Question 1

National Advertising just paid a dividend of D₀ = $0.75 per share,and that dividend is expected to grow at a constant rate of 6.50% per year in the future.The company's beta is 1.25,the required return on the market is 10.50%,and the risk-free rate is 4.50%.What is the company's current stock price?

Accepted Answer

$\begin{array}{lr}
\mathrm{D}_{0} & \$ 0.75 \
\mathrm{~b} & 1.25 \
\mathrm{r}_{\mathrm{RF}} & 4.5 \% \
\mathrm{r} \mathrm{M} & 10.5 \% \
\mathrm{D} & 6.5 \% \
\mathrm{D}_{1}=\mathrm{D}_{0}(1+\mathrm{g})= & \$ 0.798 \
\mathrm{r}_{\mathrm{s}}=\mathrm{r}_{\mathrm{RF}}+\mathrm{b}\left(\mathrm{r}_{\mathrm{M}}-\mathrm{R}_{\mathrm{RF}}\right)= & 12.0 \% \
\mathrm{P}_{0}=\mathrm{D}_{1} /\left(\mathrm{r}_{\mathrm{s}}-\mathrm{g}\right) & \$ 14.52
\end{array}$

Question 2

If D₁ = $1.50,g (which is constant)= 6.5%,and P₀ = $56,what is the stock's expected capital gains yield for the coming year?

Accepted Answer

$\begin{array}{lr}
D_{1} & \$ 1.50 \
g & 6.5 \% \
P_{0} & \$ 56.00 \
\text { Capital gains yield }=g= & 6.50 \%
\end{array}$

Question 3

Kelly Enterprises' stock currently sells for $35.25 per share.The dividend is projected to increase at a constant rate of 4.75% per year.The required rate of return on the stock,r_s,is 11.50%.What is the stock's expected price 5 years from now?

Accepted Answer

Growth rate &emsp;&emsp;&emsp;&emsp;&emsp; &emsp;&emsp;&emsp;&emsp;$4.75 \%$
Years in the future &emsp;&emsp;&emsp;&emsp; &emsp;&emsp;&emsp;$5$
Stack price &emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;$35.25$ 
$p _ { 5 } = p _ { 0 } ( 1 + p ) ^ { 5 } =$ &emsp;&emsp;&emsp;&emsp;$\$ 44.46$

Question 4

If D₁ = $1.25,g (which is constant)= 4.7%,and P₀ = $26.00,what is the stock's expected dividend yield for the coming year?

Accepted Answer

$\begin{array}{lr}
D_{1} & \$ 1.25 \
\mathrm{g} & 4.7 \% \
\mathrm{P}_{0} & \$ 26.00 \
\text { Dividend yield }=\mathrm{D}_{1} / \mathrm{P}_{0}= & 4.81 \%
\end{array}$

Question 5

Barnette Inc.'s free cash flows are expected to be unstable during the next few years while the company undergoes restructuring.However,FCF is expected to be $50 million in Year 5,i.e.,FCF at t = 5 equals $50 million,and the FCF growth rate is expected to be constant at 6% beyond that point.If the weighted average cost of capital is 12%,what is the horizon value (in millions)at t = 5?

Accepted Answer

$$\begin{array} { l r } 
\mathrm { FCF } _ { 5 } & \$ 50 \
\mathrm { g }  & 6\% \
\mathrm { WACC } & 12 \% \
\end{array}$$ $\begin{aligned}
\mathrm{HV}_{5} &=\mathrm{FCF}_{6}/(\mathrm{WACC}-\mathrm{g})=\mathrm{FCF}_{5}(1+\mathrm{g}) /(\mathrm{WACC}-\mathrm{g}) \
&=\$ 50(1+0.06) /(0.12-0.06)=\$ 53 / 0.06=\$ \mathbf{8 8 3}
\end{aligned}$

Question 6

Kellner Motor Co.'s stock has a required rate of return of 11.50%,and it sells for $25.00 per share.Kellner's dividend is expected to grow at a constant rate of 7.00%.What was the last dividend,D₀?

Accepted Answer

$$\begin{array}{l}
\begin{array} { l } 
\text { Stack price } \
\text { Required return } \
\text { Growth rate } \
P _ { 0 } = D _ { 1 } / \left(r _ { s } - \mathrm { g } \right) , so  D _ { 1 } = P _ { 0 } \left( r _ { s } - \mathrm { g } \right) = \
\text { Last dividend } = D _ { 0 } = D _ { 1 } / ( 1 + \mathrm { D } )
\end{array}
\begin{array} { r } 
\$ 25.00 \
11.50 \% \
7.00 \% \
\$ 1.1250 \
\$ 1.05
\end{array}
\end{array}$$

Question 7

A stock just paid a dividend of D₀ = $1.50.The required rate of return is r_s = 10.1%,and the constant growth rate is g = 4.0%.What is the current stock price?

Accepted Answer

$$\begin{array} { l r } 
D _ { 0 } & \$ 1.50 \
r _ { s } & 10.1 \% \
\text { g } & 4.0 \% \
D _ { 1 } = D _ { 0 } ( 1 + \mathrm { g} ) = & \$ 1.56 \
P _ { 0 } = D _ { 1 } l \left( r _ { 5 } - \text { g } \right) & \$ 25.57
\end{array}$$

Question 8

The projected cash flow for the next year for Minesuah Inc.is $100,000,and FCF is expected to grow at a constant rate of 6%.If the company's weighted average cost of capital is 11%,what is the value of its operations?

Accepted Answer

$\begin{array}{lr}
\mathrm{FCF}_{1}: & \$ 100,000 \
\mathrm{~g}: & 6 \% \
\mathrm{WACC}: & 11 \%
\end{array}$ Value Ops $
\begin{array}{l}
=\mathrm{FCF}_{1} /(\mathrm{WACC}-\mathrm{g})=\mathrm{FCF}_{0}(1+\mathrm{g}) /(\mathrm{WACC}-\mathrm{g}) \
=\$ 100,000 /(0.11-0.06)=\$ 100,000 / 0.05=\$ 2,000,000
\end{array}
$

Question 9

Carby Hardware has an outstanding issue of perpetual preferred stock with an annual dividend of $7.50 per share.If the required return on this preferred stock is 6.5%,at what price should the preferred stock sell?

Accepted Answer

Preferted itritend &emsp; &emsp;&emsp; &emsp;&emsp; &emsp;&emsp; $\$7.50$
Required return &emsp; &emsp;&emsp; &emsp;&emsp; &emsp;&emsp; &emsp;$6.5 \%$
Preferred price $= D _ { p } / r _ { p } =$  &emsp; &emsp;$\$115.38$

Question 10

$35.50 per share is the current price for Foster Farms' stock.The dividend is projected to increase at a constant rate of 5.50% per year.The required rate of return on the stock,r_s,is 9.00%.What is the stock's expected price 3 years from today?

Accepted Answer

Stock price &emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;$\$35.50$
Growth rate &emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;$5.50\%$
Years in the future &emsp;&emsp;&emsp;&emsp;&emsp;&emsp;$3$
$P _ { 3 } = P _ { 0 } ( 1 + g ) ^ { 3 } =$ &emsp;&emsp;&emsp; $\$41.69$

Question 11

If D₀ = $1.75,g (which is constant)= 3.6%,and P₀ = $32.00,what is the stock's expected total return for the coming year?

Accepted Answer

$\begin{array}{lr}
D_{0} & \$ 1.75 \
g & \$ 3.6 \% \
P_{0} & \$ 32.00 \
D_{1}=D_{0}(1+g)= & \$ 1.81 \
\text { Total return }=r_{s}=D_{1} / P_{0}+g & 9.27 \%
\end{array}$

Question 12

If D₁ = $1.25,g (which is constant)= 5.5%,and P₀ = $44,what is the stock's expected total return for the coming year?

Accepted Answer

$\begin{array}{lr}
\mathrm{D}_{1} & \$ 1.25 \
\mathrm{~g} & 5.5 \% \
\mathrm{P}_{0} & \$ 44.00 \
\text { Total return }=\mathrm{r}_{\mathrm{s}}=\mathrm{D}_{1} / \mathrm{P}_{0}+\mathrm{g} & 8.34 \%
\end{array}$

Question 13

Dyer Furniture is expected to pay a dividend of D₁ = $1.25 per share at the end of the year,and that dividend is expected to grow at a constant rate of 6.00% per year in the future.The company's beta is 1.15,the market risk premium is 5.50%,and the risk-free rate is 4.00%.What is Dyer's current stock price?

Accepted Answer

$$\begin{array} { l r } 
D _ { 1 } & \$ 1.25 \
b _ { \text { } } & 1.15 \
r _ { RF } & 4.00 \% \
R P _ { M } & 5.50 \% \
g & 6.00 \% \
r _ { 5 } = r _ { R F } + b \left( R P _ { M } \right) = &  10.33 \% \
P _ { 0 } = D _ { 1 } / \left( r _ { 5 } - \text { g } \right) & \$ 28.90% \
\end{array}$$

Question 14

The Jameson Company just paid a dividend of $0.75 per share,and that dividend is expected to grow at a constant rate of 5.50% per year in the future.The company's beta is 1.15,the market risk premium is 5.00%,and the risk-free rate is 4.00%.What is Jameson's current stock price,P₀?

Accepted Answer

$$\begin{array} { l r } 
D _ { 0 } & \$ 0.75 \
b & 1.15 \
R _ { R F } & 4.0 \% \
R P _ { M } & 5.0 \% \
\text { g } & 5.5 \% \
D _ { 1 } = D _ { 0 } ( 1 + \mathrm { g } ) = & \$ 0.7913 \
r _ { 5 } = r _ { R F } + b \left( R P _ { M } \right) = & 9.75 \% \
P _ { 0 } = D _ { 1 } / \left( r _ { 5 } - \text { g } \right) & \$ 18.62
\end{array}$$

Question 15

A share of Lash Inc.'s common stock just paid a dividend of $1.00.If the expected long-run growth rate for this stock is 5.4%,and if investors' required rate of return is 11.4%,what is the stock price?

Accepted Answer

$$\begin{array} { l l } 
\text { Last divilend } \left( \mathrm { D } _ { \mathrm { 0 } } \right) & \$ 1.00 \
\text { Long-run gowrh rate } & 5.4 \% \
\text { Required return } & \$ 1.4 \% \
\mathrm { D } _ { 1 } = \mathrm { D } _ { 0 } ( 1 + \mathrm { g } ) = & \$ 1.054 \
\mathrm { P } _ { 0 } = \mathrm { D } _ { 1 } / \left( \mathrm { r } _ { s } - \mathrm { g } \right) & \$ 17.57
\end{array}$$

Question 16

A stock is expected to pay a dividend of $0.75 at the end of the year.The required rate of return is r_s = 10.5%,and the expected constant growth rate is g = 6.4%.What is the stock's current price?

Accepted Answer

$\begin{array}{lr}
D_{1} & \$ 0.75 \
r_{s} & 10.5 \% \
g & 6.4 \% \
P_{0}=D_{1} /\left(r_{s}-g\right) & \$ 18.29
\end{array}$

Question 17

Young & Liu Inc.'s free cash flow during the just-ended year (t = 0)was $100 million,and FCF is expected to grow at a constant rate of 5% in the future.If the weighted average cost of capital is 15%,what is the firm's value of operations,in millions?

Accepted Answer

$$\begin{array} { l r } 
\mathrm { FCF } _ { 0 } & \$ 100 \
\mathrm { g }  & 5\% \
\mathrm { WACC } & 15 \% \
\end{array}$$ Value $ \mathrm{Op} $
$$
\begin{array}{l}
=\mathrm{FCF}_{1} /(\mathrm{WACC}-\mathrm{g})=\mathrm{FCF}_{0}(1+\mathrm{g}) /(\mathrm{WACC}-\mathrm{g}) \
=\$ 100(1+0.05) /(0.15-0.05)=\$ 105 / 0.1=\$ 1,050
\end{array}
$$

Question 18

Gere Furniture forecasts a free cash flow of $40 million in Year 3,i.e.,at t = 3,and it expects FCF to grow at a constant rate of 5% thereafter.If the weighted average cost of capital is 10% and the cost of equity is 15%,what is the horizon value,in millions at t = 3?

Accepted Answer

$$\begin{array} { l r } 
\mathrm { FCF } _ { 3 } & \$ 40 \
\mathrm { g }  & 5\% \
\mathrm { WACC } & 10 \% \
\end{array}$$ $\begin{aligned}
\mathrm{HV}_{3} &=\mathrm{FCF}_{4} /(\mathrm{WACC}-\mathrm{g})=\mathrm{FCF}_{3}(1+\mathrm{g}) /(\mathrm{WACC}-\mathrm{g}) \
&=\$ 40(1+0.05) /(0.10-0.05)=\$ 42 / 0.05=\$ 840
\end{aligned}$

Question 19

Franklin Corporation is expected to pay a dividend of $1.25 per share at the end of the year (D₁ = $1.25).The stock sells for $32.50 per share,and its required rate of return is 10.5%.The dividend is expected to grow at some constant rate,g,forever.What is the equilibrium expected growth rate?

Accepted Answer

$\begin{array}{ll}
\text { Expected dividend }\left(\mathrm{D}_{1}\right) & \$ 1.25 \
\text { Stock price } & \$ 32.50 \
\text { Required return } & 10.5 \% \
\text { Dividend yield } & 3.85 \% \
\text { Growth rate }=r_{s}-\mathrm{D}_{1} / \mathrm{P}_{0}= & 6.65 \%
\end{array}$

Question 20

If D₀ = $2.25,g (which is constant)= 3.5%,and P₀ = $50,what is the stock's expected dividend yield for the coming year?

Accepted Answer

$$\begin{array} { l r } 
\mathrm { D } _ { 0 } & \$ 2.25 \
\mathrm { g }  & 3\% \
\mathrm { P } _ { 0 } &  50.5 \% \
\mathrm { D } _ { 1 } = \mathrm { D } _ { 0 } ( 1 + \mathrm { g } ) = & \$ 2.329 \
\mathrm { D } \text { ividend yield } = \mathrm { D } _ { 1 } / \mathrm { P } _ { 0 } = & 4.66 \%
\end{array}$$

Quiz 7: Valuation of Stocks and Corporations

If D₁ = $1.50,g (which is constant) = 6.5%,and P₀ = $56,what is the stock's expected capital gains yield for the coming year?

Kelly Enterprises' stock currently sells for $35.25 per share.The dividend is projected to increase at a constant rate of 4.75% per year.The required rate of return on the stock,r_s,is 11.50%.What is the stock's expected price 5 years from now?

If D₁ = $1.25,g (which is constant) = 4.7%,and P₀ = $26.00,what is the stock's expected dividend yield for the coming year?

Kellner Motor Co.'s stock has a required rate of return of 11.50%,and it sells for $25.00 per share.Kellner's dividend is expected to grow at a constant rate of 7.00%.What was the last dividend,D₀?

A stock just paid a dividend of D₀ = $1.50.The required rate of return is r_s = 10.1%,and the constant growth rate is g = 4.0%.What is the current stock price?

The projected cash flow for the next year for Minesuah Inc.is $100,000,and FCF is expected to grow at a constant rate of 6%.If the company's weighted average cost of capital is 11%,what is the value of its operations?

Carby Hardware has an outstanding issue of perpetual preferred stock with an annual dividend of $7.50 per share.If the required return on this preferred stock is 6.5%,at what price should the preferred stock sell?

$35.50 per share is the current price for Foster Farms' stock.The dividend is projected to increase at a constant rate of 5.50% per year.The required rate of return on the stock,r_s,is 9.00%.What is the stock's expected price 3 years from today?

If D₀ = $1.75,g (which is constant) = 3.6%,and P₀ = $32.00,what is the stock's expected total return for the coming year?

If D₁ = $1.25,g (which is constant) = 5.5%,and P₀ = $44,what is the stock's expected total return for the coming year?

The Jameson Company just paid a dividend of $0.75 per share,and that dividend is expected to grow at a constant rate of 5.50% per year in the future.The company's beta is 1.15,the market risk premium is 5.00%,and the risk-free rate is 4.00%.What is Jameson's current stock price,P₀?

A share of Lash Inc.'s common stock just paid a dividend of $1.00.If the expected long-run growth rate for this stock is 5.4%,and if investors' required rate of return is 11.4%,what is the stock price?

A stock is expected to pay a dividend of $0.75 at the end of the year.The required rate of return is r_s = 10.5%,and the expected constant growth rate is g = 6.4%.What is the stock's current price?

Young & Liu Inc.'s free cash flow during the just-ended year (t = 0) was $100 million,and FCF is expected to grow at a constant rate of 5% in the future.If the weighted average cost of capital is 15%,what is the firm's value of operations,in millions?

Gere Furniture forecasts a free cash flow of $40 million in Year 3,i.e.,at t = 3,and it expects FCF to grow at a constant rate of 5% thereafter.If the weighted average cost of capital is 10% and the cost of equity is 15%,what is the horizon value,in millions at t = 3?

Franklin Corporation is expected to pay a dividend of $1.25 per share at the end of the year (D₁ = $1.25) .The stock sells for $32.50 per share,and its required rate of return is 10.5%.The dividend is expected to grow at some constant rate,g,forever.What is the equilibrium expected growth rate?

If D₀ = $2.25,g (which is constant) = 3.5%,and P₀ = $50,what is the stock's expected dividend yield for the coming year?

Quiz 7: Valuation of Stocks and Corporations

If D1 = $1.50,g (which is constant) = 6.5%,and P0 = $56,what is the stock's expected capital gains yield for the coming year?

Kelly Enterprises' stock currently sells for $35.25 per share.The dividend is projected to increase at a constant rate of 4.75% per year.The required rate of return on the stock,rs,is 11.50%.What is the stock's expected price 5 years from now?

If D1 = $1.25,g (which is constant) = 4.7%,and P0 = $26.00,what is the stock's expected dividend yield for the coming year?

Kellner Motor Co.'s stock has a required rate of return of 11.50%,and it sells for $25.00 per share.Kellner's dividend is expected to grow at a constant rate of 7.00%.What was the last dividend,D0?

A stock just paid a dividend of D0 = $1.50.The required rate of return is rs = 10.1%,and the constant growth rate is g = 4.0%.What is the current stock price?

The projected cash flow for the next year for Minesuah Inc.is $100,000,and FCF is expected to grow at a constant rate of 6%.If the company's weighted average cost of capital is 11%,what is the value of its operations?

Carby Hardware has an outstanding issue of perpetual preferred stock with an annual dividend of $7.50 per share.If the required return on this preferred stock is 6.5%,at what price should the preferred stock sell?

$35.50 per share is the current price for Foster Farms' stock.The dividend is projected to increase at a constant rate of 5.50% per year.The required rate of return on the stock,rs,is 9.00%.What is the stock's expected price 3 years from today?

If D0 = $1.75,g (which is constant) = 3.6%,and P0 = $32.00,what is the stock's expected total return for the coming year?

If D1 = $1.25,g (which is constant) = 5.5%,and P0 = $44,what is the stock's expected total return for the coming year?

The Jameson Company just paid a dividend of $0.75 per share,and that dividend is expected to grow at a constant rate of 5.50% per year in the future.The company's beta is 1.15,the market risk premium is 5.00%,and the risk-free rate is 4.00%.What is Jameson's current stock price,P0?

A share of Lash Inc.'s common stock just paid a dividend of $1.00.If the expected long-run growth rate for this stock is 5.4%,and if investors' required rate of return is 11.4%,what is the stock price?

A stock is expected to pay a dividend of $0.75 at the end of the year.The required rate of return is rs = 10.5%,and the expected constant growth rate is g = 6.4%.What is the stock's current price?

Young & Liu Inc.'s free cash flow during the just-ended year (t = 0) was $100 million,and FCF is expected to grow at a constant rate of 5% in the future.If the weighted average cost of capital is 15%,what is the firm's value of operations,in millions?

Gere Furniture forecasts a free cash flow of $40 million in Year 3,i.e.,at t = 3,and it expects FCF to grow at a constant rate of 5% thereafter.If the weighted average cost of capital is 10% and the cost of equity is 15%,what is the horizon value,in millions at t = 3?

Franklin Corporation is expected to pay a dividend of $1.25 per share at the end of the year (D1 = $1.25) .The stock sells for $32.50 per share,and its required rate of return is 10.5%.The dividend is expected to grow at some constant rate,g,forever.What is the equilibrium expected growth rate?

If D0 = $2.25,g (which is constant) = 3.5%,and P0 = $50,what is the stock's expected dividend yield for the coming year?

If D₁ = $1.50,g (which is constant) = 6.5%,and P₀ = $56,what is the stock's expected capital gains yield for the coming year?

Kelly Enterprises' stock currently sells for $35.25 per share.The dividend is projected to increase at a constant rate of 4.75% per year.The required rate of return on the stock,r_s,is 11.50%.What is the stock's expected price 5 years from now?

If D₁ = $1.25,g (which is constant) = 4.7%,and P₀ = $26.00,what is the stock's expected dividend yield for the coming year?

Kellner Motor Co.'s stock has a required rate of return of 11.50%,and it sells for $25.00 per share.Kellner's dividend is expected to grow at a constant rate of 7.00%.What was the last dividend,D₀?

A stock just paid a dividend of D₀ = $1.50.The required rate of return is r_s = 10.1%,and the constant growth rate is g = 4.0%.What is the current stock price?

$35.50 per share is the current price for Foster Farms' stock.The dividend is projected to increase at a constant rate of 5.50% per year.The required rate of return on the stock,r_s,is 9.00%.What is the stock's expected price 3 years from today?

If D₀ = $1.75,g (which is constant) = 3.6%,and P₀ = $32.00,what is the stock's expected total return for the coming year?

If D₁ = $1.25,g (which is constant) = 5.5%,and P₀ = $44,what is the stock's expected total return for the coming year?

The Jameson Company just paid a dividend of $0.75 per share,and that dividend is expected to grow at a constant rate of 5.50% per year in the future.The company's beta is 1.15,the market risk premium is 5.00%,and the risk-free rate is 4.00%.What is Jameson's current stock price,P₀?

A stock is expected to pay a dividend of $0.75 at the end of the year.The required rate of return is r_s = 10.5%,and the expected constant growth rate is g = 6.4%.What is the stock's current price?

Franklin Corporation is expected to pay a dividend of $1.25 per share at the end of the year (D₁ = $1.25) .The stock sells for $32.50 per share,and its required rate of return is 10.5%.The dividend is expected to grow at some constant rate,g,forever.What is the equilibrium expected growth rate?

If D₀ = $2.25,g (which is constant) = 3.5%,and P₀ = $50,what is the stock's expected dividend yield for the coming year?