Corporate Finance: The Core (Berk/DeMarzo) Chapter 9 - Valuing Stocks 1) When discounting dividends you should use? A) the weighted average cost of capital. B) the after tax weighted average cost of capital. C) the equity cost of capital. D) the before tax cost of debt. Answer: C Explanation: A) B) C) D) Diff: 1 Topic: 9.1 Stock Prices, Returns, and the Investment Horizon Skill: Conceptual
2) Which of the following statements is false? A) The equity cost of capital for a stock is the expected return of other investments available in the market with equivalent risk to the firm’s shares. B) The price of a share of stock is equal to the present value of the expected future dividends it will pay. Div1 + P1 C) If the current stock price were less than P0 = , it would be a negative NPV investment, and we 1 + rE would expect investors to rush in and sell it, driving down the stocks price. D) The law of one price implies that to value any security, we must determine the expected cash flows an investor will receive from owning it. Answer: C Explanation: A) B) C) In this case the stock would be undervalued and we would expect investors to buy it. D) Diff: 2 Topic: 9.1 Stock Prices, Returns, and the Investment Horizon Skill: Conceptual
3) Which of the following statements is false? A) We must discount the cash flows from stock based on the equity cost of capital for the stock. B) The divided yield is the percentage return the investor expects to earn from the dividend paid by the stock. C) The firm might pay out cash to its shareholders in the form of a dividend. D) The dividend yield is the expected annual dividend of a stock, divided by its expected future sale price. Answer: D Explanation: A) B) C) D) The dividend yield is the annual dividend divided by the current price. Diff: 2 Topic: 9.1 Stock Prices, Returns, and the Investment Horizon Skill: Conceptual
4) Which of the following statements is false? A) Future dividend payments and stock prices are not known with certainty; rather these values are based on the investor’s expectations at the time the stock is purchased. B) The capital gain is the difference between the expected sale price and the purchase price of the stock. C) The sum of the dividend yield and the capital gain rate is called the total return of the stock. D) We divide the capital gain by the expected future stock price to calculate the capital gain rate. Answer: D Explanation: A) B) C) D) The capital gains rate is the capital gain divided by the current stock price. Diff: 2 Topic: 9.1 Stock Prices, Returns, and the Investment Horizon Skill: Conceptual
5) Which of the following statements is false? A) An investor will be willing to pay up to the point at which the current price of a share of stock equals the present value of the expected future dividends an expected future sale price. B) The expected total return of a stock should equal the expected return of other investments available in the market with equivalent risk. C) The total amount received in dividends and from selling the stock will depend on the investor’s investment horizon. Div1 + P1 D) If the current stock price were greater than P0 = , it would be a positive NPV investment, and 1 + rE we would expect investors to rush in and buy it, driving up the stocks price. Answer: D Explanation: A) B) C) D) It would be a negative NPV investment. Diff: 2 Topic: 9.1 Stock Prices, Returns, and the Investment Horizon Skill: Conceptual
6) Which of the following formulas is incorrect? P −P A) Capital Gains Rate = 0 1 P0 Div1 B) Dividend Yield = P0 Div1 Div2 + P2 C) + P0 = 1 + rE (1 + rE )2
D) rE = Capital Gains Rate + Dividend Yield Answer: A P −P Explanation: A) Capital Gains Rate = 1 0 P0 B) C) D) Diff: 2 Topic: 9.1 Stock Prices, Returns, and the Investment Horizon Skill: Conceptual
7) Which of the following formulas is incorrect? Div1 Div2 + P2 A) Div N P0 = + + ... + 2 1 + rE (1 + rE ) (1 + rE ) N B) P0 =
N
∑
n =1
Divn (1 + rE ) n
Div1 + P0 C) rE = P1 Div1 + P1 D) P0 = 1 + rE
Answer: C Explanation: A) B) Div1 + P1 C) rE = P0 D) Diff: 2 Topic: 9.1 Stock Prices, Returns, and the Investment Horizon Skill: Conceptual
Use the information for the question(s) below. Von Bora Corporation is expected pay a dividend of $1.40 per share at the end of this year and a $1.50 per share at the end of the second year. You expect Von Boraʹs stock price to be $25.00 at the end of two years. Von Boraʹs equity cost of capital is 10% WS1) The price you would be willing to pay today for a share of Von Bora stock, if you plan to hold the stock for two years is closest to: A) $23.15 B) $20.65 C) $21.95 D) $21.90 Answer: A Div1 Explanation: A) Div2 + P2 1.40 1.50 + 25.00 P0 = + = + = $23.17 2 1 + .10 1 + rE (1 + rE ) (1 + .10) 2 B) C) D) 8) Suppose you plan to hold Von Bora stock for one year. The price would would expect to be able to sell a share of Von Bora stock in one year is closest to: A) $26.50 B) $22.70 C) $23.15 D) $24.10 Answer: D Explanation: A) B) C) Div2 + P2 D) 1.50 + 25.00 P1 = = = $24.10 1 (1 + rE ) (1 + .10) 2 Diff: 2
Topic: 9.1 Stock Prices, Returns, and the Investment Horizon Skill: Analytical
9) Suppose you plan to hold Von Bora stock for only one year. Your capital gain from holding Von Bora stock for the first year is closest to: A) $0.95 B) $1.40 C) $1.85 D) $1.25 Answer: A Div2 + P2 Explanation: A) 1.50 + 25.00 = = $24.10 P1 = 1 (1 + .10) (1 + rE ) P0 =
Div1 Div2 + P2 1.40 1.50 + 25.00 + = + = $23.17 2 1 + .10 1 + rE (1 + .10) 2 (1 + rE )
Capital Gain = P1 - P0 = 24.10 - 23.17 = $0.93 B) C) D) Diff: 2 Topic: 9.1 Stock Prices, Returns, and the Investment Horizon Skill: Analytical
10) Suppose you plan to hold Von Bora stock for only one year. Your capital gain rate from holding Von Bora stock for the first year is closest to: A) 3.5% B) 4.0% C) 6.0% D) 4.5% Answer: B Explanation: A) Div2 + P2 B) 1.50 + 25.00 P1 = = = $24.10 1 (1 + .10) (1 + rE ) P0 =
Div1 Div2 + P2 1.40 1.50 + 25.00 + = + = $23.17 2 1 + .10 1 + rE (1 + .10) 2 (1 + rE )
Capital Gain = P1 - P0 = 24.10 - 23.17 = $0.93 Capital Gain rate = capital gain/ P0 = 0.93 / 23.17 = .0401 or 4.0% C) D) Diff: 2 Topic: 9.1 Stock Prices, Returns, and the Investment Horizon Skill: Analytical
11) Suppose you plan to hold Von Bora stock for only one year. Your dividend yield from holding Von Bora stock for the first year is closest to: A) 6.0% B) 4.0% C) 6.5% D) 5.5% Answer: A
Div1 Explanation: A) Div2 + P2 1.40 1.50 + 25.00 + = + = $23.17 P0 = 2 1 + .10 1 + rE (1 + .10) 2 (1 + rE )
Dividend yield = Div1 / P0 = $1.40 / 23.17 = .0604 or 6.0% B) C) D) Diff: 2 Topic: 9.1 Stock Prices, Returns, and the Investment Horizon Skill: Analytical
WS2) Suppose you plan on purchasing Von Bora stock in one year, right after the $1.40 dividend is paid. You then plan on selling your stock at the end of year two, right after the $1.50 dividend is paid. The capital gain rate that you will receive on your investment is closest to: A) 4.00% B) 3.75% C) 6.25% D) 3.50% Answer: B Explanation: A) Div2 + P2 B) 1.50 + 25.00 P1 = = = = $24.10 1 (1 + .10) (1 + rE ) So capital gain rate = (P2 - P1) / P1 = ($25.00 - $24.10) / $24.10 = .03734 or 3.73% C) D) Diff: 3 Topic: 9.1 Stock Prices, Returns, and the Investment Horizon Skill: Analytical
12) Suppose you plan on purchasing Von Bora stock in one year, right after the $1.40 dividend is paid. You then plan on selling your stock at the end of year two, right after the $1.50 dividend is paid. The dividend yield that you will receive on your investment is closest to: A) 5.75% B) 6.50% C) 6.25% D) 4.00% Answer: C Explanation: A) B) Div2 + P2 C) 1.50 + 25.00 P1 = = = $24.10 1 (1 + .10) (1 + rE ) So dividend yield = $1.50 / $24.10 = .0622 or 6.22% D) Diff: 3 Topic: 9.1 Stock Prices, Returns, and the Investment Horizon Skill: Analytical
13) Suppose you plan on purchasing Von Bora stock in one year, right after the $1.40 dividend is paid. You then plan on selling your stock at the end of year two, right after the $1.50 dividend is paid. The total return that you will receive on your investment is closest to: A) 9.50% B) 10.75% C) 10.25% D) 10.00% Answer: D Explanation: A) B) C) Div2 + P2 D) 1.50 + 25.00 P1 = = = $24.10 1 (1 + .10) (1 + rE ) So dividend yield = $1.50 / $24.10 = .0622 or 6.22% So capital gain rate = (P2 - P1) / P1 = ($25.00 - $24.10) / $24.10 = .03734 or 3.73% Total return = capital gains rate + dividend yield = 3.73% + 6.22% = 9.95% Diff: 3 Topic: 9.1 Stock Prices, Returns, and the Investment Horizon Skill: Analytical
WS3) Suppose you plan to hold Von Bora stock for only one year. Calculate your total return from holding Von Bora stock for the first year. Div2 + P2 Answer: 1.50 + 25.00 P1 = = = $24.10 1 (1 + .10) (1 + rE ) P0 =
Div1 Div2 + P2 1.40 1.50 + 25.00 + = + = $23.17 2 1 + .10 1 + rE (1 + rE ) (1 + .10) 2
Capital Gain = P1 - P0 = 24.10 - 23.17 = $0.93 Capital Gain rate = capital gain / P0 = 0.93 / 23.17 = .0401 or 4.0% Dividend yield = Div1 / P0 = $1.40 / 23.17 = .0604 or 6.0% Total return = capital gain rate + dividend yield = 4.0% + 6.0% = 10% Diff: 3 Topic: 9.1 Stock Prices, Returns, and the Investment Horizon Skill: Analytical
9.2 The Dividend-Discount Model 14) Which of the following formulas is incorrect? earningst A) Divt = × Dividend Payout Rate shares outstandingt DivN B) PN = rE − g
C) earnings growth rate = retention rate x return on new investment DivN DivN +1 Div1 Div2 D) 1 P0 = + + ... + + × N N 2 1 + rE rE − g (1 + rE ) (1 + rE ) (1 + rE ) Answer: B Explanation: A) DivN +1 B) PN = rE − g C) D) Diff: 2 Topic: 9.2 The Dividend-Discount Model Skill: Conceptual
15) JRN enterprises just announced that it plans to cut its dividend from $2.50 to $1.50 per share and use the extra funds to expand its operations. Prior to this announcement, JRNʹs dividends were expected to grow at 4% per year and JRNʹs stock was trading at $25.00 per share. With the new expansion, JRNʹs dividends are expected to grow at 8% per year indefinitely. Assuming that JRNʹs risk is unchanged by the expansion, the value of a share of JRN after the announcement is closest to: A) $25.00 B) $15.00 C) $31.25 D) $27.50 Answer: A Explanation: A) Two steps. Step #1 solve for rE, rE = Div1 / P0 + g = 2.50 / 25.00 + .04 = .14 or 14% Step #2 solve for new stock price: P0 = Div1 / (rE - g) = 1.50 / (.14 - .08) = 25.00 B) C) D) 16) You expect that Bean Enterprises will have earnings per share of $2 for the coming year. Bean plans to retain all of its earnings for the next three years. For the subsequent two years, the firm plans on retaining 50% of its earnings. It will then retain only 25% of its earnings from that point forward. Retained earnings will be invested in projects with an expected return of 20% per year. If Beanʹs equity cost of capital is 12%, then the price of a share of Beanʹs stock is closest to: A) $17.00 B) $10.75 C) $27.75 D) $43.50 Answer: C
Explanation: A) B) C) Year 1 2 3 4 5 6
Earnings Dividends $2.00 $0.00 $2.40 $0.00 $2.88 $0.00 $3.46 $1.73 $3.80 $1.90 $4.18 $3.14
g 20% 20% 20% 10% 10% 5%
P0 = 1.73 / (1.12)4 + 1.90 / 1.125 + (3.14 / (.12 - .05)) / 1.125 = 27.63 Each g is calculated as the 20% return on the projects × the retention ratio. D) Diff: 3 Topic: 9.2 The Dividend-Discount Model Skill: Analytical
17) MJ LTD is expected to grow at various rates over the next five years. The company just paid a $1.00 dividend. The company expects to grow at 20% for the next two years (effecting D1 and D2), then the company expects to grow at 10% for three additional years (D3, D4, D5) after which the company expects to grow at a constant rate of 5% per year indefinitely. If the required rate of return on MJʹs common stock is 12%, then what is a share of MJʹs stock worth? Answer: Time Period 1 2 3 4 5 6
Dividend $1.00(1.20) $1.00(1.20)2
Present Value $1.00(1.20) / (1.12) = 1.071 $1.00(1.20)2 / (1.12)2 = 1.148
$1.00(1.20)2(1.10)1 $1.00(1.20)2(1.10)2
$1.00(1.20)2(1.10) / (1.12)3 = 1.127 $1.00(1.20)2(1.10)2 / (1.12)4 = 1.107
$1.00(1.20)2(1.10)3 $1.00(1.20)2(1.10)3(1.05)
$1.00(1.20)2(1.10)3 / (1.12)5 = 1.088 $1.00(1.20)2(1.10)3(1.05) / [(.12-.05)(1.12)5] = 16.313
Current Value of Share = 1.071 + 1.148 + 1.127 + 1.107 + 1.088 + 16.313 = $21.85 Diff: 3 Topic: 9.2 The Dividend-Discount Model Skill: Analytical
18) Growing Real Fast Company (GRF) is expected to have a 25 percent growth rate for the next four years (effecting D1, D2, D3, and D4). Beginning in year five, the growth rate is expected to drop to 7 percent per year and last indefinitely. If GRF just paid a $2.00 dividend and the appropriate discount rate is 15 percent, then what is the value of a share of GRE? Answer: Time Period Dividend Present Value 1 1 $2.50(1.25) $2.00(1.25) / (1.15) = 2.174 2 $2.00(1.25)2 $2.00(1.25)2 / (1.15)2 = 2.363 3 3 $2.00(1.25) $2.00(1.25)3 / (1.15)3 = 2.568 4 $2.00(1.25)4 $2.00(1.25)4 / (1.15)4 = 2.792 4 5 $2.00(1.25) (1.07) $2.00(1.25)4(1.07) / [(.15-.07)(1.15)4 ] = 37.34
Current Value of Share = 2.174 + 2.363 + 2.568 + 2.792 + 37.34 = $47.24 Diff: 3 Topic: 9.2 The Dividend-Discount Model Skill: Analytical
9.3 Total Payout and Free Cash Flow Valuation Models 19) Which of the following equations is incorrect? V0 + Debt - Cash A) P0 = Shares Outstanding FCFN VN FCF1 FCF2 B) + + ... + + V0 = 2 N 1 + rwacc (1 + rwacc ) (1 + rwacc ) (1 + rwacc ) N
C) Free Cash Flow = EBIT × (1 - τc) + Depreciation - Capital Expenditures - DNWC D) Enterprise Value = Market Value of Equity + Debt - Cash Answer: A V + Debt - Cash Explanation: A) P0 = 0 Shares Outstanding B) C) D) Diff: 2 Topic: 9.3 Total Payout and Free Cash Flow Valuation Models Skill: Conceptual
20) The Rufus Corporation has 125 million shares outstanding and analysts expect Rufus to have earnings of $500 million this year. Rufus plans to pay out 40% of its earnings in dividends and they expect to use another 20% of their earnings to repurchase shares. If Rufusʹ equity cost of capital is 15% and Rufusʹ earnings are expected to grow at a rate of 3% per year, then the value of a share of Rufus stock is closest to: A) $13.35 B) $33.50 C) $20.00 D) $16.00 Answer: C Explanation: A) B) C) Dividends = $500 × .40 = $200 million Repurchases = $500 × .20 = $100 million PV(Future Total Dividends and Repurchases) = ($200 + $100) / (.15 - .03) = $2,500 million P0 = $2,500 million/125 million shares = $20 per share D) Diff: 2 Topic: 9.3 Total Payout and Free Cash Flow Valuation Models Skill: Analytical
Use the information for the question(s) below. You expect CCM Corporation to generate the following free cash flows over the next five years: Year FCF ($ millions)
1 25
2 28
3 32
4 37
5 40
Following year five, you estimate that CCMʹs free cash flows will grow at 5% per year and that CCMʹs weighted average cost of capital is 13%. 21) The enterprise value of CCM corporation is closest to: A) $396 million B) $290 million C) $382 million D) $350 million Answer: A FCFN VN FCF1 FCF2 Explanation: A) V0 = + + ... + + 2 N 1 + rwacc (1 + rwacc ) (1 + rwacc ) (1 + rwacc ) N 40 25 28 32 37 V0 = + + + + .13 − .05 = 395.58 million 1 + .13 (1 + .13) 2 (1 + .13)3 (1 + .13) 4 (1 + .13) 4
B) C) D) Diff: 2 Topic: 9.3 Total Payout and Free Cash Flow Valuation Models Skill: Analytical
22) If CCM has $150 million of debt and 12 million shares of stock outstanding, then the share price for CCM is closest to: A) $49.50 B) $11.25 C) $20.50 D) $22.75 Answer: C Explanation: A) B) FCFN VN FCF1 FCF2 C) V0 = + + ... + + 2 N 1 + rwacc (1 + rwacc ) (1 + rwacc ) (1 + rwacc ) N 40 25 28 32 37 .13 − .05 = 395.58 million or 396 million. + + + V0 = + 2 3 4 1 + .13 (1 + .13) (1 + .13) (1 + .13) (1 + .13) 4
Equity value = $396 - $150 (debt) = $246 million / 12 million shares = $20.50 D) Diff: 2 Topic: 9.3 Total Payout and Free Cash Flow Valuation Models Skill: Analytical
Use the information for the question(s) below. You expect DM Corporation to generate the following free cash flows over the next five years: Year FCF ($ millions)
1 75
2 84
3 96
4 111
5 120
Beginning with year six, you estimate that DMʹs free cash flows will grow at 6% per year and that DMʹs weighted average cost of capital is 15%.
23) If DM has $500 million of debt and 14 million shares of stock outstanding, then what is the price per share for DM Corporation? a) 37.00 b) 38.00 c) 39.00 d) 40.00 FCFN VN FCF1 FCF2 Answer: V0 = + + ... + + 2 N 1 + rwacc (1 + rwacc ) (1 + rwacc ) (1 + rwacc ) N 120 75 84 96 111 120 .15 − .06 = 1017.66 million or $1018 V0 = + + + + + 2 3 4 5 1 + .15 (1 + .15) (1 + .15) (1 + .15) (1 + .15) (1 + .15)5
million Equity value = $1018 - $500 (debt) = $518 million/14 million shares = $37.00 Diff: 3 Topic: 9.3 Total Payout and Free Cash Flow Valuation Models Skill: Analytical
9.4 Valuation Based on Comparable Firms 24) Which of the following statements is false? A) The fact that a firm has an exceptional management team, has developed an efficient manufacturing process, or has just secured a patient on a new technology is ignored when we apply a valuation multiple. B) Valuation multiples have the advantage that they allow us to incorporate specific information about the firm’s cost of capital or future growth. C) For firms with substantial tangible assets, the ratio of price to book value of equity per share is sometimes used. D) Using multiples will not help us determine if an entire industry is overvalued. Answer: B Explanation: A) B) Discounted cash flows methods have the advantage that they allow us to incorporate specific information about the firmʹs cost of capital or future growth. C) D)
Diff: 3 Topic: 9.4 Valuation Based on Comparable Firms Skill: Conceptual
Use the information for the question(s) below. Suppose that Texas Trucking (TT) has earnings per share of $3.45 and EBITDA of $45 million. TT also has 5 million shares outstanding and debt o $150 million (net of cash). You believe that Oklahoma Logistics and Transport (OLT) is comparable to TT in terms of its underlying business, but OLT has no debt. OLT has a P/E of 12.5 and an enterprise value to EBITDA multiple of 7. 25) Based upon the price earnings multiple, the value of a share of Texas Trucking is closest to: A) $49.30 B) $43.10 C) $24.15 D) $27.60 Answer: B Explanation: A) B) Price = forward earnings × P / E = 3.45 × 12.5 = 43.12 C) D) Diff: 2 Topic: 9.4 Valuation Based on Comparable Firms Skill: Analytical
ased upon the enterprise value to EBITDA ratio, the value of a share of Texas Trucking is closest to: B 1 1 ) A) $33.00 B) $82.50 C) $43.10 D) $21.25 Answer: A Explanation: A) Enterprise value = EBITDA × multiple = $45 × 7 = $315 - $150 debt = $165 equity value / 5 million shares = $33.00 per share B) C) D) Diff: 2 Topic: 9.4 Valuation Based on Comparable Firms Skill: Analytical
