This returns us to the original objective function, with which we started this discussion, which is the maximization of firm value. In this section, we link the investment, financing and dividend decisions to the value of the firm.
The basics of valuation are no different from the basics of project analysis. The value of any asset is the present value of the expected cash flows over its life.
In equity valuation, we look at the entire analysis from the perspective of equity investors in the firms. (This is analogous to an equity approach in investment analysis) In firm valuation, we try to value the underlying business, with all the different claims on it (debt, equity and preferred stock)
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.
One way to think about the value of the firm is in terms of the different claimholders in the firm. The cash flow to the firm is the cumulated cash flows obtained by all claimholders in the firm (Equity investors get dividends, debt holders get interest and principal payments and preferred stockholders get preferred dividends). The appropriate discount rate for these cash flows has to be the weighted average of all of their required rates of return, which is the cost of capital.
Both approaches need the same amount of information. In the case of equity valuation, leverage has to be explicitly modeled into the cash flows in the form of interest and principal payments. In the case of firm valuation, leverage has to show up in the discount rate. Practically speaking, it might be simpler to do the latter than the former when leverage is changing.
This principle of consistency implies that Cash flows to equity (firm) be discounted at the cost of equity (capital) Dollar (DM) cash flows be discounted at dollar (DM) discount rates Nominal (real) cash flows be discounted at nominal (real) discount rates
In practical terms, this means that we have to estimate detailed cash flows until we expect the firm to be in stable growth. The alternative way of applying closure, which is to estimate the terminal value by applying a multiple of earnings to the fifth or tenth year’s earnings ends up being a relative valuation rather than a discounted cash flow valuation. (The value is heavily influenced by the multiple used to get terminal value)
To apply the terminal value approach, the firm has to be in a growth rate that is sustainable forever. Since no firm can grow faster than the economy in which it operates forever, this puts the logical bound of the economy’s growth rate on this number. If this is done in real terms, it will be the economy’s real growth rate To the extent that a firm (like Coca Cola) services the world economy the real growth rate of the world economy can be used. The nominal growth rate that can be used will depend upon the currency in which the cash flows are estimated. The expected inflation rate in that currency can be added to the real growth rate to arrive at the nominal growth rate. As a simple rule of thumb, this nominal growth rate should not be much higher than the long term government bond rate.
There is a strong subjective element to this process, since we are looking at estimates for the future. Everything you know about the firm, the sector in which it operates and the overall economy will go into making this judgment. Microsoft, for instance, is a very large firm, but the barriers to entry it has created may allow it to maintain high growth for a long period.
Biogen, because it has greater barriers to entry can be expected to have a logner growth period. Earthlink might be well managed, but the excess returns will draw competitors into the business, which, in turn, will reduce the potential for high growth in the future.
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.
Valuation models represent some combination of these three choices - a cash flow, a discount rate and a growth pattern.
The principles underlying discount rates in valuation are the same as the principles underlying discount rates in investment analysis.
A dividend-growth model estimates the cost of equity to be the dividend yield plus expected growth in earnings in the firm. It is, however, based upon two assumptions: The firm is in stable growth, and paying dividends = FCFE The firm is correctly valued by the market Because of these limitations, you have to use a risk and return model to estimate value.
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.
The cost of capital is a weighted average of the cost of equity and the cost of debt, with the weights based upon market value. In a firm valuation, every input in this model can be year-specific. The leverage can change over time, and so can the costs of debt and equity.
This is the bottom-up beta calculation for Disney, using the different businesses Disney is in, the unlevered betas of these businesses and the weights based upon operating income. The debt ratios used for all but the real estate division, which carries its own debt, is the debt ratio for Disney as a firm (without real estate).
This summarizes the cost of capital computation for Disney. It is identical to the cost of capital used in the investment analyses and capital structure sections.
This is the short form of FCFE that we will be using to forecast FCFE. Implicitly, we are assuming that leverage will stay stable at the specified debt ratio.
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 cash flow to the firm is the cumulated cash flow to all its claimholders.
Since the FCFE is after debt payments and preferred dividends anyway, it is far simpler to estimate the cash flows by acting as if debt and preferred stock do not even exist. Since leverage does not affect this cash flow, it is called an unlevered cash flow. The tax savings from interest payments are ignored, because they will be considered in the cost of capital, as a benefit. Counting it in as an additonal cash flow here will lead to a double counting of the benefit.
The FCFF for Disney is estimated using the after-tax operating income, net cap ex and change in non-cash working capital in 1996. The FCFF is, in a sense, an artificial cash flow, since a levered business will never see this cash flow.
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.
The Gap’s expected growth = .25 * .7 = 17.5% J.P. Morgan’s expected growth = .15 * .5 = 7.5% The return on equity is the ceiling on expected growth.
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.
E(growth) = .8 (.18) = 14.4% E(growth after restructuring) = .7 (.20 + .25(.20-.06)) = 16.45% The firm will have a higher growth rate in earnings per share, but it will also be riskier (the higher leverage will lead to a higher beta and cost of equity). While I think the growth effect will dominate (because return on equity is greater than the cost of equity), the net effect, in general, can be positive or negative. In other words, higher growth, by itself, does not imply higher value.
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 growth in operating income will almost always be lower than growth in earnings per share. Thus, using analyst projections of growth (which are usually based upon earnings per share) in firm valuation can lead to inflated estimates of value. This also looks past the magnitude of the growth at the quality of growth. A firm can report high growth rates in operating income, but if the growth is created by high reinvestment rates (rather than high returns on capital), the firm might not be creating value.
Note that the forecasted reinvestment rate should include acquisitions as well. For high-tech companies, the expensing of R&D creates a problem. This approach which looks at net capital expenditures will yield very low growth rates in operating income for these firms. To get a viable estimate, you will have to strip R&D expenses from the income statement, and look at the after-tax R& D expense as part of reinvestment.
A firm cannot have zero reinvestment and expect to have high growth in operating income. In fact, if net cap ex is zero and there are no working capital requirements, there is no reinvestment and growth rates have to be zero.
Whether firms increase their return on capital by increasing their margin or increasing turnover depends upon the strategic perspectives they bring to the process and what their differential advantages are. If their differential advantages lie primarily in economies of scale, they may choose to increase turnover. If their differential advantage lie primarily in brand name or product quality, they might focus on increasing margin.
As the growth rate for a firm is changed during the course of a valuation, the other characteristics also have to change for consistency.
In stable growth, you are really looking at a firm very different from the one you are looking at today. Firms in stable growth should share a lot of common characteristics. A Microsoft is stable growth may have more in common with a GM in stable growth then it does with another software firm. In valuation, it is important to get a sense of what is reasonable and what is sustainable. This is particularly true of the characteristics given a firm in stable growth, since these get locked in forever beyond that point.
This allows us to estimate the payout ratio that a stable growth firm can have, given its project returns. This insight can be used to use the dividend discount model to value non-dividend paying firms. While they might not pay dividends currently, when they have high growth rates, the expected dividends in future periods will not be zero, especially as growth is adjusted downwards.
This uses the fundamental growth formulation to estimate how much a firm will need to reinvest to grow at its stable growth rate. Thus, firms which have a higher return on capital will have a higher terminal value for a given growth rate because they will need to reinvest less This reinvestment covers both net capital expenditures and working capital needs.
This is true in mathematical terms. This is false, however, in practical terms because the terminal value is affected significantly by assumptions made during the high growth period. A higher growth rate in earnings will generally translate into a higher terminal value.
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.
This is a pictorial representation of the dividend discount model. It is a valuation of J.P. Morgan that illustrates Where growth comes from: In this case, growth comes from projects taken (ROE) and reinvestment (through the retention ratio) The interrelationship between the different assumption. Thus, a change in investment policy will change both the return on equity (and thus the growth rate) and the beta (which affects the cost of equity). Note in stable growth that we set the beta =1 (stable growth firms are generally average risk firms). The terminal price is computed as follows: New Payout Ratio = 1 - g/ROE = 1 -.05/.143 = 0.65 $6.80 (1.0859) 5 (1.05) (.65)/(.125-.05) = $ 100.29 This terminal price will be discounted back at the current cost of equity of 12.83%.
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.
This is a pictorial representation of the FCFE model, showing the interrelationships between the different assumptions. Note again the changes in assumptions after year 5 (Beta moved to 1, Cap Ex as as percentage of depreciation moved towards industry averages). This was a valuation of NCR, when it was acquired by AT&T in 1991. Note that AT&T ended up paying almost twice this amount (presumably for the synergy)
The FCFE model will generally yield a higher value than the DDM, because FCFE tends to be higher than dividends for most firms. The difference will narrow if dividend payout is expanded to include expected stock buybacks over time.
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.
This summarizes the Disney valuation, and shows the interplay of corporate financing decisions (investment, financing and dividend) and valuation. This is a simple way of thinking about value enhancement. There are three levers for creating value: Take better projects -> This will increase the return on capital , which pushes up growth or lowers reinvestment needs, and may increase the length of the high growth period . Choose a better financing mix -> This will lower the cost of capital and increase the present value of the cash flows Choose a better reinvestment policy -> If the projects being taken at the margin have returns lower than the cost of capital , reinvesting less will create value (the loss in growth will be more than offset by the gain in cash flows). If the projects at the margin have excess returns , reinvesting more will create value. Note the close linkage to value enhancement strategies like EVA that attempt to simplify this process by looking at the difference between the return on capital and the cost of capital.
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
It is often argued that equity valuation requires more assumptions than firm valuation, because cash flows to equity require explicit assumptions about changes in leverage whereas cash flows to the firm are pre-debt cash flows and do not require assumptions about leverage. Is this true?
Never mix and match cash flows and discount rates.
The key error to avoid is mismatching cashflows and discount rates , since discounting cashflows to equity at the weighted average cost of capital will lead to an upwardly biased estimate of the value of equity, while discounting cashflows to the firm at the cost of equity will yield a downward biased estimate of the value of the firm.
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
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 of return that investors require to make an equity investment in a firm. There are two approaches to estimating the cost of equity;
a risk and return model
a dividend-growth model.
Using the CAPM, for instance, gives you a cost of equity based upon the beta of the equity in 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.
Earnings: Since Aracruz’s 1996 earnings are “abnormally” low, I used the average earnings per share from 1992 to 1996.
Capital Expenditures per share next year = 0.24 BR/share
Depreciation per share next year = 0.18 BR/share
Change in Working Capital = 0.03 BR/share
Debt Ratio = 39%
24.
Cashflow to Firm C l a i m h o l d e r C a s h f l o w s t o c l a i m h o l d e r E q u i t y I n v e s t o r s F r e e C a s h f l o w t o E q u i t y D e b t H o l d e r s I n t e r e s t E x p e n s e s ( 1 - t a x r a t e ) + P r i n c i p a l R e p a y m e n t s - N e w D e b t I s s u e s P r e f e r r e d S t o c k h o l d e r s P r e f e r r e d D i v i d e n d s F i r m = F r e e C a s h f l o w t o F i r m = E q u i t y I n v e s t o r s F r e e C a s h f l o w t o E q u i t y + D e b t H o l d e r s + I n t e r e s t E x p e n s e s ( 1 - t a x r a t e ) + P r e f e r r e d S t o c k h o l d e r s + P r i n c i p a l R e p a y m e n t s - N e w D e b t I s s u e s + P r e f e r r e d D i v i d e n d s
You attempting to estimate expected growth for The Gap and J.P. Morgan. The Gap has a return on equity of 25% and pays out 30% of its earnings as dividends. J.P. Morgan has a return on equity of 15% and pays out 50% of its earnings as dividends. Estimate the expected growth rate for each of these companies –
Assume that you estimating the effect of a recent restructuring at Rubbermaid on expected growth. Rubbermaid has a return on assets of 18% , has no leverage and pays out 20% of its earnings as dividends. It is planning to sell of low-return assets and increase its return on assets to 20%, increase its debt equity ratio to 25% and pay 30% of its earnings as dividends. The tax rate is 40%, and the pre-tax borrowing rate is 10%. Estimate the growth rate before and after restructuring:
E(growth) before restructuring =
E(growth) after restructuring =
Does the higher growth automatically mean that the value of the stock will increase?
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.
Actual reinvestment rate in 1996 = Net Cap Ex/ EBIT (1-t)
Net Cap Ex in 1996 = (1745-1134)
EBIT (1- tax rate) = 5559(1-.36)
Reinvestment Rate = (1745-1134)/(5559*.64)= 7.03%
Forecasted Reinvestment Rate = 50%
Real Return on Capital =18.69%
Expected Growth in EBIT =.5(18.69%) = 9.35%
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%.
Many analysts assume that capital expenditures offset depreciation, when doing valuation. Is it an appropriate assumption to make for a high growth firm?
Yes
No
If the net cap ex is zero and there are no working capital requirements, what should the expected growth rate be?
36.
Return on Capital, Profit Margin and Asset Turnover
Return on Capital
= EBIT (1-t) / Total Assets
= [EBIT (1-t) / Sales] * [Sales/Total Assets]
= After-tax Operating Margin * Asset Turnover
Thus, a firm can improve its return on capital in one of two ways:
It can increase its after-tax operating margin
It can improve its asset turnover, by selling more of the same asset base
This is a useful way of thinking about
choosing between a low-price, high-volume strategy and a high-price, lower-volume strategy
the decision of whether to change price levels (decrease or increase) and the resulting effect on volume
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.
The bulk of the present value in most discounted cash flow valuations comes from the terminal value. Therefore, it is reasonable to conclude that the assumptions about growth during the high growth period do not affect value as much as assumptions about the terminal price.
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%.
48.
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%.
Most firms can be valued using FCFE and DDM valuation models. Which of the following statements would you most agree with on the relationship between this two values?
The FCFE value will always be higher than the DDM value
The FCFE value will usually be higher than the DDM value
The DDM value will usually be higher than the FCFE value
The DDM value will generally be equal to the FCFE value
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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