Homework #7

Phoenix Industries has pulled off a miraculous recovery. Four years ago it was near bankruptcy. Today, it announced a $2 per share dividend to be paid a year from now, the first dividend since the crisis. Analysts expect dividends to increase by $1 a year for another 2 years. After the third year (in which dividends are $4 per share) dividend growth is expected to settle down to a more moderate long-term growth rate of 5%. If the firm's investors expect to earn a return of 17% on this stock, what must be its price? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Explanation Some values below may show as rounded for display purposes, though unrounded numbers should be used for actual calculations. DIV1 = $2 DIV2 = $3 DIV3 = $4 g = 0.05 P3 = ($4 × 1.05) / (0.17 − 0.05) = $35.00 P0=$2/1.17 +$3/(1.17)^2 +$4 + $35.00/(1.17)^3 =$28.25

BMM Industries pays a dividend of $1.10 per quarter. The dividend yield on its stock is reported at 3.90%. What is the stock price? (Round your answer to 2 decimal places.)

Explanation Some values below may show as rounded for display purposes, though unrounded numbers should be used for actual calculations. Dividend yield=Next annual dividend / Stock price =DIV1 / P0 0.039=($1.10 × 4) / P0 P0=$112.82

Favorita Candy's stock is expected to earn $4.40 per share this year. Its P/E ratio is 22. What is the stock price? (Round your answer to 2 decimal places.)

Explanation Some values below may show as rounded for display purposes, though unrounded numbers should be used for actual calculations. P/E ratio=Price / Earnings per share 22.0=P0 / $4.40 P0=$96.80

Steady As She Goes Inc. will pay a year-end dividend of $2.60 per share. Investors expect the dividend to grow at a rate of 6% indefinitely. a. If the stock currently sells for $26.00 per share, what is the expected rate of return on the stock? (Do not round intermediate calculations. Enter your answer as a whole percent.) b. If the expected rate of return on the stock is 18.50%, what is the stock price? (Do not round intermediate calculations. Enter your answers rounded to 2 decimal places.)

Explanation Some values below may show as rounded for display purposes, though unrounded numbers should be used for actual calculations. a. P0=DIV1 / (r − g) $26=$2.60 / (r − 0.06) r=0.16, or 16% b. P0=DIV1 / (r − g) =$2.60 / (0.185 − 0.06) =$20.80

Arts and Crafts, Inc. will pay a dividend of $7 per share in 1 year. It sells at $70 a share, and firms in the same industry provide an expected rate of return of 14%. What must be the expected growth rate of the company's dividends? (Do not round intermediate calculations. Enter your answer as a whole percent.)

Explanation Some values below may show as rounded for display purposes, though unrounded numbers should be used for the actual calculations. P0 = DIV1 / (r − g) This formula can be rearranged to: r = DIV1 / P0 + g This states that the total rate of return is equal to the dividend yield plus the capital gains yield. You will find it useful to know both versions of this equation. r=DIV1 / P0 + g 0.14=$7 / $70 + g g=0.04, or 4%

You believe that the Non-Stick Gum Factory will pay a dividend of $5 on its common stock next year. Thereafter, you expect dividends to grow at a rate of 5% a year in perpetuity. If you require a return of 17% on your investment, how much should you be prepared to pay for the stock? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Explanation Some values below may show as rounded for display purposes, though unrounded numbers should be used for the actual calculations. P0=DIV1 / (r - g) =$5 / (0.17 - 0.05) =$41.67

Integrated Potato Chips just paid a $1.1 per share dividend. You expect the dividend to grow steadily at a rate of 5% per year. a. What is the expected dividend in each of the next 3 years? b. If the discount rate for the stock is 11%, at what price will the stock sell today? c. What is the expected stock price 3 years from now? d. If you buy the stock and plan to sell it 3 years from now, what are your expected cash flows in (i) year 1; (ii) year 2; (iii) year 3? e. What is the present value of the stream of payments you found in part (d)?

Explanation Some values below may show as rounded for display purposes, though unrounded numbers should be used for the actual calculations. a. DIV1=DIV0 × (1 + g) =$1.10 × 1.05 =$1.16 DIV2=DIV0 × (1 + g)2 =$$1.10 × 1.052 =$1.21 DIV2=DIV0 × (1 + g)3 =$1.10 × 1.053 =$1.27 b. To calculate P0, you must use DIV1 as the dividend must be one year ahead of the price: P0=DIV1 / (r - g) =($1.10 × 1.05) / (0.11 - 0.05) =$19.25 c. To calculate P3, you must use DIV4 as the dividend must be one year ahead of the price: P3=DIV4 / (r - g) =($1.10 × 1.054) / (0.11 - 0.05) =$22.28 d. Your payments will be the sum of dividends plus the sales price (in year 3): Year 1 DIV$1.16 Year 2 $1.21 Year 3 $1.27 Selling price $22.28 Total cash flow $1.16 $1.21 $23.56 e. Now we discount the cash flows using a discount rate of 11% Year 1 PV of cash flow $1.16 1.11 $1.04 Year 2 $1.21 1.11^2 $0.98 Year 3 $23.56 1.11^3 $17.23 Sum of PV = $19.25, the same as the answer to part (b).

No-Growth Industries pays out all of its earnings as dividends. It will pay its next $3 per share dividend in a year. The discount rate is 16%. a. What is the price-earnings ratio of the company? (Do not round intermediate calculations. Round your answer to 2 decimal places.) b. What would the P/E ratio be if the discount rate were 10%? (Round your answer to 2 decimal places.)

Explanation Some values below may show as rounded for display purposes, though unrounded numbers should be used for the actual calculations. a. Earnings = DIV1 = $3 Growth rate = g = 0 P0 =$3/0.16 − 0 = $18.75 P/E = $18.75 / $3 = 6.25 b. If r = 0.10 ⇒⇒ P0 =$3 /0.10 = $30 ⇒⇒ P/E increases to $30 / $3 = 10

You expect a share of stock to pay dividends of $1.70, $1.95, and $2.20 in each of the next 3 years. You believe the stock will sell for $29.00 at the end of the third year. a. What is the stock price if the discount rate for the stock is 20%? (Do not round intermediate calculations. Round your answer to 2 decimal places.) b. What is the dividend yield for year 1? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.) c. What will be the dividend yield at the start of year 2? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

Explanation Some values below may show as rounded for display purposes, though unrounded numbers should be used for the actual calculations. a. P0=DIV1 / (1 + r) + DIV2 / (1 + r)2 + (DIV3 + P3) / (1 + r)3 =$1.70 / 1.20 + $1.95 / 1.202 + ($2.20 + 29) / 1.203 =$20.83 Calculator computations: CF0 = $0 CO1 = $1.70, FO1 = 1 CO2 = $1.95, FO2 = 1 CO3 = $31.20, FO3 = 1 I = 10% NPV CPT = $20.83 b. Dividend yield=DIV1 / P0 =$1.70 / $20.83 =0.0816, or 8.16% C. P1=$1.95 / 1.20 + ($2.20 + $29) / 1.202 =$23.29 DIV2 / P1=$1.95 / $23.29 = 0.0837 =8.37%

Gentleman Gym just paid its annual dividend of $3 per share, and it is widely expected that the dividend will increase by 5% per year indefinitely. a. What price should the stock sell at if the discount rate is 12%. (Do not round intermediate calculations. Round your answer to 2 decimal places.) b. What price should the stock sell at if the discount rate is 10%. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Explanation Some values below may show as rounded for display purposes, though unrounded numbers should be used for the actual calculations. a. P0=DIV1 / (r − g) =[DIV0 × (1 + g)] / (r − g) =($3 × 1.05) / (0.12 − 0.05) =$45.00 b. P0=DIV1 / (r − g) =[DIV0 × (1 + g)] / (r − g) =($3 × 1.05) / (0.10 − 0.05) =$63.00

Trend-Line Inc. has been growing at a rate of 8% per year and is expected to continue to do so indefinitely. The next dividend is expected to be $3 per share. a. If the market expects a 10% rate of return on Trend-Line, at what price must it be selling? (Do not round intermediate calculations.) b. If Trend-Line's earnings per share will be $10 next year, what part of its value is due to assets in place? (Do not round intermediate calculations.) c. If Trend-Line's earnings per share will be $10 next year, what part of its value is due to growth opportunities? (Do not round intermediate calculations.)

Explanation Some values below may show as rounded for display purposes, though unrounded numbers should be used for the actual calculations. a. P0=DIV1 / (r − g) =$3 / (0.10 − 0.08) =$150 b. If Trend-Line followed a zero-plowback strategy, it could pay a perpetual dividend of $10. Its value would be: P=DIV / r =$10 / 0.10 =$100 c. The remainder of its value must be due to growth opportunities, so: PVGO=$150 - 100 =$50

Fincorp will pay a year-end dividend of $3.90 per share, which is expected to grow at a rate of 2% for the indefinite future. The discount rate is 12%. a. What is the stock selling for? (Do not round intermediate calculations. Round your answer to 2 decimal places.) b. If earnings are $4.20 a share, what is the implied value of the firm's growth opportunities? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Explanation Some values below may show as rounded for display purposes, though unrounded numbers should be used for the actual calculations. a. P0=DIV1 / (r − g) =$3.90 / (0.12 − 0.02) =$39.00 b. No-growth value = E / r = $4.20 / 0.12 = $35.00 PVGO = P0 − No-growth value = $39 − 35.00 = $4.00

Castles in the Sand generates a rate of return of 20% on its investments and maintains a plowback ratio of 0.30. Its earnings this year will be $5 per share. Investors expect a rate of return of 15% on the stock. a. Find the price and P/E ratio of the firm. (Do not round intermediate calculations. Round your answers to 2 decimal places.) b. Find the price and P/E ratio of the firm if the plowback ratio is reduced to 0.20. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Explanation Some values below may show as rounded for display purposes, though unrounded numbers should be used for the actual calculations. a. g = 20% × 0.30 = 6% P0 = $5(1 − 0.30) / (0.15 − 0.060) = $38.89 P/E = $38.89 / $5 = 7.78 b. g = 20% × 0.20 = 4% P0 = $5(1 − 0.20) / (0.15 − 0.04) = $36.36 P/E = $36.36 / $5 = 7.27 P/E falls because the firm's value of growth opportunities is now lower: It takes less advantage of its attractive investment opportunities.

Web Cites Research projects a rate of return of 20% on new projects. Management plans to plow back 20% of all earnings into the firm. Earnings this year will be $6 per share, and investors expect a rate of return of 12% on stocks facing the same risks as Web Cites. a. What is the sustainable growth rate? b. What is the stock price? c. What is the present value of growth opportunities (PVGO)? d. What is the P/E ratio? e. What would the price and P/E ratio be if the firm paid out all earnings as dividends? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Explanation Some values below may show as rounded for display purposes, though unrounded numbers should be used for the actual calculations. a.g = ROE × Plowback ratio = 20% × 0.20 = 4.00% b. EPS = $6, r = 0.12 P0 =$6 × (1 − 0.20)/ 0.12 − 0.04 =$60.00 c. No-growth value = EPS / r = $6 / 0.12 = $50.00 PVGO = P0 − No-growth value = $60 − $50 = $10.00 d. P/E = $60 / $6 = 10.00 e. If all earnings were paid as dividends, price would equal the no-growth value ($50) and P/E would be $50 / $6 = 8.33.

A stock sells for $50. The next dividend will be $5 per share. If the rate of return earned on reinvested funds is a constant 15% and the company reinvests a constant 20% of earnings in the firm, what must be the discount rate? (Do not round your intermediate calculations. Enter your answer as a whole percent.)

Explanation Some values below may show as rounded for display purposes, though unrounded numbers should be used for the actual calculations. g=Return on equity × Plowback ratio =0.15 × 0.20 =0.03, or 3% r=DIV1 / P0 + g =$5 / $50 + 0.03 =0.13, or 13 %