Damodaran Valuation Practice Test Questions

Using the output from question (3), what is the likelihood that this firm will go bankrupt sometime over the next 8 years? a. 0.00% b. 22.17% c. 50.36% d. 69.37% e. 76.64% f. 77.83%

f. 77.83%. It is N(d2) that gives you the risk neutral probability that this option will be in the money (will have asset value > face value of debt). Therefore the probability that it will not have enough to cover its debt = 1- .2217 = .7783

A stock that trades at less than book value is cheap, because you can liquidate the company and get the book value of equity. a. True b. False

False. The book value of equity does not measure what you can get in liquidation. If the business for a firm has deteriorated, it can trade at less than book value and not be cheap.

You decide to value equity as a call option on a troubled chemical company, with significant debt outstanding. You believe that the operating assets of the company can generate $ 80 million in expected cash flows next year, growing 2% a year in perpetuity and that the cost of capital for these assets (to a healthy firm) is 10%. The company has only one debt issue, a $1.5 billion zero coupon bond with 8 years left to maturity. The short term treasury bill rate is 1%, the longer term (6-10 years) treasury bond rate is 3% and the standard deviation in firm values for chemical companies is 45%. List the inputs that you will use in valuing equity as a liquidation option in this firm: a. S = b. K = c. t = d. r = e. Standard deviation = f. y (Dividend yield) = Bonus: Value equity as a liquidation option

Inputs to the option pricing model a. S = 1000 = 80/ (.10-.02) b. K = 1500 = Face value of the zero coupon bond c. r = 3% d. t = 8 years e. σ = 45% = Standard deviation of chemical firm values f. y (Cost of delay) = 0 (If the company had a contractual commitment to make cash flows every year, you could have used that cash flow to get your dividend yield)

You have just valued Liszt Software, a small technology company, with a proprietary patent for the next 15 years. You have computed a DCF value of $100 million for the company, but believe that the patent could give you an entrée into a larger market. Based upon what you know today, you believe that the cost of expansion into the larger market is $500 million but that the present value of the cash flows from expansion is $300 million. A simulation of this present value yields a standard deviation of 25% and the risk free rate is 3%. What are the inputs that will you use to value the option to expand? a. S = b. K = c. r = d. t = e. σ = f. y (Cost of delay) = Bonus: Value the option

Inputs to the option pricing model a. S = 300 = PV of cash flows, if you expand today b. K = 500 = Cost of expansion today c. r = 3% d. t = 15 (Years of patent life left) e. σ = 25% (from simulation) f. y (Cost of delay) = 1/15 (You will lose one year of patent life by waiting) Bonus: The value that I get for d1, d2 and the option are below: d1 = -0.6115, N(d1) = 0.2704 d2= -1.5798, N(d2) = 0.0571 Value of the option to expand = $11.65 million. You would add this to your DCF value.

Which of the following payoff features best characterizes buying a call option? a. Limited losses, potentially unlimited profits b. Potentially unlimited losses, limited profits c. Limited losses, limited profits d. Potentially unlimited losses and profits

a. Limited losses, potentially unlimited profits. The key to option payoffs is that the buyer of an option can never lose more than what he or she paid for the option and hence has limited losses. At least with call options, since the stock price can keep rising without a bond, you have unlimited profits.

Let us assume that you value the patent to be worth $133 million, using an option pricing model, and that you used the remaining life of the patent (which is 15 years) as the option life in your valuation. How would your assessment of the value change if you were told that a competitor is working on a close substitute to treat Alzheimer's and is planning to bring the drug to the market in 5 years? a. Lower the value of the patent b. Have no effect on the value of the patent c. Increase the value of the patent Explain.

a. Lower the value: It will be negative for two reasons. The first is that your cash flows will be lower, if you have competition and the second is that your option life will be reduced to 5 years.

The essence of real options is that you learn from what is happening around you and adapt your behavior based upon what you learn. You can capture this in an option pricing model but you can also capture it using decision trees. a. True b. False

a. True. A correctly constructed decision tree, with discount rates that vary depending on where you are in the tree and probabilities attached to each branch should deliver the same value as the option model. Session 20: Post class test solutions

You are a better candidate for using discounted cash flow valuation, if you are a long-term investor who believes that markets make mistakes in pricing individual companies and that these mistakes get corrected over time. a. True b. False

a. True. For intrinsic valuation to have any chance of delivering returns, markets have to make mistakes and correct them over time, and having a longer time horizon improves your odds.

You are a better candidate for using relative valuation, if you are a portfolio manager with clients with short time horizons and you are judged on a relative basis (against other portfolio managers). a. True b. False

a. True. If your clients don't have the patience or time horizons needed for markets to correct their intrinsic value mistakes, you are better off using relative valuation. If you are judged on a relative basis, it becomes even more appropriate to use relative valuation.

Now assume that you are looking at the income statement for Abel Stores. The business reported $ 500,000 in after-tax operating income last year, but you note that the owner (who fills multiple roles in the business) has not charged herself a salary. You believe that it will take two hired employees to do the work that the owner used to do and that you would have to pay $150,000 to hire these employees. If your tax rate is 40%, estimate the adjusted after-tax operating income for last year. a. $350,000 b. $410,000 c. $440,000 d. $560,000 e. $590,000

b. $410,000.Subtract the after-tax salary expense from the after-tax operating income: After-tax operating income = 500,000 Adjusted after-tax operating income = 500,000 - 150,000 (1-.4) = 410,000

You are trying to compute the levered beta that you will use to value Abel Stores. The company has a book value of equity of $600 million and a book value of debt of $ 600 million. If the typical apparel store company trades at three times book value of equity and the market value of debt = book value of debt, what is the debt to equity ratio that you will use to compute the levered beta for Abel Stores? (The marginal tax rate is 40%) a. 25% b. 33.33% c. 100% d. 300% e. None of the above

b. 33.33%. First, estimate the market values of debt and equity: • Market value of equity = 600 * 3 = 1800 • Market value of debt = 600 • D/E ratio = 600/1800 = 33.33%

If you buy into the notion that equity in deeply troubled firms can be viewed as options, in which of the following highly levered, money losing companies will equity be most highly valued? a. A company in a stable business with predominantly short term debt b. A company in a risky business with predominantly long term debt c. A company in a stable business with predominantly long term debt d. A company in a risky business with predominantly short term debt

b. A company in a risky business with predominantly long-term debt. The value of equity as an option increases with uncertainty (risky business) and with the option maturity (long term debt).

When you use a real options argument to value an asset that you have already valued using a discounted cash flow model, which of the following will you expect to see as your real option value? a. A value equal to that of the DCF value b. A value greater than the DCF value c. A value less than the DCF value

b. A value greater than the DCF value. If an option exists in an asset, the DCF valuation of that asset will not capture the optionality and a premium has to be added on to that value.

Intrinsic and relative valuations, done right, should deliver the same value for an asset. a. True b. False

b. False. Intrinsic and relative valuations, even if done right, may not deliver the same value for an asset, because the market may be mispricing an entire group of assets or sector (thus skewing the relative valuation).

If you are looking for a cheap stock on a PE ratio basis, which of the following combinations is the best one for you? a. Low PE, high growth, high risk, high payout b. Low PE, high growth, low risk, high payout c. Low PE, high growth, low risk, low payout d. Low PE, high growth, high risk, low payout e. Low PE, low growth, low risk, high payout

b. Low PE, high growth, low risk, high payout. This company offers the best of all worlds. It is cheap, has high growth, low risk and high quality earnings (enabling it to pay out lots in dividends while growing).

If you use relative valuation in investing, which of the following assumptions are you making about markets? a. Markets never make mistakes b. Markets are right on average but that they are wrong in pricing individual assets c. Markets are wrong on average and they are wrong in pricing individual assets

b. Markets are right on average but they are wrong on pricing individual assets. Since you are getting your estimates of value by looking at how the market is pricing similar assets, markets have to be right on average.

If you are valuing fine art, the best approach to valuing a piece of fine art is to use: a. Discounted Cash Flow Valuation b. Relative Valuation c. Sum of the parts valuation d. Historical Cost e. None of the above

b. Relative Valuation. You cannot estimate cash flows (ruling out discounted cash flow valuation), slice it up into pieces (removing sum of the parts valuation from the mix) and the historical cost is meaningless.

Assume now that you have decided to employ an option pricing approach to value a patent on a drug to treat Alzheimer's. You believe that, if the drug were introduced today, it would generate expected cash flows of $ 150 million/year for the next 15 years, and that the cost of commercially developing the drug today is $2 billion. If the risk free rate is 3% and the cost of capital for pharmaceutical companies is 10%, what would you use as the value of the underlying asset (S) in the option pricing model? a. -$859 million b. $250 million c. $ 1,141 million d. $1,791 million e. $2,250 million f. None of the above

c. $1,141 million. It is the present value of $150 million for 15 years, using the cost of capital of 10% as your discount rate.

Now assume that you are doing a relative valuation of Wyckham Inc. and have been provided with the EBITDA (in millions) and the median EV/EBITDA of in each business: Business EBITDA EV/EBITDA multiple for sector Steel 300 8 Chemicals 200 5 Technology 100 6 If the company has $1 billion in debt outstanding and $500 million in cash, what is the value of equity in the company? a. $2,500 million b. $3,000 million c. $3,500 million d. $4,000 million e. $4,500 million

c. $3,500 million. Value the company first by estimating the value of the businesses: Business EBITDA EV/EBITDA multiple Steel 300 8 2400 Chemicals 200 5 1000 Technology 100 6 600 4000 Value of equity = 4000 + 1000 - 500 = $3,500 million

Now assume that you have plugged in the right values into an option pricing model and are looking at the following output from the model. d1 = 0.5036, N(d1) = .6937 d2 = -0.7664, N(d2) = .2217 What is the right interest rate on the debt? a. 3.00% b. 6.13% c. 12.91% d. 22.17% e. None of the above

c. 12.91%. Plugging in the values of N(d1) and N(d2) into the equation , we get: • Value of equity = 1000 (.6937) + 1500 exp-(.03)(8)(.2217) = $432.09 • Value of zero coupon bond = 1000 - 432.09 = 567.91 • Interest rate on zero coupon bond = (1000/567.91)1/8-1= .1291

You are valuing Abel Stores, a small, privately owned apparel store for sale to another private individual, who will be investing all of his wealth in the business. The unlevered beta for publicly traded apparel stores is 1.20 and the average R-squared across the apparel stories (with the market) is 0.36.What is the unlevered beta that you will use, in estimating the cost of equity in this transaction? a. 0.72 b. 1.20 c. 2.00 d. 3.33 e. None of the above

c. 2.00.To get the value, you divide the average unlevered beta across the sector by the correlation coefficient: • Correlation coefficient = Square root of R2 = 0.36.5 = 0.6 • Total beta = 1.20/0.6 = 2.00

You have completed your discounted cash flow valuation of Abel Stores, using a total beta and adjusted operating income, and arrived at a value of $ 4.2 million for the equity in the firm. While you have a base liquidity discount of 20% that you usually apply to equity value in a private company, you believe that the discount should be smaller at Abel Stores. Which of the following is a good reason for attaching a smaller discount? a. The total beta already results in a discount on value. b. You feel that your cash flow estimates are precise c. Abel Stores has more revenues than the typical companies that you value d. Abel Stores borrows less money than the typical firm in the retail business e. None of the above f. All of the above

c. Abel Stores has more revenues than the typical companies that you value. None of the other stated reasons would affect the illiquidity discount that you would attach to the company.

An option gives the buyer the right to buy (call) or sell (put) an asset at a fixed price. As the underlying asset becomes more volatile, which of the following will happen to your option values (holding all else constant). a. Call options will become more valuable & put options less. b. Call options will become less valuable & put options more. c. Both call & put options will become more valuable d. Both call & put options will become less valuable e. Call and put options will be unaffected in value

c. Both call and put options will become more valuable. Since your losses are limited on all options (calls and puts), increased risk/volatility in the underlying asset can only help you and increase value.

The key person discount is the discount attached to a private business to reflect the expected loss in cash flows, as a result of a key person (often the owner) leaving. Assuming that you are the owner of the business and are trying to sell the business, which of the following actions would you take to reduce the key person discount? a. Agree to stay on for a transition phase, where you help the new owner connect with your customers b. Agree not to start a similar business in a hundred mile radius, after you sell the business c. Both d. Neither

c. Both. Both would serve to reduce the fear of lost business and reduce the key person discount.

You are a gold mining company with substantial undeveloped reserves of gold and relatively little gold production. Which of the following combinations will make your gold reserves more valuable? a. High gold prices with low volatility in those prices b. High gold prices with high volatility in those prices c. Low gold prices with low volatility in those prices d. Low gold prices with high volatility in those prices

c. High gold prices with high volatility. When gold prices are high, the exercise value of the reserves will be high. When volatility is high, there will be a higher option premium on these reserves.

An analyst valuing a social media company argues that a conventional DCF valuation will understate the value of the company because it does not consider the fact that the online advertising market is very large and that there is an option embedded in these companies which will make their values greater than the DCF value. Do you agree? a. Yes. b. No c. Maybe, if ____________________________. Explain.

c. Maybe, if the social media company can use its user base to enter new markets that are unknown at the moment. The key, though, is that having the user base gives you partial exclusivity that cannot be matched easily by others.

You have been asked to value a portfolio of patents that is owned by a technology company and are considering using option pricing in the endeavor. In which of the following cases is using a real options approach likely to yield a much higher value than using a discounted cash flow approach? a. A viable patent with 3 years to expiration in a safe business b. A viable patent with 12 years to expiration in a safe business c. A non-viable patent with 1 year to expiration in a risky business d. A non-viable patent with 12 years to expiration in a risky business e. All of the above f. None of the above

d. A non-viable patent with 12 years to expiration in a risky business. The option premium over the DCF value is greatest when an option is on a risky underlying asset, has a long time to expiration and is out of the money.

For an investment to be valued as a real option, which of the following would you need as requirements? a. An underlying asset whose value changes b. A payoff that is contingent on the underlying asset's value change c. A limited life for the investment d. All of the above

d. All of the above. An option needs an underlying asset with a variable price, a payoff contingent on that price and a limited life.

You are a US consumer product company that is interested in investing in Brazil. Based on your assessment of the Brazilian market, you believe that the present value of the cash flows from investing in the market today is $100 million and that the cost of entry is $150 million. However, the market is a very large one and you believe that if the initial investment does better than expected, your expansion potential is large. Which of the following would you do? a. Don't invest. The NPV is negative. b. Invest, because there is expansion potential. c. Invest, but only if the expansion potential has a positive NPV > $50 million today. d. Invest, but only if the expansion potential comes with exclusivity. e. Invest, but only if the expansion potential comes with exclusivity and you believe that the option to expand has a value greater than $50 million f. Invest, but only if the expansion potential comes with exclusivity and you believe that the option to expand has a value greater than $150 million g. None of the above

d. Invest, but only if the expansion potential comes with exclusivity and you believe that the option to expand has a value greater than $50 million. The initial investment has a net present value of -$50 million. For the expansion potential to tip the scales, its value has to be greater than $50 million and that can happen only if there is exclusivity.

In computing the EV/EBITDA multiple, we estimate the enterprise value of a firm by adding together the values of debt and equity and netting out cash. Which of the following is the reason for netting out cash in computing this multiple? a. Cash is easy to value. b. Cash is liquid c. Cash can be used to pay down debt d. The income from cash is not part of EBITDA e. None of the above

d. The income from cash is not part of EBITDA. To preserve consistency, you have to net out the cash (and any other assets whose income is not part of EBITDA from the numerator).

The option to abandon refers to the choice that a company has to abandon or scale down an investment, if the cash flows do not measure up to expectations. In which of the following cases will the option to abandon be most valuable? a. A short term, small, risky investment to a large company b. A long term, large, risky investment to a large company c. A long term, large, safe investment to a large company d. A short term, small, risky investment to a small company e. A long term, large, risky investment to a small company f. A long term, large, safe investment to a small company

e. A long term, large, risky investment to a small company. The option to abandon will have more value in a risky project than a safe one, a longer term project than a shorter term one and on a large project (relative to the size of the company taking it) than a small one.

A key input into option pricing models is the expected volatility in the underlying asset's value. In valuing a Alzheimer's drug patent as an option, which of the following approaches can you use to estimate the volatility in the underlying asset? a. A simulation of the present value of the cash flows from developing the drug today, with different assumptions about the market size and profitability b. The standard deviation in the firm values of small publicly traded, pharmaceutical companies. c. The implied standard deviation in the options traded on stocks of publicly traded pharmaceutical companies, funded primarily with equity. d. The standard deviation in the cash flows of drugs introduced in the past e. Any of the above

e. All of the above. Any of the approaches can be used, though each comes with its own baggage. The standard deviations from publicly traded companies may not be reflective of the risk in the projects that these companies take. The simulation is only as good as the distributions used to derive the results.

There is a basis for the argument that equity in a publicly traded company can be viewed as a call option on the company's assets. For this argument to be made, which of the following would need to hold? a. Equity investors have limited liability, i.e., they cannot lose more than their equity investment b. Equity investors run the business and can choose to liquidate the business at any time c. Equity investors have a residual claim on the liquidation proceeds, i.e., they get all of the value left over after lenders have been paid. d. The debt holders claim is on the liquidation proceeds is restricted to the outstanding debt (and unpaid interest expenses from prior periods) e. All of the above

e. All of the above. For equity to be viewed as a call option, equity investors have to be running the firm, have a residual claim on the assets in liquidation and have limited liability.

In liquidation valuation, you are trying to value a company in liquidation, where you plan to sell its assets to the highest bidders. Which of the following is best valuation approach in making this estimate? a. An intrinsic value of assets in place and growth potential b. An intrinsic value of assets in place c. An intrinsic value of growth assets d. A relative valuation of assets in place and growth potential e. A relative valuation of assets in place f. A relative valuation of growth assets

e. A relative valuation of assets in place. Relative valuation works better than intrinsic valuation at estimating what you can get for the assets in the market place today. You cannot liquidate growth assets.

You have just completed a discounted cash flow valuation of Rallye Inc. a publicly traded company, and have estimated a value of $500 million for the equity in the company. The company has 100 million shares trading at $5 a share, and 25 million employee options with an exercise price of $5/share. Estimate the value of equity per share using a. The fully diluted share approach b. The treasury stock approach Explain the difference.

Either (c) or (e). You can either use a higher discount rate for the illiquid asset (which will lower value) or discount the DCF value that you get with the same discount rate as a liquid asset. You cannot do both.

Tymba Inc. generated $20 million in after-tax operating income on revenues of $100 million during the course of the most recent year. You expect revenues to grow 10% a year next year and margins to stay stable. The firm's non-cash current assets are $40 million and its non-debt current liabilities are $50 million, and non-cash working capital as a percent of revenues is expected to remain unchanged next year. If the net cap ex is expected to be $10 million next year, what is your estimate of the FCFF for the next year? a. $13 million b. $11 million c. $8 million d. $23 million e. None of the above

a. $13 million. To compute the FCFF, first compute the non-cash working capital in both dollar terms and as a percent of revenues: • Non-cash WC = 40 -50 = -10 • Non-cash WC as percent of revenues = -10/100 = -10% • Expected revenues next year = $110 million • Expected non-cash WC = -$11 million • Change in WC = -10-(-11) = 1 FCFF = 20 (1.10) - $10 +1 = $13 million

Wayfarers Inc. is a risky technology company that is expected to have a cost of capital of 12% for the next 10 years. At the end of year 10, it is anticipated that the firm will become a mature company, earning a return on invested capital equal to its stable period cost of capital of 10% in perpetuity. If the expected after-tax operating income in year 11 is $80 million and the expected growth rate in perpetuity is 3%, estimate the present value of the terminal value at the end of year 10 a. $257.58 million b. $308.43 million c. $367.97 million d. $440.62 million e. None of the above

a. $257.58 million. The first step is to estimate the terminal value at the end of year 10 • Reinvestment Rate = g/ ROC = 3%/10% - 30% • Terminal value = 80 (1-.30)/(.10-.03) = $800 million • PV of terminal value = $800/1.1210 = $257.58 million

Viaconda Inc. is a tourism company that reported $10 million in net income on a book value of equity of $110 million in the most recent year the company generated $ 1 million in after-tax interest income on a cash balance of $20 million. The company also reported net capital expenditures of $4 million, an increase in working capital of $ 2 million and an increase in total debt of $3 million during the year. Assuming that it maintains its current non-cash ROE and equity reinvestment rate, estimate the expected growth in non-cash net income in the future. a. 3.33% b. 6.67% c. 3.33% d. 6.00% e. None of the above

a. 3.33%. First, compute the non-cash ROE and equity reinvestment rate • Non-cash Net Income= 10 -1 = $9 • Non-cash ROE = (10-1)/ (110-20) = 10% • Equity reinvestment rate = (4+2-3)/ 9 = 33.33% • Expected growth rate = 10% (.3333) = 3.33%

The key driver of revenue multiples is profit margins. Which of the following measures of profit margin is the most direct determinant of price to sales ratios? a. Net Profit margin b. Gross profit margin (Gross profit/Sales) c. Pre-tax operating margin (EBIT/Sales) d. After-tax operating margin (After tax EBIT/Sales) e. EBITDA margin

a. Net Profit margin. Since the multiple that you are using uses equity value in the numerator, you should use the net profits (the profits to equity investors) in the margin computation.

The distribution for any multiple will tend to be asymmetric. Given that a multiple cannot be less than zero but is unconstrained on the upside, which of the following would you expect to see in the summary statistics? a. The average should be higher than the median b. The average should be lower than the median c. The average will be roughly equal to the median d. The average can be higher or lower than the median

a. The average should be higher than the median. The positive outliers will tend to pull the average up, above the median.

Lixit Inc. is a publicly traded company that reported $100 million in revenues in the most recent fiscal year that ended on December 31st. You are valuing the company in April and know that the company reported $30 million in revenues for the first quarter, up from the $22 million it reported in revenues in the same quarter of the previous year. In valuing Lixit today, which of the following numbers would you use for your base year revenues, if you want an updated valuation? a. $ 100 million b. $108 million c. $92 million d. $120 million e. $130 million

b. $108 million. Last year's revenues - Revenues in first quarter last year + Revenues in first quarter this year = 100 -22 + 30 = 108

Voltar Inc. is a company with 600 million non-voting shares and 400 million voting shares. You have valued the company, run by the existing management, at $ 10 billion but you believe that with new management, the company would have a value of $12 billion. If the probability of management changing is 20%, what is the value of each voting share? a. $10.00/share b. $10.40/share c. $11.00/share d. $12.00/share e. $14.00/share

b. $11/share. First, divide the status quo value by total # shares Value per non-voting share = 10,000/ (600 + 400) = $10/share Expected value of control = (12000 -10000) *.2 = $400 million Control Value per voting share = 400/400 = $1 Value per voting share = $10 + $1 = $11/share

Allwyn Inc. is a stable growth, dividend-paying firm that is expected to pay out 60% of its expected earnings per share of $1.50 next year as dividends. If the earnings are expected to grow 3% a year in perpetuity and the cost of equity is 9%, what PE ratio would you expect the firm to have? a. 6.00 b. 9.00 c. 10.00 d. 20.00 e. None of the above

c. 10.PE = 0.60/ (.09-.03)= 10

DBK Bank paid out $ 80 million in dividends on net income of $100 million in the most recent year. The book value of equity for the firm is $800 million. Assuming that the bank maintains its current payout ratio and return on equity in perpetuity, what is the expected growth in earnings per share in perpetuity? a. 8% b. 2% c. 5% d. 2.5% e. None of the above

d. 2.5%. The payout ratio is 80% (80/100) and the return on equity is 12.5% (100/800). The expected growth rate in earnings per share = (1- Payout ratio) (Return on equity) = (1-.8) (.125) = 2.5%.

Investments that are less liquid are usually valued lower than otherwise similar liquid investments. Which of the following is a way of incorporating the effect of illiquidity on value. a. Use a lower discount rate for the illiquid asset and reduce the DCF value by an illiquidity discount b. Use a higher discount rate for the illiquid asset and reduce the DCF value by an illiquidity discount c. Use the same discount rate for the illiquid asset (as you would for a liquid asset) and reduce the DCF value by an illiquidity discount. d. Use a lower discount rate for the illiquid asset and don't adjust the DCF value. e. Use a higher discount rate for the illiquid asset and don't adjust the DCF value.

The fully diluted approach adjusts just the number of shares and does not count the exercise proceeds, and thus will undervalue equity. The treasury stock approach counts the exercise proceeds, but ignores the time value of the option. It will therefore over value equity. • Fully diluted value/share = 500/ (100+25) = $4/share • Treasury stock approach = (500+25*$5)/ (100+25) = $5/share

Which of the following would you do if you were valuing the entire business? a. Discount cash flows before debt payments at the cost of equity b. Discount cash flows after debt payments at the cost of equity c. Discount cash flows before debt payments at the cost of capital d. Discount cash flows after debt payments at the cost of capital

c. Discount cash flows before debt payments at the cost of capital

Alfred Inc. is a publicly traded sporting goods company. The company has $ 250 million in book value of debt, reported interest expenses of $ 12.5 million in the most recent year and has an average maturity of 5 years for the debt. The pre-tax cost of debt for the firm is currently 4%. What is your best estimate of the market value of debt outstanding at the firm? (You can assume annual interest payments and a marginal tax rate of 40%) a. $261.12 million b. $250.00 million c. $280.29 million d. $243.01 million e. $156.68 million

a. $261.12 million. To compute the market value of the debt, discount the expected interest expenses and the principal on the debt at the pre-tax cost of debt • Market value of debt = =12.5*(1-1.04-5 )/0.04+250/1.045 = $261.12 m • The first term is the present value of $12.5 million as an annuity for 5 years, discounted back at 4%. The second term is the present value of the face value of the debt at the end of year 5

Nowitzki Inc. is a publicly traded company that owns 60% of Bowden Inc, another publicly traded firm. You have valued the operating assets of Nowitzki by discounting the cash flows (from Pagano's consolidated financials) at the cost of capital to arrive at a value of $1 billion for the operating assets. Nowitzki reports debt of $200 million and cash of $100 million on its consolidated balance sheet. While Nowitzki also shows a minority interest of $120 million on the balance sheet, you believe that the intrinsic value of all of Bowden's equity is closer to $500 million. Estimate the value of equity for Nowitzki. a. $700 million b. $1.1 billion c. $880 million d. $1,120 million e. $ 600 million

a. $700 million. To get to the value of equity, you need to add cash, subtract out debt and subtract out the estimated market value of the minority interest in the consolidated subsidiary. • Value of equity = 1000+ 100 - 200 - .4(500) = $ 700 m • Optimally, you would have liked to value the parent company as a standalone entity but you don't have that information.

Livewire Inc. is a technology company that reported a pre-tax operating loss in the most recent year of $10 million, after expensing R&D expenses of $30 million during the year. The company reported invested capital of $40 million at the end of the most recent year. You are told that the R&D typically takes 3 years to pay off in this business, and that Livewire had R& D expenses of $24 million, $18 million and $12 million in each of the last 3 years. Assuming that you decide to capitalize R&D expenses, what is the pre-tax return on capital for Livewire? a. 2.17% b. 5.00% c. -10.87% d. 43.48% e. None of the above

a. 2.17%. To compute this return on capital, you have to start with the R&D expenses: R&D expenses Unamortized Amortization Current $30 $30 $0 -1 $24 $16 $8 -2 $18 $6 $6 -3 $12 $0 $4 $52 $18 Adjusted operating income = -10 m + 30 m - 18 m = $2 million Adjusted capital invested = 40 m + $52 m = $ 92 million Pre-tax return on capital = 2/ 92 = 2.17%

Classify the following actions into value changing and value neutral actions. If value changing, specify whether it will increase or decrease the intrinsic value of equity in a business. a. A stock dividend b. Impairment of goodwill from a past acquisition (not tax deductible) c. A non-cash restructuring charge (not tax deductible) d. Impairment of goodwill from a past acquisition (a portion is tax deductible) e. A non-cash restructuring charge (tax deductible) f. A corporate name change with no change in business focus g. A corporate name change with a change in business focus

a. A stock dividend: Value neutral, no cash flow change b. Impairment of goodwill from a past acquisition (not tax deductible): Value neutral, no effect on cash flows, past mistake (sunk cost) c. A non-cash restructuring charge (which is not tax deductible): Value neutral, no effect on cash flows, past mistake (sunk cost) d. Impairment of goodwill from a past acquisition (a portion is tax deductible): Value increasing, Tax savings lead to higher cash flows e. A non-cash restructuring charge (which is tax deductible): Value increasing, Tax savings lead to higher cash flows. f. A corporate name change with no change in business focus: Value neutral g. A corporate name change with change in business focus: Value changing, increase or decrease depends upon returns in new business

One concern with using sector-average betas, even if you adjust for financial leverage, is that you are assuming that the operating leverage for your firm is similar to that of the other firms. Assume that 70% of the costs in your company are fixed costs, whereas only 50% of the costs in the average company in the sector are fixed costs. If the unlevered beta for the sector is 0.80, what would you expect the unlevered beta for your company to be? a. Higher than 0.80 b. Lower than 0.80 c. About 0.80 Bonus: Can you estimate the operating-leverage corrected beta?

a. Higher than 0.80 Having higher fixed costs should increase your beta. If you want to work out by how much, here is what you would do: • Unlevered beta for business = Unlevered Beta/ (1+ FC/ VC) • Unlevered beta for business = 0.80 (1 + 50/50) = 0.40 • Unlevered beta for company = 0.40 (1 + 70/30) = 1.33

In asset-based valuation, you try to value a company by valuing its individual assets and adding up these asset values to arrive at the value of the company. In which of the following scenarios is asset-based valuation likely to work best? a. Mature companies with separable, stand alone assets b. Growth companies with separable, stand alone assets c. Mature companies with interrelated, connected assets d. Growth companies with interrelated, connected assets

a. Mature companies with separable, stand alone assets. Growth assets and interrelated assets are difficult to value in asset based valuation.

The PE ratio usually cannot be computed when a company has negative earnings. Assume that you have a sample of 100 firms and that 30 of these firms have negative earnings. Let's say that you compute a market cap weighted PE ratio for the 70 firms with PE ratios and an aggregate PE ratio by dividing the total market capitalization of all firms in the sector by the total net income of all firms in the sector. Which one will yield the lower value? a. The weighted average PE ratio across the money making firms b. The aggregate PE ratio across all firms c. Either can happen

a. The weighted average PE ratio across all firms. The firms that you were unable to compute PE ratios for had negative earnings and positive market capitalizations. If you added their market capitalization to the market capitalization of the companies that you were able to compute the PE ratio for and added the net income (or loss) to the net income of the firms that you were able to compute the PE ratio for, you will end up with a lower aggregate PE ratios since the numerator will become higher and the denominator will become smaller.

If you use the price to sales ratio to compare the pricing of companies in a sector where there are wide differences in debt ratios, you will tend to find that companies with a lot of debt look cheap (even if they are not), a. True b. False

a. True. If you use just market capital (equity) in the numerator, companies that fund themselves more with debt and generate the same revenues will look cheaper on a price to sales ratio basis.

You are looking at valuing the brand name of a consumer product company that has an enterprise value of $2.5 billion on revenues of $ 1 billion. If companies in the same sector that produce generic substitutes trade at an EV/Sales ratio of 1.5, what is the approximate value of brand name at the company? a. $ 0.5 billion b. $1 billion c. $1.5 billion d. $2.5 billion e. $3.5 billion

b. $1 billion. If you apply the EV/Sales ratio of the generic company to the brand name company's revenues, you get $1.5 billion as enterprise value. Subtracting this from the total enterprise value of $2.5 billion yields a value of $ 1 billion.

You are using a dividend discount model to value a bank, which is expected to generate a 15% return on equity in perpetuity. The company paid dividends of $40 million on net income of $100 million in the most recent year and is expected to maintain high growth for the next 3 years, before settling into stable growth, growing 3% a year in perpetuity. If the cost of equity is 9%, estimate the terminal value at the end of year 3 a. $889.25 million b. $1778.51 million c. $2223.13 million d. $741.04 million e. None of the above

b. $1778.51 million. To get the terminal value, you have to first estimate the earnings in year 4, followed by the payout ratio in year 4: • Expected growth rate for next 3 years = .6*.15 = .09 or 9% • Net Income in year 4 = 100 (1.093)(1.03) = $133.39 million • Payout ratio in year 4 = g/ ROE = 3%/15% = 20% • Terminal value in year 3 = 133.39 (1-.20)/(.09-.03) = $1778.51 m

Now, assume that you decide to value the employee options in Rallye Inc., using an option-pricing model and arrive at a value of $1.00 for each option. What is the value of equity per share, if you decide to use the option value approach? a. $5/share b. $4.75/share c. $3.80/share d. $4.20/share e. None of the above

b. $4.75.To compute the value per share, you first net out the option value of the employee options from the DCF value of equity, and then divide by the actual number of shares outstanding. • Value per share = (500 - 25*$1)/ 100 = $4.75/share

You are a venture capitalist, who is interested in investing in Lam Media, a social media company. You expect revenues to be $600 million in 3 years and believe that you can sell the company for three times revenues at the end of year 3.The cost of capital for the company is 15%, it has no cash or debt and there is a 20% chance that the firm will not make it (in which case you will get nothing for the assets). Ignoring cash flows in the next 3 years, what is your estimate of the value of equity in the company today (in millions)? a. $ 236.7 b. $ 946.8 c. $1183.5 d. $1440.0 e. $1800.0

b. $946.8 million. Start by estimating the expected EV at the end of year 3 and discounting back to today at the cost of capital for 15%: • Expected EV = 3* 600 = $1800 million Discount back at the cost of capital • EV value today = 1800/1.153 = $1183.5 million Adjust for survival • Value of equity today = 1183.5*.8 = $946.8 million

You are reading an analyst reports that claims that banks collectively are cheap, because they are trading at 0.80 times book value of equity. You believe that the truth is that banks are perceived as riskier than they used to be. If the current return on equity for banks is 10% and the expected growth rate in perpetuity is 2%, what is the cost of equity that investors are attaching to banks? (Assume that banks collectively are in stable growth) a. 8% b. 12% c. 12.5% d. 15% e. None of the above

b. 12%. Since banks are mature, you can use the simple version of the price to book ratio: PBV = 0.80 = (ROE -g)/ (Cost of equity -g) = (.10-.02)/ (Cost of equity - .02) Cost of equity = 12% If you use (1+g) in your equation, you will get a cost of equity slightly lower than 12%.

Telsome Publishing is a small, publicly traded firm and has reported the following earnings over the last five years: Year Earnings (in millions) Current $180.00 Year -1 $100.00 Year -2 $150.00 Year -3 $115.00 Year -4 $120.00 Year -5 $90.00 What is the geometric average annual growth rate over the last five years? a. 20.00% b. 14.87% c. 21.25% d. 12.47% e. None of the above

b. 14.87%. To compute the geometric average growth rate, you just need the starting and ending numbers: Geometric average = (180/90)^(1/5)-1 = 0.1487 or 14.87% The arithmetic average annual growth rate is 21.25%. Year Earnings (in millions) Growth rate Current $180.00 80.00% Year -1 $100.00 -33.33% Year -2 $150.00 30.43% Year -3 $115.00 -4.17% Year -4 $120.00 33.33% Year -5 $90.00 Arithmetic average 21.25%

Genesis is a closed end mutual fund, with $250 million invested in publicly traded securities (net asset value). The fund is an average risk fund (beta = 1) and has earned an annual return of 9% over the last 5 years the market return over the period was 12%. If you expect the market return in the future to be 8% and Genesis to continue under performing the market by the same amount as it has for the last 5 years, estimate the discount that the fund will trade at (assuming no growth in the fund, in perpetuity). a. 25% b. 37.5% c. 11.1% d. 58.33% e. None of the above

b. 37.5%. To compute the discount, assume that you invest $100 in Genesis today. If they continue to earn 3% less than the required return, as they have in the past, the expected cash flow each year will be 5% (8% - 3%). Discounting this expected cash flow at the required return o 8%: • Market value of fund = 5/.08 = $62.5 • Discount as % = 1- 62.5/100 = .375 or 37.5%

Pokemon Inc. is a toy manufacturer that reported after-tax operating income of $50 million in the most recent year. At the start of the year, the company reported book value of equity of $400 million, book value of debt of $250 million and a cash balance of $150 million. The company also reported capital expenditures of $75 million, depreciation of $ 30 million and a decrease in noncash working capital of $5 million. Assuming that it plans to maintain its current return on invested capital and reinvestment rate, what is the expected growth in operating income? a. 6.15% b. 8.00% c. 13.33% d. 10.00% e. None of the above

b. 8%. The keys are the reinvestment rate and return on invested capital: • ROIC = 50/ (400 +250-150) = 10% • Reinvestment Rate = (75-30-5)/50 = 80% (Decrease in WC reduces reinvestment) • Expected growth rate = 10% (.80) = 8%

Which of the following would you do if you were valuing the equity in a business? a. Discount cash flows before debt payments at the cost of equity b. Discount cash flows after debt payments at the cost of equity c. Discount cash flows before debt payments at the cost of capital d. Discount cash flows after debt payments at the cost of capital

b. Discount cash flows after debt payments at the cost of equity

It is true that in a discounted cash flow valuation, the terminal value accounts for a large proportion (60% or more) of the value. It follows that the assumptions you make about terminal value are the most critical determinants of value. a. True b. False

b. False. The terminal value is determined in large part by your assumptions about growth during the high growth period. The cash flow you have in your terminal value equation will be much higher, if you use higher growth during the growth period and thus the terminal value will be significantly impacted by what you assume will happen during high growth.

If you invest in complex firms, you know far less than when you value in simple firms. However, as you get more diversified, the lack of knowledge will become less important because it will get averaged out in your portfolio. a. True b. False

b. False. While diversification will average out risk, it works only if the risk can cut both ways (be good news or bad news). With complex firms, it is more likely to be bad news.

One argument that is used by those who use multiples/relative valuation is that there are fewer assumptions in relative valuation than in intrinsic valuation. Is this true or false? a. True b. False

b. False. You may make fewer explicit assumptions but you ultimately make the remaining assumptions implicitly. Put differently, the number of assumption embedded in both approaches is the same, but you may make judgments on fewer of them.

The implied equity risk premium is a forward-looking premium, estimated from the level of stock prices (the index) today and expected earnings/cash flows in the future. Assume that you compute the implied ERP at the start of a year and the market goes up 20% during the course of the year and that you compute the implied ERP again at the end of the year. Assuming that the risk free rate and growth rate do not change over the course of the year, which of the following would you expect to happen to the implied ERP? a. The ERP will go down b. The ERP will go down, if the earnings/ cash flows went up by less than 20% during the year c. The ERP will go down, if the earnings/ cash flows went up by more than 20% during the year d. The ERP will not change e. The ERP will go up

b. The ERP will go down, if the earnings/ cash flows went up by less than 20% during the year. If the growth rate and risk free rate don't change, the effect will depend upon how much stocks go up, relative to earnings/cashflows. If the stock market goes up by more than earnings go up, the ERP will go down.

If you are asked to value an acquisition, using relative valuation, which of the following will yield the best estimate of relative value? a. The median multiple for the peer group (companies in the same business) b. The multiple for the peer group, adjusted for differences on risk, growth & cash flows between the target company and the peer group. c. The median multiple for other companies that have been acquired in the recent past d. The multiple for other companies that have been acquired in the recent past, adjusted for differences on risk, growth & cash flows between the target company and this group.

b. The multiple for the peer group, adjusted for differences on risk, growth & cash flows between the target company and the peer group. The peer group is a less biased sample than the group of companies that have been acquired in transactions, since the latter will generally include acquirers who overpaid on acquisitions. It is always better to adjust multiples for differences in fundamentals than to use just the median value.

You are comparing the PE ratios for pharmaceutical firms and have chosen to run a regression of PE ratios against expected growth rates at these companies: PE = 4.0 + 80 (Expected growth rate in EPS) (Thus, if your expected growth rate is 10%, your PE = 4.0 + 80 (.10) = 12) Assume that you are looking at a company that is trading at a PE ratio of 16 and has an expected growth rate of 20%. Given the regression, which of the following conclusions would you draw? a. The stock is overvalued by 20% b. The stock is under valued by 20% c. The stock is over valued by 25% d. The stock is under valued by 25% e. The stock is correctly valued

b. Under valued by 20%. Predicted PE, given growth = 4 + 80 (.20) = 20 Actual PE = 16 Under valuation = 16/20 -1 = -20% (Actual is less than predicted)

You are trying to value Zimco Telecom Inc., a money losing company that reported EBITDA of -$80 million in the most recent year on revenues of $ 1 billion. You expect revenues to grow 6% a year for the next 5 years and the EBITDA/Revenue margin to improve to 8% by year 5.If healthy telecom companies trade at a multiple of 6 times EBITDA and you choose to apply this multiple to the fifth year's expected EBITDA, estimate the value of equity per share today. (You have a cost of capital of 12% for the next 5 years, a cash balance of $ 50 million, debt outstanding of $200 million and 12 million shares outstanding today.) a. $0.00 b. $10.19 c. $17.87 d. $41.03 e. None of the above

c. $17.87.To get the value, you first need to estimate the expected EBITDA in year 5: • Expected revenues in year 5 = 1000 *1.065 = $1,338 million • Expected EBITDA in year 5 = 1,338 *.08 = $107.05 million Applying the EV/EBITDA multiple (6) for a healthy telecom firm • Expected EV = 107.05 * 6 = $642.3 million Discounting back at 12% for five years, we get: • EV today = $642.3 million/ 1.125 = $364.5 million • Equity value today = $364.5+ 50 - 200 = $214.5 million • Equity value per share = $214.5/12 = $17.87/share

Charisma Software is a technology company is expected to report after-tax operating income of $ 1 billion next year, earned on an invested capital base of $10 billion. The company is expected to grow 1% a year in perpetuity and has a cost of capital of 9%. The firm wants to double its growth rate in perpetuity, while maintaining its current return on capital. How much will the value of its operating assets change in dollar terms? a. Decrease value b. No change c. $178.57 million d. $1607.14 million e. $1785.71 million f. None of the above How would your answer change if the invested capital base were $ 11 billion? How about if it were $12 billion?

c. $178.57 million. First, value the firm with an expected growth rate of 1%. Return on capital = 1000/10000= 10% Reinvestment rate = g/ ROC = 1%/10% = 10% Value = 1000 (1-.10)/(.09-.01) = $11,250 million With a 2% growth rate Reinvestment rate = g/ ROC = 2%/10% = 20% Value = 1000 (1-.20)/(.09-.02)= $11,428.57 Change in value = $11,428.57 - $11,250 = $178.57 Bonus: If the invested capital were $11 billion, the return on capital would become 9.1%, barely higher than the cost of capital. The change in firm value will become much smaller ($18 million). If the invested capital were $12 billion, the return on capital < cost of capital and increasing growth will lower value.

Loomix Inc,is a company that has a history of losing money and has accumulated $100 million in net operating losses. You expect the company to generate an operating loss of $50 million next year, followed by pre-tax operating profits of $75 million and $125 million in the following two years. If your marginal tax rate is 40%, how much will Loomix pay cumulatively as taxes in the next three years? a. $90 million b. $60 million c. $20 million d. $30 million e. None of the above

c. $20 million. The current NOL is $100 million. After next year, that NOL will increase to $150 million. That will cover the operating income in year 2 of $75 million fully, with $75 million carried into year 3.Offsetting this against the net income of $125 million in year 3 yields a taxable income of $50 million and taxes of $20 million.

Roomba Inc. is a manufacturer of vacuum cleaners and you have estimated a FCFF of $50 million for firm for the most recent year. Roomba's total debt decreased from $100 to $85 million during the course of the year and it reported interest expense of $10 million for the year. If Roomba's tax rate is 30%, estimate the FCFE for the most recent year. a. $ 25 million b. $ 58 million c. $ 28 million d. $ 55 million e. None of the above

c. $28 million. To get from FCFF to FCFE, you subtract out the after-tax interest expense and the net debt change (if debt increases, it is a cash inflow whereas a debt decrease is cash outflow). • FCFF - Interest expense (1-t) + Change in Debt = FCFE • 50 - 10 (1-.30) -15 = $28 million

You are trying to value Wyckham Inc., a conglomerate operating in three businesses, with projected after-tax operating income (in millions) in the next period. Business Expected EBIT (1-t) ROIC Cost of capital Steel $150 9% 8% Chemicals $100 12% 9% Technology $ 50 15% 13% The companies are in stable growth, growing 3% a year in perpetuity. What is the sum of the parts value for Wyckham Inc.? a. $3,000 million b. $3,500 million c. $3,650 million d. $4,250 million e. $5,167 million

c. $3,650 million. To estimate the value of each business, you first have to estimate the reinvestment rate: Reinvestment rate = Expected growth rate/ ROIC The value can then be estimated as follows: Value = Expected EBIT (1-t) (1- Reinvestment rate)/ (Cost of capital -g) Business EBIT (1-t) ROIC Reinvestment rate Cost of capital Value Steel 150 9% 33.33% 8% 2000 Chemicals 100 12% 25.00% 9% 1250 Technology 50 15% 20.00% 13% 400 Company 3650

Avalon Inc. is a high growth publicly traded firm that is expected to become a stable growth firm after 5 years. You have estimated an expected after-tax operating income of $60 million in year 6 and believe that the firm will generate a return on capital of 12% in perpetuity. If the cost of capital is 10% and the expected growth rate in perpetuity after year 5 is 3%, what will the terminal value be at the end of year 5? a. $857.14 million b. $666.67 million c. $642.86 million d. $450 million e. None of the above

c. $642.86 million. To compute the terminal value after year, you first have to estimate a reinvestment rate: • Reinvestment rate = 3%/12% = 25% • FCFF in year 6 = 60 (1-.25)/ (.10-.03) = $642.86 million

Which of the following approaches can be used to estimate he risk adjusted value of an asset in an intrinsic valuation (more than one answer can apply)? a. Discounting the certainty equivalent cash flows at a risk adjusted discount rate b. Discounting the expected cash flows at a risk free rate c. Discounting the expected cash flows at a risk-adjusted discount rate d. Discounting the certainty equivalent cash flows at a risk free rate

c. & d. You can either adjust the cash flows for risk or the discount rate, not both.

In the melded country risk premium approach, you estimate the country risk premium by multiplying the country default spread by the volatility of equity markets, relative to the volatility in government bonds in that market. Assume that your estimate for a mature market equity risk premium is 6%, that the default spread for Indonesia is 2% and that the standard deviation of Indonesian equities is 24% (while the standard deviation of the Indonesian government bond is 12%). Estimate the total equity risk premium for Indonesia a. 12% b. 8% c. 10% d. 6% e. 4%

c. 10%. The country risk premium is 4%, obtained by multiplying the default spread of 2% by the relative standard deviation of equity (to bond) of 2 (24%/12%). This has to be added to the mature market equity risk premium of 6$ to get to the total equity risk premium of 10%.

Nevis Enterprises reported a return on invested capital of 15% in the most recent year and a reinvestment rate of 60%. The firm expects its return on capital to rise to 18% over the next 5 years on both existing investments and new investments. What will the compounded average annual expected growth rate be over the five years? a. 10.8% b. 9% c. 14.51% d. 12.71% e. None of the above

c. 14.51%. Since the return on capital is changing on existing and new investments, there are two components to the expected growth: • Expected growth from new investments = .6*.18 = 10.8% • Expected efficiency growth over 5 years = (.18-.15)/.15 = 20% • Expected efficiency growth per year= (1.20)1/5-1 = 3.71% • Expected annual growth = 10.8% + 3.71% = 14.51%

Tinga Inc., a poorly run restaurant chain, is currently fairly valued, based on the expectation that it would generate $25 million in after-tax operating income next year, growing at 2% a year. The company has $500 million in invested capital and is expected to maintain its current return on investment capital its cost of capital is 8%. You believe that you can run the firm better and double its aftertax operating income without adding any invested capital. Assuming that you can maintain your return on capital in perpetuity as well, how much of a control premium (in percentage terms, over and above current value) would you be willing to pay for Tinga? a. 20% b. 100% c. 167% d. 200% e. None of the above

c. 167%. First, value the firm run by the existing management: After-tax operating income = 25 million, ROC = 5%, Reinvestment rate = 2%/5% = 40% Value = 25 (1-.4)/ (.08-.02) = $250 million Second, value the firm with you running it. After-tax operating income = 50 million, ROC = 10%, Reinvestment rate = 2%/10% = 20% Value = 25 (1-.2)/ (.08-.02) = $666.67 million Control premium = 666.67/250 -1 = 166.67%

Pagano Holdings is a publicly traded company with a 10% minority holding in Gigante Enterprises. You have discounted Pagano's free cash to the firm back at Pagano's cost of capital and arrived at a value of $250 million for Pagano's equity. Assume that Gigante Holdings has an aggregate book value of equity of $100 million and that you estimate the intrinsic value of its equity to be $200 million. Estimate the value of equity for Pagano Holdings. a. $250 million b. $260 million c. $240 million d. $270 million e. $230 million

d. $270 million. Since this is a minority holding, it is not reflected in your current operating income, cash flow or value of $250 million. You have to add the estimated market value of this holding to your value: • Estimated market value of holding = 10% of $200 m = $20 m • Estimated value of Pagano = $250 m + $20 m = $270 m

You are forecasting the operating earnings for TalkMedia, a young, high growth social media company. Last year 1 2 3 4 Revenues $100 $200 $320 $450 $600 Operating Margin -10% -5% 0% 5% 10% Operating Income -$10.00 -$10.00 $0.00 $22.50 $60.00 The firm currently has invested capital of $50 million. If the sales-to-capital ratio is 2.00, what will the pre-tax return on capital be in year 4? a. 120% b. -20% c. +20% d. 10% e. None of the above

c. 20%. The key is to estimate the reinvestment each year, based upon the change in revenues and the sales to capital ratio. That reinvestment adds to the invested capital each year: Last year 1 2 3 4 Revenues $100 $200 $320 $450 $600 Operating Margin -10% -5% 0% 5% 10% Operating Income -$10.00 -$10.00 $0.00 $22.50 $60.00 Reinvestment $50.00 $60.00 $65.00 $75.00 Invested Capital $50.00 $100.00 $160.00 $225.00 $300.00 Return on capital -20% -10% 0% 10% 20%

it has an expected growth rate in revenues of 6% for the next 5 years and a cost of capital of 10%. Assuming that this stock is fairly priced, what is Astor's effective tax rate? a. 0% b. 15% c. 25% d. 40% e. 50%

c. 25%. To estimate the growth rate, recognize that the firm is correctly priced right now: Current EV/EBITDA multiple = 480/100 = 4.80 Set equal to the expected value in the regression 4.80 =5+80*(0.06)-20*(0.10)-12(Tax rate) Solve for the tax rate, tax rate = 25%

Oneida Inc. is a publicly traded company with a 60% cross holding in Cyclops Inc., also a publicly traded company. You are given the following information from Oneida Inc's consolidated financials and Cyclop's financials: Oneida Cyclops Market Cap 5000 2000 Debt 1000 400 Cash 800 100 EBITDA 900 500 Minority interest 400 0 (The market cap number is the share price times number of shares. All of the other numbers come from financial statements). What is the EV/EBITDA multiple for Oneida on a consolidated basis? a. 5.78 b. 6.22 c. 6.67 d. 8.00 e. None of the above

c. 6.67.To get the EV/EBITDA for the consolidated company, I first compute the market value of the 40% of Cyclops that does not belong to Oneida, which yields: • Market cap of 40% of Cyclops = 0.40 (2000) = 800 • Since the debt, cash and EBITDA numbers are already fully consolidated, you can now compute the EV/EBITDA multiple: EV/ EBITDA = (5000+800+ 1000-800)/ 900 = 6.67

Lester Inc. has 5 million shares outstanding, trading at $20/share. The company has one convertible bond, with a face value of $ 100 million, a ten-year maturity and a coupon rate of 2% the bond has a market value of $120 million. If the current cost of equity for the firm is 10% and the pre-tax cost of debt is 5%, what is the cost of capital for the firm? (The marginal tax rate is 40%) a. 5.20% b. 6.18% c. 7.55% d. 8.25% e. None of the above

c. 7.55%. The first step is to decompose the convertible bond into its debt and equity components. To do this, value the convertible bond as if it were a straight bond by discounting the coupons and face value back at the pre-tax cost of debt: • Value of straight bond portion = $2 million (PV of annuity for 10 years @5%) + $100 million/1.0510 = $76.83 million • Value of conversion option = Market value of convertible - Straight bond value = $120 - $76.83 = $43.17 million • Overall value of equity = $143.17 million • Cost of capital = 10% (143.17/(143.17+76.83)) + 5% (1-.4) (76.83/(143.17+76.83)) = 7.55%

Caribou Enterprises is an all-equity funded company with a cost of equity of 9% the risk free rate is 3% and the equity risk premium is 6%. The company is considering borrowing money at 5% (pre-tax) and pushing its debt to capital ratio to 20%. If the marginal tax rate is 40%, what will the new cost of capital be at 20%? a. 7.80% b. 8.20% c. 8.52% d. 8.92% e. 9.00%

c. 8.52%. First, compute the unlevered beta using the current cost of equity. Unlevered beta = (9%- 3%)/ 6% = 1.00 D/E ratio at a 20% debt to capital ratio = 20/80 = 25% Levered beta = 1.00 (1+ (1-.4)(.25)) = 1.15 Cost of equity = 3% + 1.15 (6%) = 9.90% Cost of capital = 9.9% (.8) + 5% (1-.4) (.2) = 8.52%

The CAPM beta is a measure of relative risk, but it comes with significant baggage (a belief in modern portfolio theory, a trust that stock prices are driven by fundamentals, an assumption of liquidity). Assume that you want a measure of relative risk that is not dependent upon assumptions of diversified investors and credible stock prices. Which of the following would you use as your relative risk measure? a. A ratio of standard deviation in your company's stock price to the average standard deviation across all stocks b. An implied beta, backed out of current stock prices and expected future cash flows c. A ratio of the standard deviation in your company's historical earnings to the average standard deviation in earnings of other companies in the market d. The PE ratio for your firm, relative to the average PE ratio of other firms in the market (Low = Less risky) e. None of the above

c. A ratio of the standard deviation in your company's earnings relative the average standard deviation in earnings of other companies in the market. All of the other measures are price based, in one way or the other or build on traditional portfolio theory.

One alternative to a regression beta is to use a sector-average beta or bottom-up beta. In computing this sector-average beta, you have to come up with a list of comparable firms. Assume that you are trying to compute the beta for a Argentine steel company. Which of the following is likely to yield the best estimate? a. A simple average of betas of 4 Argentine steel companies b. A simple average of betas of 12 Latin American steel companies c. A simple average of betas of 85 emerging market steel companies d. A market-cap weighted average of betas of 4 Argentine steel companies e. A market-cap weighted average of betas of 12 Latin American steel companies f. A market-cap weighted average of betas of 85 emerging market steel companies

c. A simple average of betas of 85 emerging market steel companies. For the law of large numbers to work in your favor, you want larger samples rather than smaller ones. Using weighted averages also undercuts the benefits of averaging, since it counts the larger firms more and the smaller firms less.

Which of the following assets is best suited for intrinsic valuation? a. A finite life asset with no cash flows associated with it b. An infinite life asset with no cash flows associated with it c. An asset with uncertain cash flows over any life period d. An asset with cash flows contingent on an event happening e. None of the above

c. An asset with uncertain cash flows over any time period. You cannot do intrinsic valuation on non-cash flow generating assets (collectibles, paintings, gold). An asset with contingent cash flows is best valued as an option.

If you are dividing the market capitalization by book value to arrive at a price to book value ratio for a company, which of the following will you use as your measure of book value? a. Book value of assets b. Book value of liabilities c. Book value of common equity d. Book value of invested capital (debt + equity - cash) e. None of the above

c. Book value of equity. If the numerator is market capitalization which is the market value of equity, the denominator should be the book value of equity.

In recent years, analysts have shifted away from PE ratios to EV/EBITDA multiples in large segments of the equity markets. Which of the following is a sensible reason for this shift? (The others may be reasons but they may not be sensible). a. EV/EBITDA multiples will yield values that are generally lower than PE ratios b. EV/EBITDA multiples are not affected by growth c. EBITDA is a good measure of free cash flow to the firm d. EV/EBITDA can be compared across companies that use different depreciation methods e. EBITDA can be used to service debt f. All of the above

c. EV/EBITDA can be compared across companies that use different depreciation methods. Companies that use accelerated depreciation will report lower net income than companies that use straight line depreciation and may look more expensive on a PE ratio basis. None of the other reasons hold up: EV/EBITDA is affected by cost of capital, which can be affected by financial leverage and while EBITDA may be a measure of intermediate cash flow, it is not free (since you still have to pay taxes and cover capital expenditures).

In valuation, your risk free has to be a long term, default-free rate. When valuing a company in US dollars, we often use the 10-year US T. bond rate as the risk free rate. In the last few years, there have been questions about whether the US treasury is really default-free. If you share these concerns, which of the following will you do, assuming that you are still estimating cash flows in US dollars? a. Continue to use it the 10-year bond rate the risk free rate since you have no choice b. Switch to using the US treasury bill rate, since default is less likely in the short term c. Estimate a default spread for the US government and reduce the treasury bond rate by that spread d. Use the rate on a 10-year Swiss Government bond, denominated in Swiss francs (since the Swiss government has no default risk) e. None of the above

c. Estimate a default spread for the US government and reduce the T. bond rate by that spread. You could obtain the spread for the US sovereign CDS and net it out from the US treasury bond rate. You cannot use as short term rate or a rate from a bond denominated in a different currency.

Assume that you are doing a valuation, where you are comparing the price to book ratio of GenSys Bank to other banks. GenSys has a price to book ratio of 2.00 and a return on equity of 16%. The average price to book ratio across all banks is 1.20 but you have run a regression of price to book against return on equity across banks and arrived at the following: PBV = 0.72 + 80 (ROE) Based on this regression, which of the following conclusions would you draw? a. Gensys is under valued (cheap) b. Gensys is over valued (expensive) c. Gensys is fairly valued

c. Fairly valued. Plugging the ROE for GenSys into the regression PBV = 0.72 + 80 (.16) = 2.00 The stock is trading at 2 times book value. Hence, it is fairly priced.

You are looking at a group of mature insurance companies, with the intent of finding an undervalued company. Which of the following combinations would you be looking for? a. Low price to book, low risk, low return on equity b. Low price to book, high risk, high return on equity c. Low price to book, low risk, high return on equity d. Low price to book, low risk, low return on equity

c. Low price to book, low risk, high return on equity. Low price to book is an indication of cheapness, low risk of a low cost of equity and a high return on equity of high returns on investments.

A consumer product company plans to cut prices on its products with the intent of generating more sales. Which of the following is the most likely set of consequences from this action? a. Higher margins, Higher EV/Sales b. Higher margins, Lower EV/Sales c. Lower margins, Lower EV/Sales d. Lower margins, Higher EV/Sales Bonus: Will this translate into higher value for the company?

c. Lower margin, lower EV/Sales ratio. The margin will drop if prices drop and the lower margins will translate into a lower multiple of revenues. However, the company can still emerge as a more valuable company, if its sales go up more than proportionately.

There are variations on PE ratio, based upon whether you use earnings per share from the most recent fiscal year, the last 12 months (trailing) or expected earnings per share in the next 12 months (forward). In periods of economic health and earnings growth, which of the measures of PE will yield the lowest value? a. Most recent fiscal year b. Trailing 12 months c. Next 12 months

c. Next 12 months

You are valuing a Spanish company in Euros. Which of the following would you use as your risk free rate in your valuation? a. The rate on Spanish government ten-year euro bond (5%) b. The highest of the 10-year, euro denominated government bond rates (9%). c. The lowest of the 10-year, euro denominated government bond rates (1.5%) d. The lowest of the European government bond rates, which is the Swiss Government bond rate, denominated in Swiss francs (0.75%) e. None of the above

c. The lowest of the 10-year, euro denominated government bond rates (probably ECB or German 10-year). The Spanish 10-year bond rate is not risk free and the Swiss government bond is in a different currency.

When you value assets, you are implicitly assuming that a. The market is always right b. The market is always wrong c. The market is sometimes wrong, but that it corrects itself eventually d. The market is sometimes wrong, and that it does not correct itself eventually e. None of the above

c. The market is sometimes wrong, but that it corrects itself eventually. You need the market to make mistakes for your valuation to have a chance, but you need the market to correct its mistakes, if you want to make money.

What would you use as your risk free rate if you were valuing a Peruvian company in Peruvian Sol? (You can still assume that the Peruvian sovereign CDS is trading at 1%.) a. The rate on a Peruvian 10-year Sol denominated bond (6%) b. The rate on a Peruvian 10-year US $ denominated bond (3.5%) c. The rate on a Peruvian 10-year Sol denominated bond minus the Peruvian CDS spread (6%-1% =5%) d. The rate on a 10-year US treasury bond (2%) e. None of the above

c. The rate on the Peruvian Sol bond, net of the CDS spread (6%-1% = 5%). There is a small mismatching problem since the CDS sp

In the most recent year, Revco Inc. reported capital expenditures of $ 80 million and depreciation & amortization of $ 60 million. It also spent $ 100 million in acquisitions, paying $40 million in cash and $ 60 million in stock. Estimate the net capital expenditures for the firm for use in computing the free cash flow to the firm. a. $ 80 million b. $ 20 million c. $ 60 million d. $120 million e. $ 180 million

d. $20 million. Include all acquisitions, whether paid for with cash or stock in cap ex. Net cap ex = 80 + 100 -60 = 120

Sigma Casino is a publicly traded firm that is burdened with too much debt and is in significant financial trouble. It has 10-year zero coupon bonds that are trading at 50% of face value and a DCF valuation of the firm as a going concern has generated a value of $6/share for the equity. If the risk free rate is 3% and you expect the equity to be worth nothing if the company folds, what would you be willing to pay per share for Sigma Casino? a. Nothing b. $1.97 c. $3.00 d. $4.03 e. $6.00

d. $4.03.First, back out the probability of default from the zero coupon bond and the risk free rate: • Value of bond = $500 = $1000 (1- Probability of default)/ 1.0310 • Probability of default = 32.80% Since the equity will be worth nothing if the company defaults, • Value per share = $6 (.6720) + $0 (.328) = $4.03

You are analyzing Sterling Stores, a retail company. The company reported $25 million in pre-tax operating income in the most recent year and invested capital of $125 million. The operating income, though, was computed after operating lease expenses that amounted to $25 million in the most recent year and the company has commitments to make $20 million in lease payments every year for the next 8 years. Assuming that Sterling Stores has a pre-tax cost of debt of 4% and that you decide to capitalize operating leases, what is the pre-tax return on capital is for Sterling Stores? a. 26.53% b. 10.53% c. 19.26% d. 12.77% e. None of the above

d. 12.77%. The first step is to capitalize the lease commitments present value of $20 million/year for 8 years @ 4% is $134.65 million. The second is to compute the depreciation on the leased asset: • Depreciation on leased asset = $134.65/ 8 = $16.38 • Adjusted Operating Income = $25 m + $25 m - $16.38 = $33.17 million • Adjusted capital invested = $125 + $134.65 = $259.65 • Pre-tax Return on capital = 33.17/259.65 = 12.77%

A key input into your terminal value is the expected growth rate in perpetuity. Assuming that you are valuing a company in a currency with a risk free rate of 3%. Which of the following growth rates is not feasible? a. -3% in perpetuity b. 0% in perpetuity c. 2% in perpetuity d. 4% in perpetuity e. None of the above

d. 4% in perpetuity. Using a growth rate that exceeds the risk free rate is dangerous, since the risk free rate operates as a proxy for nominal growth in the economy.

The annual standard deviation in stock returns is about 20%. Assuming that annual returns are independent of each other, how many years of historical data will you need to lower the standard error in your estimate to 1%? a. 25 years b. 100 years c. 200 years d. 400 years e. None of the above

d. 400 years. If annual returns are independent, the standard error is the standard deviation divided by the square root of the number of years of returns that you have. With a 20% standard deviation, that would require 400 years.

Lipscott Inc. is a publicly traded company that has $100 million in bank loans on its books, with a stated interest rate of 3% and $150 million in publicly traded bonds, with a coupon rate of 3.6%. The company currently has a bond rating of BBB, with a default spread of 1.5% over the risk free rate. If the current T.Bill rate is 1%, the ten-year T.Bond rate is 3.5% and the marginal tax rate is 35%, what is the pre-tax cost of debt? a. 3.36% b. 3.60% c. 5.00% d. 2.50% e. 3.50%

d. 5.00%. The pre-tax cost of debt is a long term cost of borrowing money today. • Pre-tax cost of debt = 3.5% + 1.5% = 5%

Faraday Enterprises is a publicly traded company. It currently has 10 million shares trading at $12/share and $150 million in book value of equity. The firm also has book value of debt of $ 75 million and market value of debt of $ 80 million. The cost of equity for the company is 9%, the pre-tax cost of debt is 4% and the marginal tax rate is 40%. What is the cost of capital? a. 7.4% b. 7.0% c. 7.7% d. 6.36% e. None of the above

d. 6.6%. The first step is to compute the market value weights of debt and equity • Debt to capital ratio = 80/(120+80) = 40% • Cost of capital = 9%(.6) + 4% (1-.4) (.4) = 6.36%

In the last example, what would the EV/EBITDA multiple for Oneida be, just as a parent company? a. 4.11 b. 4.44 c. 7.25 d. 9.25 e. 10.00 f. None of the above

d. 9.25.To estimate the EV to EBITDA for just the parent company, I have to clean up each of the numbers for Cyclop's holdings • Parent company equity = 5000 -0.6 (2000) = 3800 • Parent company debt = 1000-400 = 600 • Parent company cash = 800 - 100 = 700 • Parent company EBITDA = 900-500 = 400 • Parent company EV/EBITDA = (3800+600-700)/400 = 9.25

If you have to estimate a regression beta for a publicly traded US technology company, listed on the NASDAQ, whose largest stockholders are global mutual funds, which of the following will yield your best estimate of the regression beta? a. A regression of the stock returns against a technology stock index b. A regression of the stock returns against the NASDAQ c. A regression of the stock returns against the S&P 500 d. A regression of the stock returns against the MSCI e. None of the above

d. A regression of the stock returns against the MSCI. If your marginal investors are globally diversified, they will measure risk against a global equity index.

When you use relative valuation, you are trying to price assets based upon what similar assets are being priced at. In comparing across these assets, which of the following do you have to do? a. Find similar or comparable assets, with trading prices b. Standardize the prices to a common variable available for all assets c. Control the standardized prices for differences across the assets d. All of the above e. None of the above

d. All of the above. You have to find traded, similar companies, standardize prices to a common variable and adjust for differences across companies.

Which of the following assets is best suited for relative valuation? a. An untraded, unique asset with nothing comparable or similar to it. b. A traded, unique asset with nothing comparable or similar to it. c. An asset that is similar to other assets, none of which have traded prices. d. An asset that is similar to other assets, many of which are traded at regular intervals. e. None of the above

d. An asset that is similar to other assets, many of which are traded. You need similar assets for the comparison and the trading for the prices on these assets.

The conventional wisdom is that if a company increases its growth rate, the PE ratio should go up. When is this not true? a. When the company has a growth rate< riskfree rate b. When the company is risky c. Whey the company is safe d. When the company earns a ROE> Cost of equity e. When the company earns a ROE < Cost of equity

e. When the company earns a ROE < Cost of equity. A company that increases growth by investing in projects that earn less than the cost of equity will destroy value and see its PE ratio go down. In terms of mechanics, the gain in growth will be offset by the loss in cash flows to equity (or dividends) in the near term.

What type of investor will get the biggest payoff from using intrinsic valuation? a. An investor with a short time horizon that believes that markets are always wrong. b. An investor with a long time horizon that believes that markets are always wrong. c. An investor with a short time horizon that believes that markets make mistakes on pricing but that they correct them over time. d. An investor with a long time horizon that believes that markets make mistakes on pricing but that they correct them over time. e. An investor that believes that markets are always right.

d. An investor with a long time horizon that thinks that markets are wrong at points in time but that they correct themselves over time. If markets are always wrong, you will not make any money on your intrinsic valuation and you need a long time horizon to improve your odds of markets correcting themselves.

You are trying to compute the change in working capital to use in computing free cash flow to the firm for Zapata Inc. The firm's total working capital increased from $100 million last year to $120 million this year. However, this working capital includes cash and short term debt last year's cash balance had $ 30 million in cash and $15 million in short term debt, whereas this year's cash balance has $20 million in cash and $25 million in short term debt. What effect did working capital have on your cash flow this year? a. Decreased cash flow by $20 million b. Decreased cash flow by $30 million c. Decreased cash flow by $35 million d. Decreased cash flow by $40 million e. None of the above

d. Decreased cash flow by $40 million. Compute the non-cash working capital for each year: • Non-cash WC = WC - Cash + ST Debt • Non-cash WC last year = 100 - 30 +15 = 85 • Non-cash WC this year = 120 -20 + 25 = 125 • Change in non-cash WC = 125 - 85 = +40 (Decreases CF)

Delray Stores is a retail company that is facing a shrinking market. The firm generated $ 50 million in after-tax operating income in the most recent year, but expects to shut down 10% of its stores, each year for the next 5 years. Which of the following would you most expect to see in the next 5 years? a. Increasing operating income each year and after-tax cash flows < operating income b. Increasing operating income each year and after-tax cash flows > operating income c. Decreasing operating income each year and after-tax cash flows < operating income d. Decreasing operating income each year and after-tax cash flows > operating income

d. Decreasing operating income each year and after-tax cash flows > operating income. The company will have a negative reinvestment rate and since these are moneymaking stores (though the ROC is terrible), the operating income will decline. However, the store closings will generate cash flows, thus resulting in cash flows > after-tax operating income.

Gerard Enterprises is a publicly traded company. You are trying to estimate how much debt it has outstanding, to compute a cost of capital. Which of the following items would you not include in debt and why? a. Short term bank loans b. Commercial paper c. Corporate bonds d. Deferred Tax Liabilities e. None of the above

d. Deferred tax liabilities. These are not legal commitments in the conventional sense but accounting liabilities (reflecting expectations that the firm will have to pay more in taxes in the future).

You are valuing two companies. Company A is a mature company, with a long and stable history. Company B is a young, start-up with substantial uncertainty about the future and little history. Which of the following statements would you subscribe to? a. I will be able to value Company A less precisely than Company B, and there will be a bigger payoff to valuing Company b. b. I will be able to value Company A more precisely than Company B, and there will be a bigger payoff to valuing Company A. c. I will be able to value Company A less precisely than Company B, but there will be a bigger payoff to valuing Company A. d. I will be able to value Company A more precisely than Company B, but there will be a bigger payoff to valuing Company B.

d. I will be able to value Company A more precisely than Company B, but there will be a bigger payoff to valuing Company B. With its long and stable history, you should be able to value company A more precisely, but so will everyone else. You will value Company B less precisely, but most people will give up. Your payoff will be greater with Company B.

Publicly traded companies often accumulate cash that is usually invested in riskless, liquid securities that yield low returns. Which of the following is a good reason for punishing companies that hold cash (by discounting the cash)? a. The cash earns a lower rate of return than the cost of equity b. The cash earns a lower rate of return than investments in operating assets c. Investors can earn a higher return on the cash, if it was returned to them. d. The company has a good track record on operating investments and you are afraid that the company will not invest the cash e. The company has a bad track record on operating investments and you are afraid that the company will invest the cash

d. The company has a bad track record on operating investments and you are afraid that the company will invest the cash. Cash earns a low rate of return, but it is a fair rate of return. So, it is neither a value destroyer not does it create value. It is your concern that it may be wasted by investing a project/business where you earn less than the cost of capital that triggers the discount..

You have been asked to value the chemical division of a multi business conglomerate and have been provided with the cash flows for the division. What discount rate would you use to discount this cash flow? Year 1 Year 2 Year 3 Earnings before interest and taxes (1- tax rate) $100 $105 $110 - Reinvestment in chemical business $20 $22 $25 Cash flow $80 $83 $85 a. The cost of equity of the company b. The cost of capital of the company c. The cost of equity for the chemical business d. The cost of capital for the chemical business e. None of the above

d. The cost of capital for the chemical business. The cash flows are computed using operating income (rather than net income) and have no debt flows (repayments of debt or new debt issues). They are also for the chemical business.

You are valuing a Peruvian company in US dollars. The Peruvian government has a CDS (Credit Default Swap) that is trading at 1%. Which riskfree rate would you use in your valuation? a. The rate on a Peruvian 10-year Sol denominated bond (6%) b. The rate on a Peruvian 10-year US $ denominated bond (3.5%) c. The rate on a Peruvian 10-year Sol denominated bond minus CDS spread d. The rate on a 10-year US treasury bond (2%) e. None of the above

d. The rate on a US T.Bond. If the valuation is done in dollars, the Sol rate is not the right riskfree rate. The Peruvian dollar bond rate has default risk in it (it is trading at a higher rate than the T.Bond)

Given your understanding of fair value accounting, which of the following best describes the mission? a. To estimate the intrinsic value of assets in place b. To estimate the intrinsic value of growth assets c. The estimate the intrinsic value of asset in place and growth potential d. To estimate the relative value of assets in place e. To estimate the relative value of growth assets f. To estimate the relative value of assets in place and growth assets

d. To estimate the relative value of assets in place, Since fair value accounting requires you to estimate what a market participant will pay for an asset in an arms-length transaction rather than the value of the asset, it is really a relative valuation assessment. And since growth is entirely in the future, it is difficult to see how you can fair value that number and put it on an accounting balance sheet.

Assume that Zisco Inc., a technology company, has 200 million shares outstanding, trading at $8/share. The company also has 10 million options outstanding, with an exercise price of $4/share and an option value of $7.5/option. What is the total market value of equity in Zisco? a. $1.525 billion b. $1.56 billion c. $1.6 billion d. $1.64 billion e. $1.675 billion

e. $1.675 billion. In this case, we are starting with the market value of the traded shares (rather than the DCF value of all equity). Consequently, if there are options outstanding, they will depress the stock price. To get to the total value of equity, you should add the option value of outstanding options. • Value of equity = (200*$8) + (10*7.50) = $1,675 million

Aspic Inc. is a US-based company that operates in two countries: the United States and Mexico. The total equity risk premium is 5% for the United States and 9% for Mexico. Which of the following estimates of the equity risk premium would you use for Aspic? a. 5%: the US equity risk premium, because it is US based b. 7%, a simple average of the US and Mexico equity risk premiums c. 6.2%, the weighted average based upon the revenues that the company gets from the two countries (70% from US, 30% from Mexico) d. 5.8%, the weighted average based upon the assets that the company has in the two countries (80% in the US, 20% in Mexico) e. 6.6% the weighted average based upon the value that the company attaches to its operations in the countries (60% US, 40% Mexico)

e. 6.6%. the weighted average based upon the value that the company attaches to its operations in the countries (60% US, 40% Mexico). You want to use value weights for equity risk premiums optimally. In practice, we use revenues, assets or operating income as proxies but only because we do not have access to value.

Most analysts and appraisers get their equity risk premium by looking at the past: the historical risk premium is the difference between what you would have earned invested in stocks over a past period over what you would have earned on a risk free investment. Which of the following are problems with this approach? a. The estimate is subjective, since it depends upon the time period and averaging approach used. b. The estimate is backward looking c. The estimate has substantial standard error d. The estimate moves counter intuitively: down after crisis and up after prosperity e. All of the above

e. All of the above. Historical ERP are a function of your estimation choices, backward looking, noisy and move in counter intuitive ways. If stocks have a really bad year, as they tend to during a crisis, the historical risk premium will get smaller, not larger.

The standard approach to estimating betas is to run a regression of returns of an individual stock against returns on a market index. Which of the following is a problem with this approach? a. It yields an estimate with significant standard error. b. It is subject to estimation choices: different regression periods, return intervals and market indices. c. It will not yield a good estimate for the future, if a company's business mix has changed recently. d. It will not yield a good estimate for the future, if a company's financial leverage has changed over the regression period e. All of the above.

e. All of the above. Regression betas can be dangerous as a result of each and every one of these. They can be most dangerous when they look good, since that can be accomplished by using a narrow market index.

Claremont Inc. is a company that has two divisions, both of which are in stable growth (growing 2% a year) and have a cost of capital of 10%. You have been provided with the following information on the divisions (in millions): Expected After-tax Operating Income next year Invested Capital Food $150 $1,000 Chemicals $50 $1,000 Assume that if you continue to run the chemical business, your return on capital will stay at existing levels and that you can divest the business for $ 800 million. What effect will the divestiture have on company value? a. Decrease value by $200 million b. No change in value c. Increase value by $175 million d. Increase value by $300 million e. Increase value by $ 425 million

e. Increase value by $425 million. To estimate the value of the chemicals division as a continuing entity, first compute the return on capital: Return on capital = 50/1000 = 5% Reinvestment rate for a growth rate of 2% = 2%/5% = 40% Value of chemical business = 50 (1-.4)/(.10-.02) = $375 million Divestiture proceeds = $800 million Value effect = 800 - 375 = +425 million

The biggest enemy of good valuation is bias. To minimize bias in valuation, you should a. Read/review what other people think about the value of a company b. Meet with the management of the company c. Look at the market price d. Get paid more to do the valuation e. None of the above

e. None of the above. All of the actions will only add to the bias.

You have finished a discounted cash flow valuation of a company, discounting free cash flows to the firm at the cost of capital to arrive at a value of $ 2 billion. You have also valued individual assets on the company's balance sheet. Which of the following assets would you add to your estimated value to arrive at the value of the overall business? a. Goodwill of $500 million b. Brand name value of $ 300 million c. Value of property, plant & equipment (manufacturing facilities) of $ 600 million d. Value of real estate (headquarters building) of $200 million e. None of the above

e. None of the above. All of these assets contribute to generating the cash flows that you have discounted to arrive at your value of $ 2 billion. Adding them on to that value would be double counting.

Infrastructure companies often trade at low multiples of EV to EBITDA. Which of the following is the best explanation for this phenomenon? a. They pay little in taxes b. They have high earnings c. They have high growth d. They have high depreciation and amortization e. They have high net capital expenditures (difference between capital expenditures and depreciation)

e. They have high net capital expenditures. High depreciation, high earnings and lower taxes, by themselves, should push up your EV/EBITDA multiple. Having high net capital expenditures, holding growth constant, will lead to lower EV to EBITDA.

Carpe Inc. is a publicly traded company that is considering merging with Diem Inc., another publicly traded company in the same business, motivated by the potential for cost savings from business overlap. The combination is expected to save $30 million in after-tax operating cash flows (increasing operating income) next year, with a growth rate of 2% a year in perpetuity. The following table lists the costs of equity and capital for the two companies and the merged entity: Carpe Diem Carpe Diem (combined) Cost of equity 10.00% 12.00% 10.50% Cost of capital 9.00% 10.80% 9.60% What is the value of the cost savings synergy in this merger? a. $300.00 million b. $340.91 million c. $352.94 million d. $375.00 million e. $394.74 million f. $428.57 million

f. $394.74 million. It is the combined firm that gets these savings and since they are in operating income (not equity income), I would use the cost of capital of 9.6% for the combined firm: Value of synergy = 30/ (.096-.02) = $394.74 million

Valuation is a skill set that is necessary only for a. Investment bankers who may want to assess the value of acquisitions or IPOs b. Management consultants who want to provide good corporate finance advice c. CFOs who want to understand what drives the value of their businesses d. Investors who want to find cheap and expensive stocks e. Entrepreneurs who have to negotiate with buyers and VCs about the values of their businesses f. All of the above

f. All of the above. Everybody needs to have a grasp of valuation.