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Unformatted text preview: QUIZ 2: REVIEW SESSION Aswath Damodaran This quiz will cover… ¨ The last two ingredients into DCF valuaHon ¤ ¤ ¨ The loose ends of DCF valuaHon ¤
¤ ¨ Expected Growth: Historical, analyst & parHcularly fundamental growth (to EPS, net income, operaHng income and when margins are changing) Terminal value Cash and cross holdings Assets that have not been counted yet Debt and other potenHal liabiliHes Employee opHons and restricted stock The mechanics of DCF valuaHon ¤
¤ EsHmaHng FCFF and FCFE Dealing with changing discount rates Checking inputs for consistency 2! Fundamental Growth Earnings Measure Reinvestment Measure Return Measure Earnings per share RetenHon RaHo = % of net income retained by the company = 1 – Payout raHo Return on Equity = Net Income/ Book Value of Equity Net Income from non-‐cash Equity reinvestment Rate = assets (Net Cap Ex + Change in non-‐cash WC – Change in Debt)/ (Net Income) Non-‐cash ROE = Net Income from non-‐cash assets/ (Book value of equity – Cash) OperaHng Income Return on Capital or ROIC = A^er-‐tax OperaHng Income/ (Book value of equity + Book value of debt – Cash) Reinvestment Rate = (Net Cap Ex + Change in non-‐
cash WC)/ A^er-‐tax OperaHng Income 3! Terminal Value: The Cardinal Rules 1. 2. 3. 4. Obey the cap: Don’t let the growth rate exceed the growth rate in the economy (and use the risk free rate as your proxy) Adjust the cost of capital to reﬂect “stability): Move betas towards one, debt raHos towards stable ﬁrm levels) Think about the return on capital in perpetuity and where it will be, relaHve to the cost of capital. And use the return on capital to back into a reinvestment rate: Reinvestment rate = g/ ROIC 4! Example: Terminal value calculaHon Problem 1, part a: Fall 2011 ¨ Limroth Enterprises is a family-‐run, publicly traded company that expects to generate $ 60 million in a^er-‐tax operaHng income next year on capital invested of $ 1 billion. The ﬁrm has a cost of capital of 10% and expects to maintain its current return on capital, while growing 2% a year in perpetuity. What is the value of the operaHng assets? 5! SoluHon Expected EBIT (1-‐t) = 60 ¨ Capital invested = 1000 ¨ Return on capital = 60/1000 = 6% ¨ Cost of capital = 10% ¨ Expected growth rate = 2% ¨ Expected Reinvestment rate = 2%/6% =33.33% ¨ Value of operaHng assets = 60 (1-‐.33)/ (.10-‐.02) = = 500 ¨ 6! Loose End 1: Cash Cash, by itself, if usually a neutral asset, earning a low but fair rate of return. ¨ However, the market may discount the cash holdings of a company, if it feels that the managers will waste the cash (by invesHng at less than the cost of capital). ¨ Conversely, the market may anach a premium to the cash in some companies, if it feels that cash is a strategic weapon that can help the company make it through hard Hmes or buy distressed company assets. ¨ 7! Example: Part b of problem 1, Fall 2011 ¨ Assume that Limroth Enterprises has $ 100 million in cash and marketable securiHes and that you believe that there is a 60% chance that management will reinvest this cash to generate returns to similar to what they are earning on their exisHng operaHng assets (in investments with a similar risk proﬁle); there is a 40% probability that the cash will remain invested in commercial paper and T.Bills, earning 1%. How much value would you anach to the cash? 8! SoluHon Assuming that the cash does not get wasted Probability of happening = 40% Value of cash = $100 = 100 Assuming that cash gets wasted on projects making 6% (cost of capital of 10% Probability of happening = 60% Value of cash = 100 *.06/.10 = 60 Expected value of cash = 76 9! Loose End 2: Cross Holdings ¨ ¨ ¨ Cross holdings can broadly be classiﬁed into “minority” holdings in other companies and “majority” holdings. With minority holdings, the operaHng income will generally not include the income from the holdings and you should be adding the value of these holdings to a convenHonal DCF With majority holdings, the analysis will depend upon whether you are using the consolidated ﬁnancials or the parent only ﬁnancials. ¤ ¤ With consolidated ﬁnancials, the ﬁnancials will reﬂect 100% of the subsidiary’s revenues & operaHng income. If you do your DCF valuaHon with these numbers, you have to subtract out the value of the porHon of the subsidiary that does not belong to you. With parent ﬁnancials, you have not valued any of the subsidiary. You have to add the porHon of the subsidiary that belongs to you to your DCF value. 10! Example: Quiz from Spring 2007 ¨ You have been asked to analyze Smithtown Works, a company with a 60% holding in Kroger Appliances (which is fully consolidated into Smithtown Works) and 10% of Haverford Steel (which is reported as a minority passive investment). All three companies are in stable growth (2% forever), have a return on capital of 10% and share a cost of capital of 8%. ¤ ¤ ¤ ¨ Smithtown Works has 500 million shares outstanding, trading at $30 a share, and the consolidated balance sheet reports debt outstanding of $ 6 billion, a cash balance of $ 2 billion and $ 1 billion in minority interests. The consolidated a^er-‐
tax operaHng income reported by the company the most recent year was $ 1.5 billion. Kroger Appliances is not publicly traded and there linle informaHon on its a^er-‐tax operaHng income, debt or cash balance, but appliance companies typically trade at 3 Hmes book value. Haverford Steel reported a^er-‐tax operaHng income of $ 800 million in the most recent year. Evaluate whether the stock in Smithtown Works is fairly priced. 11! The soluHon Reinvestment rate (for all 3 firms) = 2% / 10% =
Value of Smithtown + Kroger
= 1500 (1-.2)(1.02)/(.08-.02) =
Value of Haverford Steel
= 800 (1-.2) (1.02)/(.08-.02) = $20,400.00 Value of Smithtown + Kroger $20,400.00 + 10% of Haveford steel (Estimated value) 20.00% $10,880.00 $1,088.00 + Cash (consolidated) 2000 - Debt (consolidated) 6000 - Minority Interests (Estimated market value) 3000 Value of Equity in Smithtown
Market Value of Equity in Smithtown
Stock is overvalued by $512 million $14,488.00
12! Loose End 3: Other Assets Basic rule: If an asset is being used to generate the cash ﬂows that you are discounHng, you have already valued the asset. You cannot add the “esHmated” or “market” value of that asset to your DCF valuaHon. ¨ If you have an unuHlized or vacant asset that has value but is not contribuHng to cash ﬂows, you can value it and add it to your DCF valuaHon. ¨ 13! Loose End 4: Employee OpHons Informa3on Approach required/provided Bo<om line Fully Diluted Approach Number of opHons outstanding DCF value of equity/ (Number of shares + Number of opHons) You will under value shares, because you are ignoring opHon exercise proceeds. Treasury Stock Approach Number of opHons outstanding, Exercise price (DCF value of equity+ Exercise price*OpHons)/ (Number of shares + Number of opHons) You will over value shares, since you are ignoring Hme premium on opHons. OpHon value approach OpHons characterisHcs needed to esHmate value (DCF value of equity – Value of opHons)/ Number of shares Value per share reﬂects reality 14! Problem 2, part c: Spring 2008 Quiz ¨ Now assume that the ﬁrm has 10 million shares outstanding today, and has granted 2 million opHons to its top management; the exercise price of the opHons is $ 2/share. Furthermore, analysts are predicHng that they will have to issue 8 million addiHonal shares over the next 2 years (to cover their reinvestment needs). Using the treasury stock approach, esHmate the value of equity per share today. 15! SoluHon FCFE
Compounded cost of equity
Value of equity today =
Exercise proceeds =
Number of shares = 10 + 2 =
Value per share = 1 2 3 -$20.00 -$10.00 $5.00
$3.25 16! DCF Mechanics : Cash ﬂows Cash ﬂows: When esHmaHng cash ﬂows, ﬁrst check on whether you are esHmaHng cash ﬂows to the ﬁrm or to equity. ¨ The cash ﬂows should always be a^er ¨ ¤ Taxes ¤ Reinvestment needs, with informaHon given in n Ingredient parts as cap ex, depreciaHon and working capital) n Return on capital and a growth rate (g/ ROC) n Sales to Capital raHo 17! DCF Mechanics 2: DiscounHng ¨ ¨ Match up the risk of the cash ﬂow to the discount rate. Thus, if you are given a guaranteed cash ﬂow to a risky ﬁrm, you should use the risk free rate as your discount rate. Match the discount rate up to the cash ﬂow In the same currency ¤ If CF to equity (capital), use cost of equity (capital) ¤ ¨ When your cost of capital changes over Hme, remember that you should discount at the cumulated cost of equity/capital, not that speciﬁc year’s cost of equity/
capital. 18! Example: Problem 1a, Fall 2010 ¨ Maple Telecom is in signiﬁcant ﬁnancial trouble. It reported operaHng losses of $ 20 million in the most recent year on revenues of $ 100 million. The total book value of capital invested in the ﬁrm today is $ 190 million. Assuming that the ﬁrm will revert back to health in 3 years, you have forecast revenues, a^er-‐tax operaHng income and reinvestment, as well as the cost of capital: 19! SoluHon: Value of operaHng assets (1.14* 1.12) = 1.2768!
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- Spring '17
- Net Present Value, Value theory, Instrumental value