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Unformatted text preview: THE FINAL REVIEW: THE REST OF THE MATERIAL Aswath Damodaran The ﬁnal pieces of the puzzle ¨ Real OpEons ¤
¤ ¨ AcquisiEon valuaEon ¤
¤ ¨ The three key quesEons The opEon to delay: Patents & Natural resources The opEons to expand & abandon The value of ﬁnancial ﬂexibility Equity in deeply troubled ﬁrms Key principles on risk & discount rates The value of synergy & control AcquisiEon mechanics (Exchange oﬀers) Value Enhancement ¤
¤ The drivers of value Value enhancement VoEng & non-‐voEng shares 2! Real OpEon: Key QuesEons ¨ Is there an opEon embedded in this asset/ decision? ¤
¤ ¨ Is there exclusivity? ¤
¤ ¨ Can you idenEfy the underlying asset? Can you specify the conEngency under which you will get payoﬀ? If yes, there is opEon value. If no, there is none. If in between, you have to scale value. Can you use an opEon pricing model to value the real opEon? ¤
¤ Is the underlying asset traded? Can the opEon be bought and sold? Is the cost of exercising the opEon known and clear? 3! OpEon Pricing Model: Reading the Entrails In the Black Scholes model the value of a call and put are esEmated by creaEng and valuing replicaEng por\olios. In the dividend yield adjusted versions: C = S e-‐yt N(d1) -‐ K e-‐rt N(d2) where, σ2
! S# ln" K $ + (r - y + 2 ) t and d2 = d1 -‐ σ √t d1 = σ t
¨ The value of a put can also be derived from the call P = K e-‐rt (1-‐N(d2)) -‐ S e-‐yt (1-‐N(d1)) ¨ The model has embedded in it some key features: ¤ ¤
¤ The dividend yield operates as a trigger pushing an investor to exercise early. More generically, you can think of it as the cost of delaying exercise, once an opEon becomes in the money. N(d2): Risk neutral probability that the opEon will end up in the money. N(d1): Also can be read as a probability and N(d1) – N(d2) can very loosely be thought oﬀ as the range of probability that the opEon will be in the money. 4! The Cost of Delay ¨ The cost of delay is a measure of how much you will lose in the next period if you don't exercise the opEon now as a fracEon of the current value of the underlying asset. There are three ways you can get it: OpEon 1: If you have a decent esEmate of the cashﬂows you will receive each period from exercising the opEon, it is beder to use that cashﬂow/ PV of the asset as the dividend yield. (Example: Cash ﬂows on an oil reserve) OpEon 2: If your cashﬂows are uneven or if you do not know what the cashﬂow will be each period, you should use 1/n as your cost of delay. (Patent & life() OpEon 3: If you will lose nothing in terms of cashﬂows by waiEng, you should have no cost of delay. (Olympics example) 5! The OpEon to Delay a Project PV of Cash Flows !
from Project! Initial Investment in !
Present Value of Expected !
Cash Flows on Product!
Project has negative!
in this section!
Aswath Damodaran Project's NPV turns !
in this section!
! 6! I. Valuing a Patent Input
1. Value of the Underlying Asset 2. Variance in value of underlying asset 3. Exercise Price on Option 4. Expiration of the Option 5. Dividend Yield Estimation Process
• Present Value of Cash Inflows from taking project
• This will be noisy, but that adds value.
• Variance in cash flows of similar assets or firms
• Variance in present value from capital budgeting
• Option is exercised when investment is made.
• Cost of making investment on the project ; assumed
to be constant in present value dollars.
• Life of the patent • Cost of delay
• Each year of delay translates into one less year of
Annual cost of delay = 1
n 7! Example: Problem 5, Spring 2008 ¨ a.
b. You have been asked to value a new technology for producing and distribuEng solar power. You esEmate that the technology will need an up-‐front investment of $ 1.5 billion and that the expected cash ﬂows will depend on the price of oil. For every dollar that the oil price exceeds $ 100, the ﬁrm expects to generate $ 20 million in annual aker-‐tax cash ﬂow, each year for 10 years. The expected cash ﬂows are risky and the appropriate discount rate for these cash ﬂows is 12%. The current oil price is $ 110 and the standard deviaEon in ln (oil prices) is 30%. The riskless rate is 4%. EsEmate the net present value of the solar power investment at the current oil price. Now assume that you can get the exclusive rights to this technology for the next 15 years. EsEmate how much you would be willing to pay for these exclusive rights? 8! SoluEon After=tax cash flow =
PV over 10 years =
Standard deviation =
Riskless rate =
Cost of delay = Value of the option
With no cost of delay
With 10% cost of delay
With 17.7% cost of delay 200
0% if you assume that the project life will not be truncated
10% !if you assume that the project life will be truncated if taken after yr 5 $596 million
$2 million ! Rounding off will yield about $592 million 9! II. Valuing a Natural Resource OpEon Input
1. Value of Available Reserves of the Resource
2. Cost of Developing Reserve (Strike Price)
3. Time to Expiration 4. Variance in value of underlying asset Estimation Process
• Expert estimates (Geologists for oil..); The
present value of the after-tax cash flows from
the resource are then estimated.
• Past costs and the specifics of the investment
• Relinqushment Period: if asset has to be
relinquished at a point in time.
• Time to exhaust inventory - based upon
inventory and capacity output.
• based upon variability of the price of the
resources and variability of available reserves. 5. Net Production Revenue (Dividend Yield) • Net production revenue every year as percent
of market value. 6. Development Lag • Calculate present value of reserve based upon
the lag. 10! Example: Problem 5, Spring 2011 ¨ You are valuing an oil company with signiﬁcant undeveloped reserves and have collected the following informaEon on the company: ¤ ¤ ¤
c. The company has developed reserves of 100 million barrels. It is extracEng 10 million barrels a year, and the marginal (variable) cost per barrel of oil extracted is $ 40/barrel. The price per barrel is $75/barrel. The tax rate is 40% and the company’s cost of capital is 9%. (You can assume that both oil prices and the cost per barrel are expected to stay at the same level for the foreseeable future.) The company has undeveloped reserves of 150 million barrels, and has 20 years to explore and develop them. The iniEal cost of developing all these reserves is $ 3 billion and the variable cost per barrel, once developed, will be 20% higher than it is for the current developed reserves. The standard deviaEon in oil prices is 30% and the riskfree rate is 4%. There is a one-‐year lag between the decision to develop the reserves and oil producEon commencing. Value the developed reserves for the company. Value the undeveloped reserves for the company, using opEon pricing. Now assume that you had valued this company using a convenEonal discounted cash ﬂow model, using a growth rate and the expected oil price to incorporate the undeveloped reserves. Would the value per share that you obtain by doing so be higher than, lower than or equal to the value using the opEon pricing approach? 11! SoluEon a. Developed reserves Pre-‐tax cash ﬂow/barrel Annual aker-‐tax CF = PV of CF for 10 years = b. Undeveloped reserves S = K = r = t = Standard deviaEon = Cost of delay= d1 = d2 = Value of undeveloped reserves = 35 210 1347.708117 1224.217055 ! Annual cash ﬂow = 10*27*.6 = 162; PV over 15 year 3000 4% 20 0.3 0.066666667 ! I am assuming that the extracEon capacity is 10 million barrels. I also gave full credit if you assumed it to be 7.5 million barrels (5% cost of delY) -‐0.3949 N(d1) -‐17365 N(d2) $56.20 0.3465 0.0412 c. DCF value will be lower than the opEon value, for any given oil price expectaEon. 12! B. The OpEon to Expand PV of Cash Flows !
from Expansion! Additional Investment !
Present Value of Expected !
Cash Flows on Expansion!
Firm will not expand in!
Aswath Damodaran Expansion becomes !
attractive in this section! 13! C. The OpEon to Abandon ¨ ¨ A ﬁrm may someEmes have the opEon to abandon a project, if the cash ﬂows do not measure up to expectaEons. If abandoning the project allows the ﬁrm to save itself from further losses, this opEon can make a project more valuable. PV of Cash Flows !
from Project! Cost of Abandonment!
Present Value of Expected !
Cash Flows on Project! 14!
Aswath Damodaran 14! The Value of Flexibility Expected
Needs that can
flexibility Use financing flexibility
to take unanticipated
Payoff: (S-K)*Excess Return/WACC Cost of Maintaining Financing Flexibility
Excess Return/WACC = PV of excess returns in perpetutity 15!
Aswath Damodaran Actual
Needs 15! Payoﬀ Diagram for LiquidaEon OpEon Net Payoff
on Equity Face Value
Value of firm 16!
Aswath Damodaran 16! Example: Problem 5, Spring 2010 ¨ You are helping a vulture investor decide whether he should be invesEng in the equity of Reza Steel. You have collected the following informaEon on the ﬁrm: ¤
¤ ¤ a. b. The ﬁrm is expected to report EBITDA of $ 25 million this year and a net income of -‐
$10 million for the year. Mature steel companies trade at an EV/EBITDA mulEple of 6. The standard deviaEon in ﬁrm value at these companies is approximately 30% and the standard deviaEon in equity value is 40%. Given the state of the market, you esEmate that you will face an illiquidity discount of approximately 20% on the value of the assets liquidated. The ﬁrm has substanEal debt outstanding. The ﬁrm has two zero coupon bonds outstanding, $ 120 million (face value) in ﬁve-‐year bonds and 80 million (face value) in ten-‐year bonds. The treasury bill rate is 2% and the long term treasury bond rate is 4%. If you consider equity as an opEon (to liquidate), value the equity in the ﬁrm. EsEmate the “fair” interest rate for the debt in the company. 17! SoluEon S = Liquidation value = 120 K = Face value of debt = 200 t = Weighted duration = 7 r =Long term Tbond rate =
Standard deviation in firm value = 4%
30% Valeu of equity as an option
N(d1) 0.5422 N(d2) 0.2458 Value of the call = 27.91 Value of debt = 92.09 Interest rate on debt = 0.1172 18! AcquisiEon ValuaEon Cost of equity: The cost of equity for a target company should always be based upon the risk of the target company (its unlevered beta). ¨ Cost of debt & debt raEo: Should reﬂect what the target company can borrow at (either at its exisEng or target debt raEo) ¨ 19! The value of synergy ¨ Synergy accrues to the combined company and can take the following forms: An increased capacity to carry debt, which manifests itself as a lower cost of capital ¤ Cost cuyng, which shows up as higher margins and operaEng income ¤ More value from growth, which can be reﬂected in higher returns on capital, higher reinvestment rates or longer growth periods. ¤ Savings in taxes ¤ ¨ The discount rate you apply to these cash ﬂows should reﬂect the risk in these cash ﬂows. 20! Example: Problem 3, Spring 2009 ¨ 3. Simba Inc., an entertainment company, is considering an acquisiEon of Tiger Tales, a maker of animated movies. The informaEon on the two companies is provided below ($ values are in millions): a.
b. EsEmate the value of the combined company, assuming no synergy in the merger. (2 points) Now assume that Simba Inc. believes that the combined company will be much stronger, relaEve to the compeEEon, and will therefore be able to ﬁnd more new investments in the next 4 years (doubling the reinvestment rate over that period for the combined ﬁrm) and earn a return on capital of 12% on new investments in perpetuity. (ExisEng investments at both ﬁrms will conEnue to generate their exisEng returns on capital) Aker year 4, the growth rate will drop back to 3% but the return on capital will stay at 12%. EsEmate the value of synergy in this merger. 21! SoluEon Simba
EBIT (1-t) expected next year
Book Capital invested
Cost of capital
Return on capital =
Reinvestment Rate =
Value today =
Reinvestment rate =
Return on capital =
Expected growth rate = EBIT (1-t)
Value of firm today =
Value with no synergy =
Value of synergy = Tiger Tales Combined firm 100
833.3333333 2000 30 30 120 1
$285.34 $54.54 0.666666667
4 Term year
$54.04 $2,121.71 22! The value of control ¨ To value control in an acquisiEon, you have to value the company twice: ¤ In the status quo valuaEon, you value the company based on its current management policy on invesEng, ﬁnancing and dividends. ¤ In the opEmal valuaEon, you value the company based on the changes that you expect to make in these policies. ¨ The value of control is the diﬀerence between the opEmal and status quo values, discounted back to the present (assuming that it will take you Eme to make the changes). 23! Increase Cash Flows More efficient
Higher Margins Reduce the cost of capital
* Operating Margin Reduce beta = EBIT
Divest assets that
have negative EBIT
Reduce tax rate
- moving income to lower tax locales
- transfer pricing
- risk management Reduce
leverage - Tax Rate * EBIT
= EBIT (1-t)
- Capital Expenditures
- Chg in Working Capital
= FCFF Live off past overinvestment Cost of Equity * (Equity/Capital) +
Pre-tax Cost of Debt (1- tax rate) *
(Debt/Capital) Match your financing
to your assets:
Reduce your default
risk and cost of debt Shift interest
higher tax locales Change financing
mix to reduce
cost of capital Better inventory
tighter credit policies Firm Value Increase Expected Growth
Reinvest more in
margins Increase length of growth period
Do acquisitions Reinvestment Rate
* Return on Capital
= Expected Growth Rate Increase capital turnover ratio Build on existing
advantages Create new
advantages The Expected Value of Control The Value of Control
X Probability that you can change the
management of the firm Takeover
Restrictions Voting Rules &
Aswath Damodaran Access to
Funds Size of
company Change in firm value from changing
management Value of the
optimally - Value of the
firm run status
quo 25! Example: Problem 3, Spring 2008 ¨ a. b. c. Marley Steel is a publicly traded steel company with 20 million shares outstanding, trading at $ 2 a share, and $ 60 million in outstanding debt. The cost of capital for the ﬁrm was 12%. The ﬁrm is expected to generate $ 16 million in aker-‐tax operaEng income next year and is considered to be in stable growth, growing 4% a year in perpetuity. Assuming that the ﬁrm is correctly valued by the market now, esEmate the return on capital that the ﬁrm is expected to generate in perpetuity. You believe that if you acquire control of the ﬁrm, you can sell idle assets (that are not generaEng operaEng income) for $ 40 million and pay down debt. If you do so, your cost of capital will decrease to 10%. EsEmate the new value for the ﬁrm if you can restructure it. How would your answer to b change, if your plan is not to pay down the debt but to redeploy the assets to more producEve investments, which will increase the aker-‐tax operaEng income to $ 25 million next year. The How expected growth rate will remain 4% a year in perpetuity and the cost of capital will conEnue to be 12%. 26! SoluEon Problem 3
Firm Value =
100 = 16 (1- .04/ROC)/ (.12-.04)
Solving for ROC
Return on capital = 100 ! 20*2 + 60 8% b. Pay down debt option
If you assume that the write down of capital has no impact on future ROC
Reinvestmnet rate =
50.00% ! g/ ROC = 4/8
New firm value =
If you assume that changes in the current ROC will also affect future ROC
Old capital =
200 ! EBIT (1-t)/ Old ROC
New capital =
160 ! Sold off idle assets and reduced capital
New ROC =
10.00% ! 16/160
New Reinvestment rate=
40.00% ! g/ ROC
Firm Value =
c. Redeploy capital
New EBIT (1-t) =
New ROC =
New Reinvestment rate =
Firm Value = 25
212.5 27! ImplicaEons ¨ Publicly traded stock: The stock price of every publicly traded company should reﬂect the expected value of control in that company. Thus, anything that changes that expected value (changing corporate governance, acEvist investors) should change prices. Value per share = ¨ € Status Quo Value + Probability of control change (Optimal - Status Quo Value)
Number of shares outstanding VoEng and non-‐voEng shares: Value per non - voting share = Status Quo Value
# Voting Shares + # Non - voting shares Value per voting share = Value of non - voting share +
Aswath Damodaran € Probability of control change (Optimal - Status Quo Value)
# Voting Shares 28! ...
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