Business Finance Assignment: Insights from Chapter 4

Assignment 3 Ch4 Question 1 0 / 8.33 points Universal Air forecasts growth of 8% for the next six years and 4% thereafter. Given last year's free cash flow was $10 million, what is its horizon value if the company's cost of capital is 12%? Following the textbook assumption, we have the horizon time defined as the year prior to settling down to the long run trend. Thus the horizon time is year 5. $0 $267.60 million $167.20 million $198.36 million. Hide Feedback Horizon Value at the end of year 5 = Free cash flow at the end of year 6 (FCF6)/(r-g2) FCF6 = FCF0 x (1+g1)6 where g1 is the growth rate up to year 6 and g2 is the growth rate beyond year 6. Question 2 0 / 8.33 points Continued from the above, what is the value of Universal Air company? $121.01 million 1/10 $318.48 million $149.51 million $200.00 million Hide Feedback By formula: FCF1/(1+r) + FCF2/(1+r)2 + FCF3/(1+r)3 + FCF4/(1+r)4 + (FCF5+H5)/(1+r)5 where FCF1 = FCF0 x (1+g1) FCF2 = FCF1 x (1+g1) = FCF0 x (1+g1)2 FCF3 = FCF2 x (1+g1) = FCF0 x (1+g1)3 FCF4 = FCF3 x (1+g1) = FCF0 x (1+g1)4 FCF5 = FCF4 x (1+g1) = FCF0 x (1+g1)5 H5 = FCF6/(r-g2) FCF6 = FCF5 x (1+g1) = FCF0 x (1+g1)6 g1 = the growth rate up to year 6, g2 = the growth rate beyond year 6 By Financial Calculator TIBAII Plus (Professional): C0 = 0 C01 = FCF1; F01 = 1 C02 = FCF2; F02 = 1 C03 = FCF3; F03 = 1 C04 = FCF4; F04 = 1 C05 = FCF5 + Horizon Value at year 5 (= FCF6/(r-g2)) I = 12% CPT NPV 2/10 By Excel: =NPV(rate,FCF1,FCF2,FCF3,FCF4,FCF5+H5) Question 3 0 / 8.33 points CK Company stockholders expect to receive a year-end dividend of $5 per share and then immediately sell their shares for $115 dollars per share. If the required rate of return for the stock is 20%, what is the current value of the stock? $100 $122 $132 $110 Hide Feedback We have DIV1, P1 and r. We can solve for the price in various ways. I. By Formula II. By Financial Calculator (1) By Cashflow worksheet function built in the financial calculator: C0 = 0, C01 = DIV1+P1, F01 =1, I=r, CPT NPV (2) By built-in TVM function in the financial calculator: N=1, I/Y=r, PMT=0, FV=DIV1+P1, CPT PV III. By Excel (1) NPV function: =NPV(rate,value1) = NPV(r,DIV 1+P1) (2) PV function; =PV(rate,nper,pmt,fv,[type])=PV(r,1,0,DIV1+P1) 3/10 Question 4 0 / 8.33 points Frieda Co. just paid a dividend of $3 per share out of earnings of $5 per share. If the book value per share is $40, what is the expected growth rate in dividends (g)? 5.0% 4.0% 7.5% 3.5% Hide Feedback We have g = Increase in equity/EquityBOP = Retained Earnings/ EquityBOP = Plowback rate (or Retention Rate) x Earnings/EquityBOP = Plowback rate x ROE We also know that Dividends/Earnings + Retained Earnings/Earnings = Dividend Payout Ratio + Plowback Rate = 1, that is, Plowback Ratio = 1 - Dividend Payout Ratio From the problem, we have D1 per share =$3 and Earnings Per Share (EPS) = $5, thus, dividend payout ratio and Plowback ratio can be easily obtained. We also have book value per share (BVPS) = $40, so we can obtain ROE = EPS/BVPS = Finally, g = Plowback ratio x ROE. Question 5 0 / 8.35 points Truce Company has a P/E ratio of 15 and a stock price of $60 per share. Calculate earnings per share of the company. 4/10 $4 per share $9 per share $0.25 per share $15 per share Hide Feedback P/E = Price Per Share/Earnings Per Share; EPS = Price Per Share/(P/E) Question 6 0 / 8.33 points Deluxe Company expects to pay a dividend of $2 per share at the end of year 1, $3 per share at the end of year 2, and then be sold for $32 per share at the end of year 2. If the required rate of return on the stock is 15%, what is the current value of the stock? $28.20 $32.00 $32.17 $29.18 Hide Feedback We can solve the value in 3 different ways: We have DIV1, DIV2, P2 and r. I. By Formula: We can apply the formula: P0 = $2/(1+15%) + $3/(1+15%)2 +$32/(1+15%)2 = $28.20. II. Financial Calculator - Cashflow Worksheet Function 5/10 We can use the cashflow worksheet function built in the financial calculator: C0 = 0, C01 = DIV1, F01= 1, C02 = DIV2+P2, F02 = 1, I = r, CPT NPV III. Excel - Built-in NPV function =NPV(rate,DIV1, DIV2+P2) Question 7 0 / 8.33 points The Amgen Biotec Co. just paid a dividend of $1 per share (Be careful, the word "just paid" makes the dividend of $1 a current dividend D0, not D1.). Analysts expect its dividend to grow at 25% per year for the next three years and then 5% per year thereafter. If the required rate of return on the stock is 18%, what is the current value of the stock? $15.20 $11.93 $12.97 $15.78 Hide Feedback This is a non-constant dividend growth. We apply the formula There are two different dividend growth rates. The first stage is up to year 3 (let's label the growth rate with stage 1 as g1), and the second stage is after year 3 (let's label the growth rate with stage 2 as g2). Both g1 and g2 are given in the problem. (1) Calculate P3: Since the dividend starts growing at the constant rate forever after year 3, so we set the horizon time as the end of year 3, and compute the PV of all expected future dividends looking forward from year 3 by the constant dividend growth formula: P3 = DIV4/(r-g2), where r and g2 are given directly in the problem, and we obtain DIV4 = DIV3 x (1+g2). We have: DIV1 = DIV0 x (1+g1) 6/10 DIV2 = DIV1 x (1+g1) = DIV0 x (1+g1) x (1+g1) = DIV0 x (1+g1)2 DIV3 = DIV2 x (1+g1) = DIV0 x (1+g1)2 x (1+g1) = DIV0 x (1+g1)3 DIV4 = DIV3 x (1+g2) = DIV0 x (1+g1)3 x (1+g2) DIV0, g1, and g2 are given in the problem. (2) Calculate P0: (I) By formula: P0 = DIV1/(1+r) + DIV2/(1+r)2 + DIV3/(1+r)3 + P3/(1+r)3. Note that r is given in the problem. (II) By cash flow worksheet function in your financial calculator: C0=0, C01=DIV1, F01=1, C02=DIV2, F02=1, C03=(DIV3+P3), I=r, CPT NPV (II) By Excel NPV function: =NPV(rate,value 1, value 2, ....) =NPV(r,DIV1,DIV2,DIV3+P3) Question 8 0 / 8.33 points Reliable Electric Corporation expects to pay a dividend of $6 per share next year, and the dividend payout ratio is 80%. If dividends are expected to grow at a constant rate of 6% forever, and the required rate of return on the stock is 15%, calculate the present value of growth opportunities (PVGO). $41.67 $16.67 $34.67 $26.67 Hide Feedback We have the formula: PVGO = P0 - EPS1/r To apply the formula, we need to have P0, EPS1 and r. We have r given in the problem. We have to calculate P0 and EPS1 using the information provided by the problem. 7/10 (1) Obtain P0: Since the dividend is growing at the constant rate g forever, we can obtain P0 by applying the formula: P0 = D1/(r-g) where D1, r, and g are given in the problem (2) Obtain EPS1: We have the formula :EPS1 = D1/(1- Plowback Ratio (i.e., Retention Ratio)) = D 1/Dividend Payout Ratio where D1 and Dividend Payout Ratio are given in the problem. Finally, we can then calculate PVGO by the formula: PVGO = P 0 - EPS1/r. Question 9 0 / 8.35 points Assume Generous Motors has about 5.8 billion shares outstanding and the stock price is $45. Also, assume the P/E ratio is about 25. Calculate the approximate market capitalization for GE. $285 billion $261 billion $104 billion $145 billion Hide Feedback Market capitalization = number of shares outstanding × share price Question 10 0 / 8.33 points J&J Co. just paid a dividend of $2 per share out of earnings of $4 per share. If the book value per share is $25, and its market price is $21.60 per share, calculate the required rate of return on the stock. 17.26% 16.64% 18.00% 8/10 8.00% Hide Feedback g = ROE × plowback ratio ROE = Earnings/Book Value Per Share Dividend Payout ratio = Dividend/Earnings Plowback ratio = 1 - Dividend Payout Ratio r = (D1/P0 ) + g = (D0 × (1 + g))/ P0 + g where g is just calculated Question 11 0 / 8.33 points Which of the following is TRUE? The constant dividend growth formula P0 = Div1/(r - g) assumes g is never negative. One can estimate the sustainable dividend growth rate for a stable firm as: plow-back rate/the return on equity (ROE). By EPS1/P0 = r x(1-PVGO/P0) where P0 is the currenct share price, EPS1 equals the average future earnings the firm could generate under no-growth policy, r is the capitalization rate, and PVGO is the present value of the growth opportunity, we have that EPS1/P0 is larger than the capitalization rate if there is no growth opportunity for the firm. Assuming a firm's dividend is expected to grow at the constant rate, one can estimate the expected rate of return of the common stock (or the cost of equity capital or the capitalization rate) as: Expected Dividend yield (i.e., D1/P0) + expected rate of growth in dividends. Question 12 0 / 8.33 points Using the constant-growth DCF (discounted cashflow) formula, the Price-to-Book ratio can be expressed as 9/10 where BVPS is the book value per share, ROE is the return on equity, r is the capitalization rate and b is the plowback ratio. Which of the following statement is CORRECT? When ROE > r, the Price-to-Book ratio (P0/BVPS) is larger than 1. When ROE = r, the Price-to-Book ratio (P0/BVPS) is smaller than 1. When ROE < r, the Price-to-Book ratio (P0/BVPS) is equal to 1. The Price-to-Book ratio (P0/BVPS) increases as ROE declines. 10/10