Chapter 7, Problem 12QP

a.

Summary Introduction

To determine: The expected dividends for year 1, 2 and 3.

Answer to Problem 12QP

The expected dividends for year 1 are $1.04, year 2 are $1.08 and year 3 are $1.12.

Explanation of Solution

Determine the expected dividends for year 1, 2 and 3

$\begin{array}{c}Dividends\left(D_1\right)=\left[CurrentDividends\left(D_0\right)\times \left(1+GrowthRate\left(g\right)\right)\right]\\ =\left[\$1\times \left(1+4\%\right)\right]\\ =\$1.04\\ Dividends\left(D_2\right)=\left[CurrentDividends\left(D_1\right)\times \left(1+GrowthRate\left(g\right)\right)\right]\\ =\left[\$1.04\times \left(1+4\%\right)\right]\\ =\$1.0816or\$1.08\\ Dividends\left(D_3\right)=\left[CurrentDividends\left(D_2\right)\times \left(1+GrowthRate\left(g\right)\right)\right]\\ =\left[\$1.0816\times \left(1+4\%\right)\right]\\ =\$1.124864or\$1.12\end{array}$

Therefore, the expected dividends for year 1 are $1.04, year 2 are $1.08 and year 3 are $1.12.

b.

Summary Introduction

To determine: The selling price of stock.

Answer to Problem 12QP

The selling price of stockis $13.

Explanation of Solution

Determine the selling price of stock

$\begin{array}{c}ValueofStock\left(P_0\right)=\left[\frac{CurrentDividends\left(D_0\right)}{\mathrm{Re}quired\mathrm{Re}turn\left(r\right)-GrowthRate\left(g\right)}\right]\\ =\left[\frac{\$1.04}{12\%-4\%}\right]\\ =\$13\end{array}$

Therefore, the selling price of stockis $13.

c.

Summary Introduction

To determine: The projected stock price three years from now.

Answer to Problem 12QP

The projected stock price three years from nowis $14.62.

Explanation of Solution

Determine the projected stock price three years from now

$\begin{array}{c}ExpectedStock\mathrm{Pr}ice\left(P_0\right)=\left[\frac{CurrentDividends\left(D_3\right)\times \left(1+GrowthRate\left(g\right)\right)}{\mathrm{Re}quired\mathrm{Re}turn\left(r\right)-GrowthRate\left(g\right)}\right]\\ =\left[\frac{\$1.124864\times \left(1+4\%\right)}{12\%-4\%}\right]\\ =\$14.623232or\$14.62\end{array}$

Therefore, the projected stock price three years from nowis $14.62.

d.

Summary Introduction

To determine: The projectedcash flows for years 1, 2 and 3.

Answer to Problem 12QP

The projectedcash flows for years 1 are $1.04, year 2 are $1.08 and year 3 are $15.75.

Explanation of Solution

Determine the projected cash flows for years 1, 2 and 3

The cash flows for year 1 and 2 will remain same as $1.04 and $1.08 respectively since the purchase happens only in year 3. The cash flow for year 3 is calculated below,

$\begin{array}{c}CashFlo{w}_{Year3}=\left[CurrentDividends\left(D_3\right)+ExpectedStock\mathrm{Pr}ice\left(P_0\right)\right]\\ =\left[\$1.124864+\$14.623232\right]\\ =\$15.748096or\$15.75\end{array}$

Therefore, the cash flows for year 3 is $15.75.

e.

Summary Introduction

To determine: The present value of stream of payments.

Answer to Problem 12QP

The present value of stream of payments for year 1 are $0.93, year 2 are $0.86 and year 3 are $11.21.

Explanation of Solution

Determine the cash flows for year 1, 2 and 3

Excel Spreadsheet:

Excel Workings:

Therefore, the present value of stream of payments for year 1 are $0.93, year 2 are $0.86 and year 3 are $11.21.