91Ó°ÊÓ

Question:Surgical Supplies Corporation paid a dividend of $1.12 per share over the last 12 months. The dividend is expected to grow at a rate of 2.5 percent over the next three years (supernormal growth). It will then grow at a normal, constant rate of 7 percent for the foreseeable future. The required rate of return is 12 percent (this will also serve as the discount rate).

a. Compute the anticipated value of the dividends for the next three years (D1, D2, and D3).

b. Discount each of these dividends back to the present at a discount rate of 12 percent and then sum them.

c. Compute the price of the stock at the end of the third year (P3).

P3 = D4/ (Ke - g)

d. After you have computed P3, discount it back to the present at a discount rate of 12 percent for three years.

e. Add together the answers in part b and part d to get the current value of the stock. (This answer represents the present value of the first three periods of dividends plus the present value of the price of the stock after three periods.)

Step by step solution

01

Step: 1 Calculation of anticipated dividend for the next three years

a)
$$\begin{gathered} \mathbf{Expected}\mathbf{}\mathbf{Dividend}\mathbf{\left(}\mathbf{D}\mathbf{1}\mathbf{\right)}\mathbf{=}\mathbf{Prior}\mathbf{}\mathbf{Dividend}\mathbf{×}\left(\mathbf{1}\mathbf{+}\mathbf{Growth}\mathbf{}\mathbf{rate}\right) \\ \mathbf{=}\mathbf{1}\mathbf{.}\mathbf{12}\mathbf{×}\left(\mathbf{1}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{025}\right) \\ \mathbf{=}\mathbf{\$}\mathbf{1}\mathbf{.}\mathbf{15} \\ \mathbf{Expected}\mathbf{}\mathbf{Dividend}\mathbf{\left(}\mathbf{D}\mathbf{2}\mathbf{\right)}\mathbf{=}\mathbf{Prior}\mathbf{}\mathbf{Dividend}\mathbf{×}\left(1+\mathrm{Growthrate}\right) \\ \mathbf{=}\mathbf{1}\mathbf{.}\mathbf{15}\mathbf{×}\left(1+0.025\right) \\ \mathbf{=}\mathbf{\$}\mathbf{1}\mathbf{.}\mathbf{18} \\ \mathbf{Expected}\mathbf{}\mathbf{Dividend}\mathbf{\left(}\mathbf{D}\mathbf{3}\mathbf{\right)}\mathbf{=}\mathbf{Prior}\mathbf{}\mathbf{Dividend}\mathbf{×}\left(1+\mathrm{Growth}\mathrm{rate}\right) \\ \mathbf{=}\mathbf{1}\mathbf{.}\mathbf{18}\mathbf{×}\left(1+0.25\right) \\ \mathbf{=}\mathbf{\$}\mathbf{1}\mathbf{.}\mathbf{21} \end{gathered}$$

02

Step: 2 Computation of total present value

b)

$$\begin{gathered} \mathbf{Present}\mathbf{}\mathbf{valueofD}\mathbf{1}\mathbf{=}\frac{\mathbf{D}\mathbf{1}}{\left(\mathbf{1}\mathbf{+}\mathbf{Discount}\mathbf{}\mathbf{Rate}\right)} \\ \mathbf{=}\frac{\mathbf{1}\mathbf{.}\mathbf{15}}{\mathbf{(}\mathbf{1}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{12}\mathbf{)}} \\ \mathbf{=}\mathbf{\$}\mathbf{1}\mathbf{.}\mathbf{03} \\ \mathbf{Present}\mathbf{}\mathbf{valueofD}\mathbf{2}\mathbf{=}\frac{\mathbf{D}\mathbf{2}}{{\left(\mathbf{1}\mathbf{+}\mathbf{DiscountRate}\right)}^{\mathbf{2}}} \\ \mathbf{=}\frac{\mathbf{1}\mathbf{.}\mathbf{18}}{{\mathbf{(}\mathbf{1}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{12}\mathbf{)}}^{\mathbf{2}}} \\ \mathbf{=}\mathbf{\$}\mathbf{0}\mathbf{.}\mathbf{94} \\ \mathit{P}\mathit{r}\mathit{e}\mathit{s}\mathit{e}\mathit{n}\mathit{t}\mathbf{}\mathit{v}\mathit{a}\mathit{l}\mathit{u}\mathit{e}\mathbf{}\mathit{o}\mathit{f}\mathbf{}\mathit{D}\mathbf{3}\mathbf{=}\frac{{\displaystyle \mathbf{D}\mathbf{3}}}{{\displaystyle {\left(1+\mathrm{Discount}\mathrm{Rate}\right)}^{\mathbf{3}}}} \\ \mathbf{=}\frac{{\displaystyle \mathbf{1}\mathbf{.}\mathbf{21}}}{{\displaystyle {\mathbf{(}\mathbf{1}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{12}\mathbf{)}}^{\mathbf{3}}}} \\ \mathbf{=}\mathbf{\$}\mathbf{0}\mathbf{.}\mathbf{86} \\ \mathit{T}\mathit{o}\mathit{t}\mathit{a}\mathit{l}\mathbf{}\mathit{p}\mathit{r}\mathit{e}\mathit{s}\mathit{e}\mathit{n}\mathit{t}\mathbf{}\mathit{v}\mathit{a}\mathit{l}\mathit{u}\mathit{e}\mathbf{=}\mathbf{Present}\mathbf{}\mathbf{Value}\mathbf{}\mathbf{of}\mathbf{}\mathbf{D}\mathbf{1}\mathbf{+}\mathbf{Present}\mathbf{}\mathbf{value}\mathbf{}\mathbf{of}\mathbf{}\mathbf{D}\mathbf{2}\mathbf{+}\mathbf{PresentvalueofD}\mathbf{3} \\ \mathbf{=}\mathbf{1}\mathbf{.}\mathbf{03}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{94}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{86} \\ \mathbf{=}\mathbf{\$}\mathbf{2}\mathbf{.}\mathbf{83} \end{gathered}$$

03

Step: 3 Computation of the price of the stock

c)

$$\begin{gathered} \mathbf{Price}\mathbf{}\mathbf{of}\mathbf{}\mathbf{stock}\mathbf{}\mathbf{\left(}\mathbf{P}\mathbf{3}\mathbf{\right)}\mathbf{=}\frac{\mathbf{D}\mathbf{4}}{\mathbf{Ke}\mathbf{-}\mathbf{g}} \\ \mathbf{=}\frac{\mathbf{1}\mathbf{.}\mathbf{21}\mathbf{×}\mathbf{1}.07}{\mathbf{0}\mathbf{.}\mathbf{12}\mathbf{-}\mathbf{0}\mathbf{.}\mathbf{025}} \\ \mathbf{=}\mathbf{\$}\mathbf{1}3.63 \end{gathered}$$

04

Step: 4 Computation of present value of P3

$$\begin{gathered} \mathbf{Present}\mathbf{}\mathbf{value}\mathbf{}\mathbf{of}\mathbf{}\mathbf{P}\mathbf{3}\mathbf{=}\frac{\mathbf{P}\mathbf{3}}{{\left(\mathbf{1}\mathbf{+}\mathbf{DiscountRate}\right)}^{\mathbf{3}}} \\ \mathbf{=}\frac{\mathbf{1}3.63}{{\left(\mathbf{1}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{12}\right)}^{\mathbf{3}}} \\ \mathbf{=}\mathbf{\$}\mathbf{11}.7\mathbf{3} \end{gathered}$$

05

Step: 5 Computation of current value of stock

e)

$$\begin{gathered} \mathbf{Current}\mathbf{}\mathbf{value}\mathbf{}\mathbf{of}\mathbf{}\mathbf{stock}\mathbf{=}\mathbf{Total}\mathbf{}\mathbf{present}\mathbf{}\mathbf{value}\mathbf{}\mathbf{of}\mathbf{}\mathbf{dividend}\mathbf{+}\mathbf{Total}\mathbf{}\mathbf{present}\mathbf{}\mathbf{value}\mathbf{}\mathbf{of}\mathbf{}\mathbf{stockprice} \\ \mathbf{=}\mathbf{2}\mathbf{.}\mathbf{83}\mathbf{+}\mathbf{11}.7\mathbf{3} \\ \mathbf{=}\mathbf{\$}\mathbf{14}.5\mathbf{6} \end{gathered}$$

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