to compute Cash flows from assets, cashflows to equityholders Lifeway Foods, Inc. for 2000, 2001 and 2002.

Click here for an Excel Spreadsheet with computation of cashflow to equityholders and cashflow to debtholders. (Note that the numbers on the spreadsheet are not the actual numbers from LWAY's financial statements. For convenience, some of the numbers have been modified. For example, depreciation has been set at zero and PPE is set at net PPE.) Some of the liability and asset categories have also been collapsed.)

The computations below show CF to the firm for 2000 using the standard formula for FCFF.* (Numbers for other years can be seen on the spreadsheet.) Subtracting out CF to debtholders then gives us FCFE.

 Cashflow to the firm Year: 2000 Net Income 928 Plus Interest 92 plus Depreciation 0 Less Capex 487 Less Change in WC -334 Cashflow to firm 867 Less Cashflow to creditors 669 Equals CF to equityholders 198

Note: We add back interest because that is not an outflow from the firm.

* Note that the FCFF computed here is not the number that we would use if we were looking for free cashflows to the firm to then discount using the WACC. For that purpose, we would not add back interest in full. Rather, we would reduce it by (1-tax rate); this is because we don't want to recognize the tax benefits of debt in the cashflow computation -- instead, we take it into account in the calculation of the WACC. Here, we use a marginal tax rate estimate of 35%. But our purpose in computing Cashflow to the firm is to ultimately end up with cashflow to equityholders; that's the reason we are adding interest back in full -- as an intermediate calculation.

Computing FCFE directly without going through the computation of Cashflow to the firm would give us Net Income plus Depreciation Less Capex Less change in WC Plus Net New Debt Raised. This will give us the same number as above.

Although we can compute FCFE and FCFF in this way, we can compute also CF to equityholders more directly by taking dividends paid to stockholders and adding net new equity issued. This works if we are computing historical FCFE and FCFF using financial statement information. This works because of double-entry book-keeping.

However, we normally desire to project FCFE. Under these circumstances, the standard full-fledged formula (used in the table) is more useful because it gives us guidance in forecasting. Computing FCFE by adding dividends to net new equity issued is not a useful formula because Net New Equity issued is more of a residual quantity and we can't forecast a residual quantity.

#### The Approach:

Remembering that in a market, market value = price = present value of future cashflows, we need to get cashflows to stockholders of LWAY, in the future.

Take the cashflow to equityholders for LWAY that were computed earlier for 2000, 2001 and 2002. But we need cashflows to LWAY for the future, i.e. 2005 and beyond. Here's one approach that you might try.

Use the cashflows from 2000 to 2002 to forecast future cashflows. You can do this in several ways. A simple way would be to assume that future cashflows will grow annually at the same rate as in the past. Under this assumption, simply take the annual rate of growth from 2000 to 2002. This can be computed by taking (CF2002/CF2000)0.5. Suppose this is g. Then the estimated cashflows in 2005 would be CF2002(1+g)3. We know that if the future cashflows are going to increase at a constant growth rate, r, then the PV of that cashflow is CF1/(r-g), where CF1 is the cashflow one year from now, r is the required rate of return on securities with the same risk as this cashflow, and g is the growth rate of the cashflows.

You can also get analyst estimates of the cashflow growth rate from http://finance.yahoo.com/q/ae?s=LWAY. However, if you look at the numbers, there is none for "growth rate for next 5 years." The comparable number for the industry is 8.61%. We could use this as an estimate for LWAY's growth rate. However, it is impossible for LWAY to grow at this rate forever. Hence I would suggest that we assume that this growth rate of 8.61 (maybe moderated to 8.0%) will continue for the 5 years following 2005. Thereafter, assume a growth rate of 5%. (For more information on this, go to http://webpage.pace.edu/pviswanath/notes/investments/eqval.html.) If you do not assume that the cashflows are increasing at a constant rate forever, then you need a modified formula to compute stock price. You can find an example of this around slide number 18 and 19 from the Stock Valuation slides of Chapter 6.

Now that we have the cashflows, we need a discount rate, which, from our discussion should be the required rate of return on that firm. Recall our discussion of the Capital Asset Pricing Model (CAPM). This model says that:

The required rate of a return on a firm = risk-free rate + beta(market risk premium).

The beta of LWAY can be found by going to http://finance.yahoo.com/q/ks?s=LWAY. For the risk-free rate, use the 30 year T-bond yield or the 10-year T-bond yield. This can be found at http://www.bloomberg.com/markets/index.html or at http://www.bloomberg.com/markets/rates/index.html. Use an estimate of 6% for the market risk premium.

### The Pricing of LWAY's shares

The cashflow to equityholders for 2002, 2001 and 2000 according to my computations (see excel spreadsheet for details) are \$999, \$811 and \$197 respectively (in thousands).

If we compute the growth rate from 2000 to 2001, we get 312% p.a. and if we compute it from 2001 to 2002, we get 23% per annum. We cannot expect to have the share price for LWAY grow at this rate forever. Considering that the economy as a whole has been growing over the last fifty or so years at a rate of less than 6% p.a., a company that grows at a faster rate would simply be larger than the entire economy, given enough time.

The best assumption would be to assume that the higher growth would continue for a limited period of time only, after which it would grow at the same rate of growth as the economy, say at 5.5% per annum. This assumes that once the stock starts growing at this stable rate of growth, it would be a constant percentage of the economy, in terms of market value.

Now, if we go this way, what should we posit as the rate of growth of LWAY's share price for the high-growth period, and how long should this high-growth period be? A rate of 23% is probably too high, except for a very short period. And, of course, this assumes that LWAY's growth rate in the future will be the same as that in the past. If we look at the growth rate for the industry, we see that the five-year growth rate forecast for the industry on Yahoo is 8.61%. (There is no 5-year estimate given for LWAY; note, however, that the growth rate for the next quarter and the next year are negative! Let us ignore this for now.). Let us, then, assume that LWAY's experience will be similar to that of the industry for the next five years (moderated to 8%), after which it will grow forever at 5.5% p.a.

Using this, we can price LWAY's shares in the following way. First, let us price LWAY, five years from now. In 2002, the cashflow to equity was \$999,000. Since the number of shares outstanding are 8.44m (according to http://finance.yahoo.com), this gives us a per share cashflow to equity in 2002 of \$0.11836. This implies that at a growth rate of 8% per annum for 5 years, the per share cashflow in 2009 (which is five years from now, but seven years from 2002) is 0.11836(1.08)8. = \$0.2191.

Now the 30-year T-bond rate, according to Bloomberg.com on March 23, 2004 is 4.65%; LWAY's beta, according to Yahoo is 0.54; using a market risk premium of 6%, we get a cost of equity of 4.65 + 0.54(6) = 7.89%.

Hence, the share value in 2008 can be computed as (0.2191)/(0.0789 - 0.055) = \$9.1687. (We compute the 2008 terminal value by taking CF in 2009 and dividing by (r-g)). The present value of this would be 8.4877/(1.0789)5.= \$5.806. Now the present value of the cashflows from 2005 to 2009 can be computed as a growing annuity, using the formula, PV = C[1-{(1+g)/1+r)}n]/(r-g); in our case, this works out to 0.11836(1.08)3 [1-(1.08/1.0789)5]/(0.0789-0.08) = \$0.6924.

Adding the two quantities, i.e. the present value of cashflows to equity for the next five years, plus cashflows to equity in perpetuity, thereafter, or 0.6924 + 5.806, we get \$6.50.

Now, the current price of LWAY is \$22.91. However, we have to note a few things. First of all, LWAY's shares underwent a 2-1 split. In other words, in 2002, it's shares outstanding totalled about half as much; according to the 2002 10-K, its shares outstanding were 4,268,844. If we use this number, the estimated price approximately doubles to (6.50)(8,440,000/4,268,844) or \$12.85. However, the share has now split 2-1, so each share is now only worth half as much; the per share price then drops to \$6.425. So we still have a big discrepancy between our price and the current market price of \$22.91.

Now, this could be because we were too cautious in estimating growth over the future. If we allow for higher growth, then our price estimate would increase as well. For example, if we allow for 16% for the next 10 years, the price would be 0.234(1.16)3 [1-(1.16/1.0789)10]/(0.0789-0.16) + (0.234)(1.16)13/(0.0789-0.055)(1.0789)-10 = 4.79 + 31.55 = 36.34, or accounting for the 2-for-1 split, a current market price of \$18.17. At this stage, we need to stop playing around with the numbers! Before we leave the issue, take a look at Motley Fool's comments on the share price of LWAY, as of February 18, 2004. (Note that we have, here, changed the per share value of cashflows to equity from 0.11836 to 0.234.) Keep in mind, also that, as late as Mar. 10, the stock was trading at \$15, while at the end of January, it was trading at about \$8!

(If we go ahead and assume a growth rate of 6.5% per annum for ever, then our current price would work out to 0.234(1.065)3/(0.0789-0.065) =\$20.44, which works out to a price of \$10.22 after the split!)