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Session 29: Post Class tests 1. In intrinsic valuation, you estimate the value of a business as a function of its fundamentals. One of those fundamentals is growth. Which of the following is the best description of the value of growth? a. Growth has no value b. Higher growth is always more valuable than lower growth c. Higher growth adds value only if it comes with negative excess returns d. Higher growth adds value only if comes with no excess returns e. Higher growth adds value only if it comes with positive excess returns 2. When valuing the equity in a business, which of the following do you try to do? a. Discount cash flows after debt payments and reinvestment needs at the cost of equity b. Discount cash flows after debt payments and reinvestment needs at the cost of capital c. Discount cash flows after reinvestment needs but before debt payments at the cost of equity d. Discount cash flows after reinvestment needs and before debt payments at the cost of capital 3. When valuing a business, which of the following do you try to do? a. Discount cash flows after debt payments and reinvestment needs at the cost of equity b. Discount cash flows after debt payments and reinvestment needs at the cost of capital c. Discount cash flows after reinvestment needs but before debt payments at the cost of equity d. Discount cash flows after reinvestment needs and before debt payments at the cost of capital 4. If you are valuing a business where you expect financial leverage to change over time, it is generally easier to value the business and net out debt to get to equity value than it is to value equity directly (by discounting equity cash flows at the cost of equity). Why? a. Because the cash flows to equity cannot be estimated when the debt ratio is changing b. Because the cash flows to the firm are unaffected by changing financial leverage c. Because the cost of capital is not affected by changing financial leverage d. Because the cost of equity is not affected by changing financial leverage 5. You notice that an analyst has valued a firm (business) using the expected growth rate in earnings per share as the growth rate in operating income. What effect will this have on value? a. The analyst will over estimate the value b. The analyst will under estimate the value c. The analyst will get the value wrong, though it is difficult to figure out in which direction. Session 29: Post class test solutions 1. a. Higher growth adds value only if it comes with positive excess returns. Growth creates a trade off where the higher earnings you obtain in the far future when you have high growth are offset fully or partially by the lower cash flows in the near future. That trade off works in your favor only if you generate a high return on capital, relative to your cost of capital 2. a. Discount cash flows after debt payments and reinvestment needs at the cost of equity. Cash flows after debt payments are cash flows to equity. Discounting those at the cost of equity will give you equity value 3. d. Discount cash flows after reinvestment needs and before debt payments at the cost of capital. The cash flow to the firm has to be pre-debt and the cost of capital is the weighted average cost across all your financing sources. 4. b. Because the cash flows to the firm are unaffected by changing financial leverage. You can estimate cash flows to equity when the debt ratio is changing, but it is a lot more work than changing your cost of capital (by changing your debt ratio). The cost of equity will change as your financial leverage changes. 5. a. The analyst will over estimate value. The growth in earnings per share will generally be higher than the growth in operating income, because it will be augmented both by financial leverage and reduction in share count (from buybacks). Session 30: Post Class tests 1. In the dividend discount model, you value the equity in a firm by discounting the expected dividends at the cost of equity. The model therefor cannot be used to value non-dividend paying stocks. a. True b. False 2. With FCFE models, you estimate potential dividends, by computing cash flows after debt payments and then discounting at the cost of equity. Assume that you value the same company using both the dividend discount and FCFE models, will you get the same value for equity? a. Yes b. No 3. Maxor Inc. is a manufacturing firm that generated $120 million in EBITDA in the most recent year. The tax rate was 30%, depreciation charges were $30 million and capital expenditures were $45 million for the year. If the non-cash working capital increased by $10 million during the year, estimate the free cash flow to the firm for the year. a. $ 8 million b. $38 million c. $58 million d. $66 million e. None of the above 4. In the FCFF model, what are you valuing when you take the present value of FCFF at the cost of capital? a. A value for the equity in the firm b. A value for assets in the firm c. A value for all assets whose earnings are shown as a part of operating income. d. A value for the assets in place for the firm e. None of the above. 5. When valuing a firm, you discount the FCFF at the cost of capital. Assume that the firm that you are valuing has an actual debt ratio of 10% and a target debt ratio of 40%, which it is planning to move to gradually over the next 10 years. What debt ratio should you use to compute the cost of capital for this firm? a. The actual debt ratio (10%) b. The target debt ratio (40%) c. An average of the actual and target debt ratios (25%) d. The expected debt ratio each year to get a cost of capital each year Session 30: Post class test solutions 1. b. False. Even if a firm is not paying dividends right now, you may expect it to start paying dividends in the future and you can value the stock based on expected future dividends. 2. b. No. When dividends are different from FCFE, there can be value effects from either under paying dividends or over paying dividends. For instance, if a firm pays less in dividends than FCFE and proceeds to waste the cash, the value of equity can be lower from the dividend discount model. 3. b. $38 million. EBIT = 120 - 30 = $90 million EBIT (1-t) + Depreciation - Cap Ex - Change in non-cash WC = 90 (1-.3) + 30- 45 -10 = $38 million 4. c. A value for all assets whose earnings are shown as a part of operating income. Since the FCFF builds off operating income, you value only those assets that are part of operating income. 5. d. The expected debt ratio each year to get a year-specific cost of capital. The cost of capital can and often should be different each year in a valuation. Session 31: Post Class tests 1. 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 2. 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 3. 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 non- cash 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 4. 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 5. 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 Session 31: Post class test solutions 1. 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%. 2. 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% 3. 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% 4. 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% 5. 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: Revenues Operating Margin Operating Income Reinvestment Invested Capital Return on capital Last year $100 -10% -$10.00 $50.00 -20% 1 $200 -5% -$10.00 $50.00 $100.00 -10% 2 $320 0% $0.00 $60.00 $160.00 0% 3 $450 5% $22.50 $65.00 $225.00 10% 4 $600 10% $60.00 $75.00 $300.00 20% Session 32: Post Class tests 1. 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 2. 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 3. 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 4. 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 5. 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 Session 32: Post class test solutions 1. 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. 2. 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 3. 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 4. 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. 5. 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 = 1- g/ ROE = 3%/15% = 80% Terminal value in year 3 = 133.39 (1-.20)/(.09-.03) = $1778.51 m Session 33: Post Class tests 1. 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 2. 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 3. 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 4. 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 5. 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. You 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 Session 33: Post class test solutions 1. 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.. 2. 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 3. 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 stand- alone entity but you don't have that information. 4. 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. 5. 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 Session 34: Post Class tests 1. 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 2. 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 3. 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? 4. 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% Session 34: Post class test solutions 1. 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 2. 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 3. 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 equity e. When the company earns a ROE