Additional Problems with Answers Problem 1

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Additional Problems with AnswersProblem 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?


Additional Problems with AnswersProblem 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: N I/Y PV PMT FVKey: 4 13 ? 2 30Output -24.35



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.

1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 $0.35 $0.45 $0.51 $0.65 $0.75 $0.88 $0.99 $1.10 $1.13 $1.30



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 = Div2008 = $1.30 PV = Div1999 = $0.35

n = number of years in between =9


Additional Problems with AnswersProblem 2 (Answer) (continued)

Next, use the constant growth, infinite horizon model to calculate price:

i.e. Price0 = Div1/(r-g) = Div0(1+g)/(r-g)

Div0 = Div2008= $1.30;

Div1= Div0*(1+g) =$1.30*(1.157)$1.504;

r = 18%; g = 15.7% (as calculated above)

Price0 = $1.504/(.18-.157)

Price0 = $65.40



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?



First lay out the dividends on a time line. Expected Dividend Stream of The Wonder Products Co. T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 …

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.



Next, Calculate the price at the end of Year 10, i.e. when the dividend growth rate is zero.

Price10 = Div11/r = 1.50/.15 = $10;

Using the NPV function and the annual cash flows calculate the price;

NPV(15,0,

{0.00,0.00,0.00,0.75,0.84,0.94,1.05,1.18,1.32,1.50+10.00} $5.25

Price = $5.25


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.



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.



Using r = 12% and g = 8% (constant growth phase)

i.e. P5 = D5(1+g)/(r – g)

P5 = $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


Additional Problems with AnswersProblem 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?


Additional Problems with AnswersProblem 5 (A) (Answer)

Div1 = $3.00; r = 12%; g = 4%; n = 30

Using the formula for a growing annuity we can solve for the current price.

Price0 = $37.5*0.89174 = $33.44

30

r1g11

gr1

Div

0Price

30

0 1.12

1.041

.04.12

$3.00Price


Additional Problems with AnswersProblem 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%?


Additional Problems with AnswersProblem 5 (B) (Answer)

If the growth rate is 4% forever, the price of the stock can be figured out by using the Gordon Model; D1=$3.00; r=12%

$3.00/(.12 - .04) $37.50

gr1

Div

0Price

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Additional Problems with Answers Problem 1