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© 2013 Pearson Education, Inc. All rights reserved.7-1 Additional Problems with Answers Problem 1 Pricing constant growth stock, with finite horizon: The Crescent Corporation just paid a dividend of \$2.00 per share and is expected to continue paying the same amount each year for the next 4 years. If you have a required rate of return of 13%, plan to hold the stock for 4 years, and are confident that it will sell for \$30 at the end of 4 years, How much should you offer to buy it at today?

© 2013 Pearson Education, Inc. All rights reserved.7-2 Additional Problems with Answers Problem 1 (Answer) In this case, we have an annuity of \$2 for 4 periods, followed by a lump sum of \$30, to be discounted at 13% for the respective number of years. Using a financial calculator Mode:P/Y=1; C/Y = 1 Input:NI/Y PV PMT FV Key:413 ? 2 30 Output-24.35

© 2013 Pearson Education, Inc. All rights reserved.7-3 Additional Problems with Answers Problem 2 Constant growth rate, infinite horizon (with growth rate estimated from past history: Using the historical dividend information provided below to calculate the constant growth rate, and a required rate of return of 18%, estimate the price of Nigel Enterprises’ common stock.

© 2013 Pearson Education, Inc. All rights reserved.7-4 Additional Problems with Answers Problem 2 (Answer) g = [(1.30/0.35) 1/9 – 1]  15.7% First, estimate the historical average growth rate of dividends by using the following equation: g = [(FV/PV) 1/n – 1] Where FV = Div 2008 = \$1.30 PV = Div 1999 = \$0.35 n = number of years in between =9

© 2013 Pearson Education, Inc. All rights reserved.7-5 Additional Problems with Answers Problem 2 (Answer) (continued) Next, use the constant growth, infinite horizon model to calculate price: i.e. Price 0 = Div 1 /(r-g) = Div 0 (1+g)/(r-g) Div 0 = Div 2008 = \$1.30; Div 1 = Div 0 *(1+g) =\$1.30*(1.157)  \$1.504; r = 18%; g = 15.7% (as calculated above) Price0 = \$1.504/(.18-.157)  Price 0 = \$65.40

© 2013 Pearson Education, Inc. All rights reserved.7-6 Additional Problems with Answers Problem 3 Pricing common stock with multiple dividend patterns: The Wonder Products Company is expanding fast and therefore will not pay any dividends for the next 3 years. After that, starting at the end of year 4, it will pay a dividend of \$0.75 per share to its common shareholders and increase it by 12% each year until it pays \$1.50 at the end of year 10. After that it will pay \$1.50 per year forever. If an investor wants to earn 15% per year on this investment, how much should he pay for the stock?

© 2013 Pearson Education, Inc. All rights reserved.7-7 Additional Problems with Answers Problem 3 (Answer) First lay out the dividends on a time line. Expected Dividend Stream of The Wonder Products Co. T 0 T 1 T 2 T 3 T 4 T 5 T 6 T 7 T 8 T 9 T 10 … T ∞ --- \$0.00 \$0.00 \$0.00 \$0.75 \$0.84 \$0.94 \$1.05 \$1.18 \$1.32 \$1.50 …\$1.50 Note: There are 3 distinct dividend payment patterns Years 1-3, no dividends; Years 4- 10, dividends grow at 12%; Years 11 onwards, zero-growth in dividends.

© 2013 Pearson Education, Inc. All rights reserved.7-8 Additional Problems with Answers Problem 3 (Answer) (continued) Next, Calculate the price at the end of Year 10, i.e. when the dividend growth rate is zero. Price 10 = Div 11 /r = 1.50/.15 = \$10; Using the NPV function and the annual cash flows calculate the price; NPV(15,0,{0.00,0.00,0.00,0.75,0.84,0.94,1.0 5,1.18,1.32,1.50+10.00}  \$5.25 Price = \$5.25

© 2013 Pearson Education, Inc. All rights reserved.7-9 Additional Problems with Answers Problem 4 Pricing non-constant growth common stock: The WedLink Corporation just paid a dividend of \$1.25 to its common shareholders. It announced that it expects the dividends to grow by 25% per year for the next 3 years. Then drop to a growth rate of 16% for an additional 2 years. Finally the dividends will converge to the industry median growth rate of 8% per year. If investors are expecting 12% per year on WedLink’s stock, calculate the current stock price.

© 2013 Pearson Education, Inc. All rights reserved.7-10 Additional Problems with Answers Problem 4 (Answer) Determine the dividend per share in Years 1-5 using the stated annual growth rates: D1=\$1.25*(1.25)=\$1.56; D2=\$1.56*(1.25)=\$1.95; D3=1.95*(1.25)=\$2.44; D4=\$2.44*(1.16)=\$2.83; D5=\$2.83*(1.16)=3.28 Next, Calculate the price at the end of Year 5; using the Gordon Model.

© 2013 Pearson Education, Inc. All rights reserved.7-11 Additional Problems with Answers Problem 4 (Answer) (continued) Using r = 12% and g = 8% (constant growth phase) i.e. P 5 = D 5 (1+g)/(r – g)  P 5 = \$3.28*(1.08)/(.12-.08)  3.54/.04=\$88.56 Finally calculate the present value of all the dividends in Years 1-5 and the price in Year 5, by using the NPV function….(TI-83 keystrokes shown here) NPV(12,0,{1.56, 1.95, 2.44, 2.83, 3.28+88.56} = \$58.60

© 2013 Pearson Education, Inc. All rights reserved.7-12 Additional Problems with Answers Problem 5 (A) Pricing common stock with constant growth and finite life versus infinite life. The ANZAC Corporation plans to be in business for 30 years. They announce that they will pay a dividend of \$3.00 per share at the end of one year, and continue increasing the annual dividend by 4% per year until they liquidate the company at the end of 30 years. If you want to earn a rate of return of 12% by investing in their stock, how much should you pay for the stock?

© 2013 Pearson Education, Inc. All rights reserved.7-13 Additional Problems with Answers Problem 5 (A) (Answer) Div 1 = \$3.00; r = 12%; g = 4%; n = 30 Using the formula for a growing annuity we can solve for the current price. Price 0 = \$37.5*0.89174 = \$33.44

© 2013 Pearson Education, Inc. All rights reserved.7-14 Additional Problems with Answers Problem 5 (B) If the company was to announce that it would continue increasing the dividend at 4% per year forever, how much more would you be willing to pay for its stock, assuming your required rate of return is still 12%?

© 2013 Pearson Education, Inc. All rights reserved.7-15 Additional Problems with Answers Problem 5 (B) (Answer) If the growth rate is 4% forever, the price of the stock can be figured out by using the Gordon Model; D 1 =\$3.00; r=12%  \$3.00/(.12 -.04)  \$37.50