Questions-Stock Valuations

Q1) The Starr Co. just paid a dividend of $1.80 per share on its stock. The dividends are expected to grow at a constant rate of 6 percent per year, indefinitely. Investors require a return of 11 percent on the stock. What is the current price? What will the price be in three years? What will the price be in 16 years? The constant dividend growth model is: Pt = Dt × (1 + g) / (R − g) So, the price of the stock today is: P0 = D0(1 + g) / (R − g)P0 = $1.80(1.06) / (.11 − .06)P0 = $38.16  The dividend at Year 4 is the dividend today times the FVIF for the growth rate in dividends and four years, so:  P3 = D3(1 + g) / (R − g)P3 = D0(1 + g)4 / (R − g)P3 = $1.80(1.06)4 / (.11 − .06)P3 = $45.45  We can do the same thing to find the dividend in Year 17, which gives us the price in Year 16, so: P16 = D16(1 + g) / (R − g)P16 = D0(1 + g)17 / (R − g)P16 = $1.80(1.06)17 / (.11 − .06)P16 = $96.94  There is another feature of the constant dividend growth model: The stock price grows at the dividend growth rate. So, if we know the stock price today, we can find the future value for any time in the future we want to calculate the stock price. In this problem, we want to know the stock price in three years, and we have already calculated the stock price today. The stock price in three years will be:  P3 = P0(1 + g)3P3 = $38.16(1 + .06)3P3 = $45.45  And the stock price in 16 years will be: P16 = P0(1 + g)16P16 = $38.16(1 + .06)16P16 = $96.94

Q2 The next dividend payment by ECY, Inc., will be $2.16 per share. The dividends are anticipated to maintain a growth rate of 5 percent, forever. The stock currently sells for $44 per share. What is the required return? We need to find the required return of the stock. Using the constant growth model, we can solve the equation for R. Doing so, we find:  R = (D1 / P0) + gR = ($2.16 / $44.00) + .05R = .0991, or 9.91%

Q3) The next dividend payment by ECY, Inc., will be $2.16 per share. The dividends are anticipated to maintain a growth rate of 5 percent, forever. The stock currently sells for $44 per share. What is the dividend yield? What is the expected capital gains yield? The dividend yield is the dividend next year divided by the current price, so the dividend yield is: Dividend yield = D1 / P0Dividend yield = $2.16 / $44.00Dividend yield = .0491, or 4.91% The capital gains yield, or percentage increase in the stock price, is the same as the dividend growth rate, so:  Capital gains yield = 5%

Q4) Schiller Corporation will pay a $3.26 per share dividend next year. The company pledges to increase its dividend by 6.5 percent per year, indefinitely. If you require a return of 15 percent on your investment, how much will you pay for the company’s stock today? Using the constant growth model, we find the price of the stock today is: P0 = D1 / (R − g)P0 = $3.26 / (.15 − .065)P0 = $38.35

Q5) Gruber Corp. pays a constant $8.30 dividend on its stock. The company will maintain this dividend for the next 14 years and will then cease paying dividends forever. The required return on this stock is 12 percent What is the current share price?  The price of any financial instrument is the PV of the future cash flows. The future dividends of this stock are an annuity for 14 years, so the price of the stock is the PVA, which will be:  P0 = $8.30(PVIFA12%,14)P0 = $55.01

Q6) The Spring Flower Co. has earnings of $1.85 per share. The benchmark PE for the company is 15 What stock price would you consider appropriate? What if the benchmark PE were 18? Using the equation to calculate the price of a share of stock with the PE ratio: P = Benchmark PE ratio × EPS So, with a PE ratio of 15, we find: P = 15($1.85)P = $27.75 And with a PE ratio of 18, we find: P = 18($1.85)P = $33.30

Q7) Universal Laser, Inc., just paid a dividend of $3.35 on its stock. The growth rate in dividends is expected to be a constant 4 percent per year, indefinitely. Investors require a return of 16 percent on the stock for the first three years, a rate of return of 14 percent for the next three years, and then a return of 12 percent thereafter. What is the current share price for the stock? This stock has a constant growth rate of dividends, but the required return changes twice. To find the value of the stock today, we will begin by finding the price of the stock at Year 6, when both the dividend growth rate and the required return are stable forever. The price of the stock in Year 6 will be the dividend in Year 7, divided by the required return minus the growth rate in dividends. So:    P6 = D6(1 + g) / (R − g)P6 = $3.35(1.04)7 / (.12 – .04)P6 = $55.10  Now we can find the price of the stock in Year 3. We need to find the price here since the required return changes at that time. The price of the stock in Year 3 is the PV of the dividends in Years 4, 5, and 6, plus the PV of the stock price in Year 6. The price of the stock in Year 3 is:   P3 = $3.35(1.04)4 / 1.14 + $3.35(1.04)5 / 1.142 + $3.35(1.04)6 / 1.143 + $55.10 / 1.143P3 = $46.63  Finally, we can find the price of the stock today. The price today will be the PV of the dividends in Years 1, 2, and 3, plus the PV of the stock in Year 3. The price of the stock today is: P0 = $3.35(1.04) / 1.16 + $3.35(1.04)2 / (1.16)2 + $3.35(1.04)3 / (1.16)3 + $46.63 / (1.16)3P0 = $37.98