The value of any asset is the present value of the expected cash flows on the assets.
The value of equity is the present value of cash flows to the equity investors discounted back at the rate of return that those equity investors need to make to break even (the cost of equity). In the strictest sense of the word, the only cash flow stockholders in a publicly traded firm get from their investment is dividends, and the dividend discount model is the simplest and most direct version of an equity valuation model.
A firm includes not just the equity, but all claim holders. The cash flow to the firm is the collective cash flow that all claim holders make from the firm, and it is discounted at the weighted average of their different costs.
Sets up the basic inputs: 1. Discount rates 2. Cash flows 3. Expected Growth 4. Length of the period that they can sustain a growth rate higher than the growth rate of the economy.
Recaps what we stated when we talked about investment analysis.
This reproduces the bottom-up beta estimated for Aracruz, by looking at other paper and pulp companies and factoring in its significant cash holdings. The cost of equity is estimated in real terms, by using a real risk free rate. (In the long term, this is assumed to be equal to real growth in the Brazilian economy)
This reproduces the botttom-up beta for Deutsche Bank, looking at other commercial banks in Germany, and investment banks in the US and UK. The cost of equity is estimated in nominal DM.
This is a reproduction of a page that we used to estimate costs of capital for Disney divisions as part of the investment analysis section.
Again, reproduction of an earlier page.
Shows the three different cash flows that can be used in valuation. Cap Ex includes acquisitions and the effect of R&D. (R&D is capitalized)
The FCFE for Aracruz are estimated for the current year, using normalized earnings per share rather than current earnings. Next year’s net cap ex is expected to be 0.06 BR per share. We will assume that the firm will stay at its existing debt ratio of 39%.
The working capital change is rather large. We might need to normalize before we start forecasting the cash flows.
Again, include acquisitions as part of cap ex.
As a general rule, we should use a free cash flow (rather than a dividend) to discount, if we can estimate the free cash flow. It is difficult to estimate cap ex and working capital for a financial service firm. When leverage is changing, we need to forecast debt repayments and new debt issues to estimate the free cash flow to equity. The free cash flow to the firm can be estimated much more directly.
Note that the approaches are similar, with the only difference being in how we define how much the firm reinvests and how well it reinvests.
In the short term, improvements in return on equity will translate into more than proportional increases in expected growth in earnings. In fact, the expected growth in earnings per share in any year can be written as: g EPS = b *ROE t+1 +{(ROE t+1 – ROE t )BV of Equity t )/ROE t (BV of Equity t )} Note that the larger the firm, the greater the effect (in either direction) of changes in ROE.
Note that what we need are estimates for the future. While we might start with the base year estimates, nothing in valuation requires us to stay with these inputs.
Leverage will have a positive effect on expected growth as long as the projects taken with the leverage earn more than the after-tax cost of debt. Again, while we need to use book values if our objective is to explain past growth, looking forward, we need to make the best estimates we can for each of these inputs.
This decomposes the return on equity at Disney, using 1996 numbers as the base. If Disney preserves its 1996 return on capital, and finances future investment needs at its current book value debt to equity ratio. If it finances these investments at its current market debt to equity ratio, the return on equity will be much lower.
The reinvestment rate and the return on capital should be forward-looking numbers, rather than what they were last year.
Note that we are replacing the current numbers with normalized estimates.
Firms have infinite lives. Since we cannot estimate cash flows forever, we assume a constant growth rate forever as a way of closing off the valuation. A very commonly used variant is to use a multiple of the terminal year’s earnings. This brings an element of relative valuation into the analysis. In a pure DCF model, the terminal value has to be estimated with a stable growth rate.
If the stable growth rate is set below the growth rate of the economy (as it should be), you should never find g to be greater than r, which leads to absurd values.
This is the shakiest area of valuation. The high growth period should be a function of a firm’s capacity to earn excess returns and erect and maintain barriers to entry. This is where corporate strategy meets corporate valuation.
I would expect Biogen to grow longer, because its barrier to entry (patent) is much stronger and easier to maintain.
I would not be inclined to use growth periods longer than 10 years. While there are firms like IBM, Microsoft and Coca Cola which have been able to sustain growth for much longer periods, they are more the exception than the rule. Most firms are able to maintain high growth for shorter periods. I am going to use firm valuation for Disney, because I expect leverage to change, and firm valuation is simpler when that occurs For Aracruz, I will use FCFE, since I do not expect leverage to change, and do the analysis in real terms, to avoid having to deal with expected inflation in BR For Deutsche Bank, where it is difficult to estimate free cash flows, I will use dividends and make the assumptions that dividends over time will be equal to FCFE.
When you adjust the growth rate to make it stable, make the other inputs about the firm consistent with the stable growth assumption.
There is a significant subjective judgment involved with each of these estimates. That is unavoidable.
Note that Disney’s current reinvestment rate is 50%, but it also has a higher return on capital (20%) and higher growth.
We are using the dividend discount model because it is difficult to estimate the FCFE for a bank. (What are the capital expenditure and working capital requirements of a bank?) We assume that Deutsche Bank, given its size and the competitive sector it operates in, is in stable growth. We have used a normalized return on equity of 14% (which is the industry average ROE) to estimate expected growth rate forever.
Any or all three of these explanations could hold. While it is natural to assume that you have estimated something wrong, the entire point of valuation is to take a stand when you feel that you have made reasonable assumptions. In other words, you could back out what would need to be true (in terms of growth and return on equity) for the market to be right, and then ask the question of whether this is feasible.
We use the FCFE model because dividends are less than FCFE and we assume that leverage is stable. (If you can estimate FCFE, it is better to do the valuation using FCFE rather than dividends)
This summarizes the inputs for the Aracruz valuation. Again, note That high growth is assumed to last for 5 years (This is the assumption with the least basis to it.) That the beta is assumed to move to one in stable growth Net cap ex is assumed to decrease as growth decreases to stable growth levels towards the industry average. Working capital is assumed to stay at today’s level of revenues. (An alternative is to assume that the industry average for working capital as a percent of revenues)
These are the projected FCFE the next 5 years. These FCFE are discounted back to the present at the current cost of equity.
To estimate the value of equity per share at the end of the fifth year, we use FCFE in year 6. (This is your chance to adjust the fundamentals of the company including cap ex to stable growth levels) and the stable period beta. This terminal price is discounted back to the present at today’s cost of equity. This valuation is likely to yield too high an estimate, because it assumes that earnings have already been normalized. For instance, if you do not expect earnings to be normalized for two years, you can discount 2.94 BR at 10.33% for two years to get the present value.
While Disney is a large firm, its brand name (especially in children’s entertainment and theme parks) will allow it to earn excess returns and maintain high growth for a longer period.
The transition period is used as a phase where the inputs from the high growth period can be adjusted towards stable growth levels (which reflect industry or market averages). Note that we estimate reinvestment needs using the expected growth rate and the return on capital. We are making the assumption that Disney will continue to earn excess returns even in stable growth. (The return on capital is moved towards the industry average of 16%, but it is still higher than the cost of capital). If that assumption seems over optimistic, the return on capital in stable growth can be set equal to the cost of capital. The leverage is pushed up to 30%, which was the constrained optimal we arrived at in the capital structure section.
These projected cash flows reflect the assumptions made on the previous page. As revenue change, the non-cash working capital also increases, which drains cash flows.
The cost of capital changes over time, since both beta and leverage change over time.
To estimate the terminal value, we first estimate how much needs to be reinvested. With a growth rate of 5%, and a return on capital of 16%, the total reinvestment (net cap ex + change in working capital) is Reinvestment Rate = (Net Cap Ex + WC)/ EBIT(1-t) = 5/16 = 31.25% The free cash flow to the firm is used to arrive at the terminal value, with the cost of capital in year 11 being used as the discount rate.
This computes the present value of all of the cash flows over the next 10 years, as well as the terminal value at the end of year 10.
Since the cost of capital is changing over time, the cumulated cost of capital has to be used as the discount factor. PV of year 7 cash flow = $3,932/(1.1224) 5 (1.118)(1.1138) = $1,773
The sum of the present values provides you the value of the firm. From this the value of all outstanding debt has to be subtracted. Note that the debt subtracted out at this stage has to be exactly the same debt that was used to compute the initial cost of capital. Thus, if operating leases are capitalized and treated as debt at that stage, they have to be subtracted out at this stage. The value of equity is divided by the number of shares to get to the value of equity per share. To the extent that there are other claims on equity (warrants, management options etc.), the value of these claims (using an option pricing model or market prices, if available) have to be subtracted out from the total value of equity, before dividing by the number of shares outstanding.
Brings it all together. The stock was trading at $75.38 at the end of 1996 when I did this. It has had a 2 for 1 stock split since then, and is trading at about $ 30 today.
Shows the link between our valuation and the earlier corporate financial analysis.
This is the preferred mode of valuation on Wall Street. Philosophically, it is a different way of thinking about valuation. In relative valuation, we assume that markets make mistakes on individual investments, but that they are right, on average, in how they price a sector or the market. (In discounted cash flow valuation, we assume that markets make mistakes over time.)
All multiples have their roots in fundamentals. A little algebra can take a discounted cash flow model and state it in terms of a multiple. This, in turn, allows us to find the fundamentals that drive each multiple: PE : Growth , Risk, Payout PBV: Growth, Risk, Payout, ROE PS: Growth, Risk, Payout, Net Margin . Every multiple has a companion variable, which more than any other variable drives that multiple. The companion variable for the multiples listed above are underlined. When comparing firms, this is the variable that you have to take the most care to control for. When people use multiples because they do not want to make the assumptions that DCF valuation entails, they are making the same assumptions implicitly.
Note that when people compare firms across sectors, they implicitly assume that firms in a sector have similar risk and cash flow characteristics. This is clearly a dangerous assumption to make. The PEG ratio is a simplistic way of controlling for expected growth differences across firms. A low PEG ratio is viewed as a sign of an undervalued firm. The PEG ratio is based upon the implicit assumption that PE and expected growth are linearly related.
If we assume that all of the firms in this sector have similar growth, risk and payout characteristics, Disney is correctly valued, because its PE is close to the industry average. On a PEG ratio basis, if we assume that all firms in this sector have similar risk and payout characteristics, Disney is overvalued. It is tough to say. It depends upon whether the DCF valuation is making reasonable assumptions and whether the market, on average, is pricing these firms correctly.
Invest in projects that yield a return greater than the minimum acceptable hurdle rate .
The hurdle rate should be higher for riskier projects and reflect the financing mix used - owners’ funds (equity) or borrowed money (debt)
Returns on projects should be measured based on cash flows generated and the timing of these cash flows; they should also consider both positive and negative side effects of these projects.
Choose a financing mix that minimizes the hurdle rate and matches the assets being financed.
If there are not enough investments that earn the hurdle rate, return the cash to stockholders.
The form of returns - dividends and stock buybacks - will depend upon the stockholders’ characteristics .
Objective: Maximize the Value of the Firm
3.
Discounted Cashflow Valuation: Basis for Approach
where,
n = Life of the asset
CF t = Cashflow in period t
r = Discount rate reflecting the riskiness of the estimated cashflows
The value of equity is obtained by discounting expected cashflows to equity, i.e., the residual cashflows after meeting all expenses, tax obligations and interest and principal payments, at the cost of equity, i.e., the rate of return required by equity investors in the firm.
where,
CF to Equityt = Expected Cashflow to Equity in period t
ke = Cost of Equity
The dividend discount model is a specialized case of equity valuation, and the value of a stock is the present value of expected future dividends.
The value of the firm is obtained by discounting expected cashflows to the firm, i.e., the residual cashflows after meeting all operating expenses and taxes, but prior to debt payments, at the weighted average cost of capital, which is the cost of the different components of financing used by the firm, weighted by their market value proportions.
where,
CF to Firmt = Expected Cashflow to Firm in period t
Critical ingredient in discounted cashflow valuation. Errors in estimating the discount rate or mismatching cashflows and discount rates can lead to serious errors in valuation.
At an intutive level, the discount rate used should be consistent with both the riskiness and the type of cashflow being discounted.
The cost of equity is the rate at which we discount cash flows to equity (dividends or free cash flows to equity). The cost of capital is the rate at which we discount free cash flows to the firm.
Average Unlevered Beta for Paper and Pulp firms is 0.61
Aracruz has a cash balance which was 20% of the market value in 1997, which is much higher than the typical cash balance at other paper and pulp firms. The beta of cash is zero.
When you cannot estimate the free cash fllows to equity or the firm, the only cash flow that you can discount is dividends. For financial service firms, it is difficult to estimate free cash flows. For Deutsche Bank, we will be discounting dividends.
If a firm’s debt ratio is not expected to change over time, the free cash flows to equity can be discounted to yield the value of equity. For Aracruz, we will discount free cash flows to equity.
If a firm’s debt ratio might change over time, free cash flows to equity become cumbersome to estimate. Here, we would discount free cash flows to the firm. For Disney, we will discount the free cash flow to the firm.
g EBIT = (Net Capital Expenditures + Change in WC)/EBIT(1-t) * ROC = Reinvestment Rate * ROC
Proposition 2: No firm can expect its operating income to grow over time without reinvesting some of the operating income in net capital expenditures and/or working capital.
Proposition 3: The net capital expenditure needs of a firm, for a given growth rate, should be inversely proportional to the quality of its investments.
Return on Capital =20% (Higher than this year’s 18.69%)
Expected Growth in EBIT =.5(20%) = 10%
The forecasted reinvestment rate is much higher than the actual reinvestment rate in 1996, because it includes projected acquisition. Between 1992 and 1996, adding in the Capital Cities acquisition to all capital expenditures would have yielded a reinvestment rate of roughly 50%.
A publicly traded firm potentially has an infinite life. The value is therefore the present value of cash flows forever.
Since we cannot estimate cash flows forever, we estimate cash flows for a “growth period” and then estimate a terminal value, to capture the value at the end of the period:
A key assumption in all discounted cash flow models is the period of high growth, and the pattern of growth during that period. In general, we can make one of three assumptions:
there is no high growth, in which case the firm is already in stable growth
there will be high growth for a period, at the end of which the growth rate will drop to the stable growth rate (2-stage)
there will be high growth for a period, at the end of which the growth rate will decline gradually to a stable growth rate(3-stage)
The assumption of how long high growth will continue will depend upon several factors including:
the size of the firm (larger firm -> shorter high growth periods)
current growth rate (if high -> longer high growth period)
barriers to entry and differential advantages (if high -> longer growth period)
Assume that you are analyzing two firms, both of which are enjoying high growth. The first firm is Earthlink Network, an internet service provider, which operates in an environment with few barriers to entry and extraordinary competition. The second firm is Biogen, a bio-technology firm which is enjoying growth from two drugs to which it owns patents for the next decade. Assuming that both firms are well managed, which of the two firms would you expect to have a longer high growth period?
Earthlink Network
Biogen
Both are well managed and should have the same high growth period
Profitability measures such as return on equity and capital, in stable growth, can be estimated by looking at
industry averages for these measure, in which case we assume that this firm in stable growth will look like the average firm in the industry
cost of equity and capital, in which case we assume that the firm will stop earning excess returns on its projects as a result of competition.
Leverage is a tougher call. While industry averages can be used here as well, it depends upon how entrenched current management is and whether they are stubborn about their policy on leverage (If they are, use current leverage; if they are not; use industry averages)
Use the relationship between growth and fundamentals to estimate payout and net capital expenditures.
g EBIT = (Net Capital Expenditures + Change in WC)/EBIT(1-t) * ROC = Reinvestment Rate * ROC
Moving terms around,
Reinvestment Rate = g EBIT / Return on Capital
For instance, assume that Disney in stable growth will grow 5% and that its return on capital in stable growth will be 16%. The reinvestment rate will then be:
Reinvestment Rate for Disney in Stable Growth = 5/16 = 31.25%
In other words,
the net capital expenditures and working capital investment each year during the stable growth period will be 31.25% of after-tax operating income.
Stock is tremendously overvalued: This valuation would suggest that Deutsche Bank is significantly overvalued, given our estimates of expected growth and risk.
Dividends may not reflect the cash flows generated by Deutsche Bank. TheFCFE could have been significantly higher than the dividends paid.
Estimates of growth and risk are wrong: It is also possible that we have underestimated growth or overestimated risk in the model, thus reducing our estimate of value.
The current earnings per share for Aracruz Cellulose is 0.044 BR.
These earnings are abnormally low. To normalize earnings, we use the average earnings per share between 1994 and 1996 of 0.204 BR per share as a measure of the normalized earnings per share.
Model Used:
Real valuation (since inflation is still in double digits)
2-Stage Growth (Firm is still growing in a high growth economy)
FCFE Discount Model (Dividends are lower than FCFE: See Dividend section)
The present value is computed by discounting the FCFE at the current cost of equity of 10.33%.
38.
Aracruz: Estimating Terminal Price and Value per share
The terminal value at the end of year 5 is estimated using the FCFE in the terminal year.
The FCFE in year 6 reflects the drop in net capital expenditures after year 5.
Terminal Value = 0.269/(.125-.05) = 3.59 BR
Value per Share = 0.154 + 0.152 + 0.150 + 0.149 + 0.147 + 3.59/1.1033 5 = 2.94 BR
The stock was trading at 2.40 BR in September 1997.
The value per share is based upon normalized earnings. To the extent that it will take some time to get t normal earnings, discount this value per share back to the present at the cost of equity of 10.33%.
In relative valuation, the value of an asset is derived from the pricing of 'comparable' assets, standardized using a common variable such as earnings, cashflows, book value or revenues. Examples include --
• Price/Earnings (P/E) ratios
and variants (EBIT multiples, EBITDA multiples, Cash Flow multiples)
Assume that you are reading an equity research report where a buy recommendation for a company is being based upon the fact that its PE ratio is lower than the average for the industry. Implicitly, what is the underlying assumption or assumptions being made by this analyst?
The sector itself is, on average, fairly priced
The earnings of the firms in the group are being measured consistently
The firms in the group are all of equivalent risk
The firms in the group are all at the same stage in the growth cycle
The firms in the group are of equivalent risk and have similar cash flow patterns
Invest in projects that yield a return greater than the minimum acceptable hurdle rate .
The hurdle rate should be higher for riskier projects and reflect the financing mix used - owners’ funds (equity) or borrowed money (debt)
Returns on projects should be measured based on cash flows generated and the timing of these cash flows; they should also consider both positive and negative side effects of these projects.
Choose a financing mix that minimizes the hurdle rate and matches the assets being financed.
If there are not enough investments that earn the hurdle rate, return the cash to stockholders.
The form of returns - dividends and stock buybacks - will depend upon the stockholders’ characteristics .
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