King Waterbeds has an annual cash dividend policy that raises the dividend each year by 4%. The most recent dividend, Div 0, was $ 0.50 per share. What is the stock's price if a. an investor wants a return of 7%? b. an investor wants a return of 10%? c. an investor wants a return of 11%? d. an investor wants a return of 15%? e. an investor wants a return of 18%? a. What is the stock's price if an investor wants a return of 7%? $ nothing (Round to the nearest cent.)

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18-03-2020
Business

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King Waterbeds has an annual cash dividend policy that raises the dividend each year by 4%. The most recent dividend, Div 0, was $ 0.50 per share. What is the stock's price if a. an investor wants a return of 7%? b. an investor wants a return of 10%? c. an investor wants a return of 11%? d. an investor wants a return of 15%? e. an investor wants a return of 18%? a. What is the stock's price if an investor wants a return of 7%? $ nothing (Round to the nearest cent.)

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Answer:

a) With a 7% return, the current stock price = $34.67.

b) The current stock price = $17.33, with a 10% return.

c) The current stock price = $14.86, with a 11% return.

d) The current stock price = $9.45, with a 15% return.

e) Current stock price = $7.43 assuming the interest rate is 18%

Explanation:

Requirement A

An investor wants a return of 7%,

We know,

Dividend-growth model, stock price, [tex]P_{0}[/tex] = [tex]D_{1}[/tex] ÷ ([tex]K_{e}[/tex] - g)

Here,

[tex]P_{0}[/tex] = Today's stock price = ?

[tex]k_{e}[/tex] = 7% = 0.07

g = growth rate = 4% = 0.04

[tex]D_{1}[/tex] = Next year dividend = [tex]D_{0}*(1 + g)[/tex] = $0.50 × (1 + 0.04) = $0.50 × 1.04 = $0.52

Putting the values into the above formula, we can get,

[tex]P_{0}[/tex] = [tex]D_{1}[/tex] ÷ ([tex]K_{e}[/tex] - g)

[tex]P_{0}[/tex] = $1.04 ÷ (0.07 - 0.04)

or, [tex]P_{0}[/tex] = $1.04 ÷ 0.03

Hence with a 7% return, the current stock price = $34.67.

Requirement B

An investor wants a return of 10%,

We know,

Dividend-growth model, stock price, [tex]P_{0}[/tex] = [tex]D_{1}[/tex] ÷ ([tex]K_{e}[/tex] - g)

Here,

[tex]P_{0}[/tex] = Today's stock price = ?

[tex]k_{e}[/tex] = 10% = 0.10

g = growth rate = 4% = 0.04

[tex]D_{1}[/tex] = Next year dividend = [tex]D_{0}*(1 + g)[/tex] = $0.50 × (1 + 0.04) = $0.50 × 1.04 = $0.52

Putting the values into the above formula, we can get,

[tex]P_{0}[/tex] = [tex]D_{1}[/tex] ÷ ([tex]K_{e}[/tex] - g)

[tex]P_{0}[/tex] = $1.04 ÷ (0.10 - 0.04)

or, [tex]P_{0}[/tex] = $1.04 ÷ 0.06

Hence the current stock price = $17.33, with a 10% return.

Requirement C

An investor wants a return of 11%,

We know,

Dividend-growth model, stock price, [tex]P_{0}[/tex] = [tex]D_{1}[/tex] ÷ ([tex]K_{e}[/tex] - g)

Here,

[tex]P_{0}[/tex] = Today's stock price = ?

[tex]k_{e}[/tex] = 11% = 0.11

g = growth rate = 4% = 0.04

[tex]D_{1}[/tex] = Next year dividend = [tex]D_{0}*(1 + g)[/tex] = $0.50 × (1 + 0.04) = $0.50 × 1.04 = $0.52

Putting the values into the above formula, we can get,

[tex]P_{0}[/tex] = [tex]D_{1}[/tex] ÷ ([tex]K_{e}[/tex] - g)

[tex]P_{0}[/tex] = $1.04 ÷ (0.11 - 0.04)

or, [tex]P_{0}[/tex] = $1.04 ÷ 0.07

Hence the current stock price = $14.86, with a 11% return.

Requirement D

An investor wants a return of 15%,

We know,

Dividend-growth model, stock price, [tex]P_{0}[/tex] = [tex]D_{1}[/tex] ÷ ([tex]K_{e}[/tex] - g)

Here,

[tex]P_{0}[/tex] = Today's stock price = ?

[tex]k_{e}[/tex] = 15% = 0.15

g = growth rate = 4% = 0.04

[tex]D_{1}[/tex] = Next year dividend = [tex]D_{0}*(1 + g)[/tex] = $0.50 × (1 + 0.04) = $0.50 × 1.04 = $0.52

Putting the values into the above formula, we can get,

[tex]P_{0}[/tex] = [tex]D_{1}[/tex] ÷ ([tex]K_{e}[/tex] - g)

[tex]P_{0}[/tex] = $1.04 ÷ (0.15 - 0.04)

or, [tex]P_{0}[/tex] = $1.04 ÷ 0.11

Hence the current stock price = $9.45, with a 15% return.

Requirement E

An investor wants a return of 18%,

We know,

Dividend-growth model, stock price, [tex]P_{0}[/tex] = [tex]D_{1}[/tex] ÷ ([tex]K_{e}[/tex] - g)

Here,

[tex]P_{0}[/tex] = Today's stock price = ?

[tex]k_{e}[/tex] = 18% = 0.18

g = growth rate = 4% = 0.04

[tex]D_{1}[/tex] = Next year dividend = [tex]D_{0}*(1 + g)[/tex] = $0.50 × (1 + 0.04) = $0.50 × 1.04 = $0.52

Putting the values into the above formula, we can get,

[tex]P_{0}[/tex] = [tex]D_{1}[/tex] ÷ ([tex]K_{e}[/tex] - g)

[tex]P_{0}[/tex] = $1.04 ÷ (0.18 - 0.04)

or, [tex]P_{0}[/tex] = $1.04 ÷ 0.14

Hence the current stock price = $7.43, with a 18% return.