91Ó°ÊÓ

Mel Thomas, the chief financial officer of Preston 91Ó°ÊÓ, has been asked to do an evaluation of Dunning Chemical Company by the president and chair of the board, Sarah Reynolds. Preston 91Ó°ÊÓ was planning a joint venture with Dunning (which was privately traded), and Sarah and Mel needed a better feel for what Dunning’s stock was worth because they might be interested in buying the firm in the future.

Dunning Chemical paid a dividend at the end of year one of \(1.30, the anticipated growth rate was 10 percent, and the required rate of return was 14 percent.

a. What is the value of the stock based on the dividend valuation model (Formula 10-8)?

b. Indicate that the value you computed in part a is correct by showing the value of D1, D2, and D3 and by discounting each back to the present at 14 percent. D1 is \)1.30, and it increases by 10 percent (g) each year. Also discount the anticipated stock price at the end of year three back to the present and add it to the present value of the three dividend payments.

The value of the stock at the end of year three is: P3 5 D4 _____ Ke 2 g D4 5 D3 (1 1 g)

If you have done all these steps correctly, you should get an answer approximately equal to the answer in part a.

c. As an alternative measure, you also examine the value of the firm based on the price-earnings (P/E) ratio times earnings per share. Since the company is privately traded (not in the public stock market), you will get your anticipated P/E ratio by taking the average value of five publiclytraded chemical companies. The P/E ratios were as follows during the time period under analysis:

P/E Ratio

Dow Chemical .................. 15

DuPont ............................. 18

Georgia Gulf ..................... 7

3M .................................... 19

Olin Corp .......................... 21

Assume Dunning Chemical has earnings per share of \(2.10. What is the stock value based on the P/E ratio approach? Multiply the average P/E ratio you computed times earnings per share. How does this value compare to the dividend valuation model values that you computed in parts a and b?

d. If in computing the industry average P/E, you decide to weight Olin Corp. by 40 percent and the other four firms by 15 percent, what would be the new weighted average industry P/E? (Note: You decided to weight Olin Corp. more heavily because it is similar to Dunning Chemical.) What will the new stock price be? Earnings per share will stay at \)2.10.

e. By what percent will the stock price change as a result of using the weighted average industry P/E ratio in part d as opposed to that in part c?

Step by step solution

01

Computation of the price of the stock (a)

$$\begin{gathered} \mathbf{Priceofstock}\mathbf{\left(}\mathbf{P}\mathbf{0}\mathbf{\right)}\mathbf{=}\frac{\mathbf{D}\mathbf{1}}{\mathbf{Ke}\mathbf{-}\mathbf{g}} \\ \mathbf{=}\frac{\mathbf{1}\mathbf{.}\mathbf{30}}{\mathbf{0}\mathbf{.}\mathbf{14}\mathbf{-}\mathbf{0}\mathbf{.}\mathbf{10}} \\ \mathbf{=}\mathbf{\$}\mathbf{32}\mathbf{.}\mathbf{5}0 \end{gathered}$$

02

Calculation of anticipated dividend for the next three years (b)

$$\begin{gathered} \mathbf{ExpectedDividend}\mathbf{\left(}\mathbf{D}\mathbf{2}\mathbf{\right)}\mathbf{=}\mathbf{PriorDividend}\mathbf{×}\left(\mathbf{1}\mathbf{+}\mathbf{Growthrate}\right) \\ \mathbf{=}\mathbf{1}\mathbf{.}\mathbf{30}\mathbf{×}\left(\mathbf{1}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{10}\right) \\ \mathbf{=}\mathbf{\$}\mathbf{1}\mathbf{.}\mathbf{43} \end{gathered}$$

$$\begin{gathered} \mathbf{ExpectedDividend}\mathbf{\left(}\mathbf{D}\mathbf{3}\mathbf{\right)}\mathbf{=}\mathbf{PriorDividend}\mathbf{×}\left(\mathbf{1}\mathbf{+}\mathbf{Growthrate}\right) \\ \mathbf{=}\mathbf{1}\mathbf{.}\mathbf{43}\mathbf{×}\left(\mathbf{1}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{10}\right) \\ \mathbf{=}\mathbf{\$}\mathbf{1}\mathbf{.}\mathbf{573} \end{gathered}$$

Step 2: Computation of total present value

$\begin{array}{rcl}\mathbf{PresentvalueofD}\mathbf{2}& \mathbf{=}& \frac{\mathbf{D}\mathbf{2}}{{\left(\mathbf{1}\mathbf{+}\mathbf{DiscountRate}\right)}^{\mathbf{2}}}\\ & \mathbf{=}& \frac{\mathbf{1}\mathbf{.}\mathbf{43}}{{\mathbf{(}\mathbf{1}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{14}\mathbf{)}}^{\mathbf{2}}}\\ & \mathbf{=}& \mathbf{\$}\mathbf{1}\mathbf{.}\mathbf{1}\\ & & \end{array}$

$\begin{array}{rcl}\mathbf{PresentvalueofD}\mathbf{3}& \mathbf{=}& \frac{\mathbf{D}\mathbf{3}}{{\left(\mathbf{1}\mathbf{+}\mathbf{DiscountRate}\right)}^{\mathbf{3}}}\\ & \mathbf{=}& \frac{\mathbf{1}\mathbf{.}\mathbf{573}}{{\mathbf{(}\mathbf{1}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{14}\mathbf{)}}^{\mathbf{3}}}\\ & \mathbf{=}& \mathbf{\$}\mathbf{1}\mathbf{.}\mathbf{062}\\ & & \end{array}$

$\begin{array}{rcl}\mathbf{Totalpresentvalue}& \mathbf{=}& \mathbf{PresentValueofD}\mathbf{1}\mathbf{+}\mathbf{PresentvalueofD}\mathbf{2}\mathbf{+}\mathbf{PresentvalueofD}\mathbf{3}\\ & \mathbf{=}& \mathbf{1}\mathbf{.}\mathbf{140}\mathbf{+}\mathbf{1}\mathbf{.}\mathbf{100}\mathbf{+}\mathbf{1}\mathbf{.}\mathbf{062}\\ & \mathbf{=}& \mathbf{\$}\mathbf{3}\mathbf{.}\mathbf{302}\\ & & \end{array}$

03

Computation of the price of the stock at the third year

$$\begin{gathered} \mathbf{Priceofstock}\mathbf{\left(}\mathbf{P}\mathbf{3}\mathbf{\right)}\mathbf{=}\frac{\mathbf{D}\mathbf{4}}{\mathbf{Ke}\mathbf{-}\mathbf{g}} \\ \mathbf{=}\frac{\mathbf{1}\mathbf{.}\mathbf{573}\mathbf{×}\mathbf{1}\mathbf{.}\mathbf{10}}{\mathbf{0}\mathbf{.}\mathbf{14}\mathbf{-}\mathbf{0}\mathbf{.}\mathbf{10}} \\ \mathbf{=}\mathbf{\$}\mathbf{43}\mathbf{.}\mathbf{258} \end{gathered}$$

04

Computation of present value of P3

$\begin{array}{rcl}\mathbf{PresentvalueofP}\mathbf{3}& \mathbf{=}& \frac{\mathbf{P}\mathbf{3}}{{\left(\mathbf{1}\mathbf{+}\mathbf{DiscountRate}\right)}^{\mathbf{3}}}\\ & \mathbf{=}& \frac{\mathbf{43}\mathbf{.}\mathbf{258}}{{\left(\mathbf{1}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{14}\right)}^{\mathbf{3}}}\\ & \mathbf{=}& \mathbf{\$}\mathbf{29}\mathbf{.}\mathbf{198}\\ & & \end{array}$

05

Computation of current value of stock

$\begin{array}{rcl}\mathbf{Currentvalueofstock}& \mathbf{=}& \mathbf{Totalpresentvalueofdividend}\mathbf{+}\mathbf{Totalpresentvalueofstockprice}\\ & \mathbf{=}& \mathbf{3}\mathbf{.}\mathbf{302}\mathbf{+}\mathbf{29}\mathbf{.}\mathbf{198}\\ & \mathbf{=}& \mathbf{\$}\mathbf{32}\mathbf{.}\mathbf{5}\\ & & \end{array}$

06

Computation of price using EPS and P/E (c)

$\begin{array}{rcl}\mathbf{P}\mathbf{/}\mathbf{E}& \mathbf{=}& \frac{\text{Sum of P/E Ratio of Public Company}}{\text{Number of Companies}}\\ & \mathbf{=}& \frac{15+18+7+19+21}{5}\\ & \mathbf{=}& 16\\ & & \end{array}$

$\begin{array}{rcl}\mathbf{Price}& \mathbf{=}& \mathbf{P}\mathbf{/}\mathbf{E}\mathbf{×}\mathbf{EPS}\\ & \mathbf{=}& \mathbf{16}\mathbf{×}\mathbf{2}\mathbf{.}\mathbf{1}\\ & \mathbf{=}& \mathbf{\$}\mathbf{33}\mathbf{.}\mathbf{60}\\ & & \end{array}$

07

Computation of price using EPS and weighted P/E (d)

$\begin{array}{rcl}\mathbf{WeightedP}\mathbf{/}\mathbf{Erato}& \mathbf{=}& \mathbf{P}\mathbf{/}\mathbf{Eratio}\mathbf{×}\mathbf{Weights}\\ & \mathbf{=}& \left(\mathbf{0}\mathbf{.}\mathbf{4}\mathbf{×}\mathbf{21}\right)\mathbf{+}\left(\mathbf{0}\mathbf{.}\mathbf{15}\mathbf{×}\left(\mathbf{15}\mathbf{+}\mathbf{18}\mathbf{+}\mathbf{7}\mathbf{+}\mathbf{19}\right)\right)\\ & \mathbf{=}& \mathbf{17}\mathbf{.}\mathbf{25}\\ & & \end{array}$

$\begin{array}{rcl}\mathbf{Price}& \mathbf{=}& \mathbf{P}\mathbf{/}\mathbf{E}\mathbf{×}\mathbf{EPS}\\ & \mathbf{=}& \mathbf{17}\mathbf{.}\mathbf{25}\mathbf{×}\mathbf{2}\mathbf{.}\mathbf{1}\\ & \mathbf{=}& \mathbf{\$}\mathbf{36}\mathbf{.}\mathbf{23}\\ & & \end{array}$

08

Computation of Changes in stock price and percentage change (e):

$\begin{array}{rcl}\mathbf{Changeinstockprice}& \mathbf{=}& \mathbf{StockpriceinPartd}\mathbf{-}\mathbf{Stockpriceinpartc}\\ & \mathbf{=}& \mathbf{36}\mathbf{.}\mathbf{23}\mathbf{-}\mathbf{33}\mathbf{.}\mathbf{6}\\ & \mathbf{=}& \mathbf{\$}\mathbf{2}.6\mathbf{3}\end{array}$

$\begin{array}{rcl}\mathbf{PercentageChangeinstockprice}& \mathbf{=}& \frac{\mathbf{Changeinstockprice}}{\mathbf{StockpriceinC}}\mathbf{×}\mathbf{100}\\ & \mathbf{=}& \frac{\mathbf{2}\mathbf{.}\mathbf{6}3}{\mathbf{33}\mathbf{.}\mathbf{6}}\mathbf{×}\mathbf{100}\\ & \mathbf{=}& \mathbf{7}\mathbf{.}\mathbf{8}3\mathbf{\%}\\ & & \end{array}$

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