QuestionFind the max price per share for Grips Tool if growth is 25% for 3 years, then 10%, and required return is 15%.

Studdy Solution

STEP 1

Assumptions1. Grips Tool's earnings per share in the last year were $4.25. Grips Tool's dividends per share in the last year were$ .55 (0 = $.55)
3. Grips Tool's earnings and dividends are expected to grow at25% per year for the next3 years4. After3 years, Grips Tool's earnings and dividends are expected to grow at10% per year indefinitely5. Newman Manufacturing requires a return of15% on investments with similar risk characteristics to Grips Tool

STEP 2

First, we need to calculate the dividends for the next years. We can do this by multiplying the current dividend by the growth rate for each year.
$1 = D0 \times (1 + g_{short})$ $2 = D1 \times (1 + g_{short})$ $= D2 \times (1 + g_{short})$ where $0$ is the current dividend, $g_{short}$ is the short-term growth rate (25%).

STEP 3

Plug in the given values for the current dividend and short-term growth rate to calculate the dividends for the next3 years.
$1 = \$2.55 \times (1 +25\%)$ $2 = D1 \times (1 +25\%)$ $3 = D2 \times (1 +25\%)$

STEP 4

Convert the percentage to a decimal value.
$25\% =0.25$ $1 = \$2.55 \times (1 +0.25)$ $2 = D1 \times (1 +0.25)$ $3 = D2 \times (1 +0.25)$

STEP 5

Calculate the dividends for the next3 years.

STEP 6

Next, we need to calculate the present value of these dividends. We can do this by dividing each dividend by $(1 + r)^n$ , where $r$ is the required return and $n$ is the year number.
$PV(D1) = \frac{1}{(1 + r)^1}$ $PV(D2) = \frac{2}{(1 + r)^2}$ $PV(D3) = \frac{3}{(1 + r)^3}$

STEP 7

Plug in the given values for the required return and the dividends to calculate the present value of the dividends for the next3 years.
$PV(D1) = \frac{1}{(1 +15\%)^1}$ $PV(D2) = \frac{2}{(1 +15\%)^2}$ $PV(D3) = \frac{3}{(1 +15\%)^3}$

STEP 8

Convert the percentage to a decimal value.
$15\% =0.15$ $PV(D1) = \frac{1}{(1 +0.15)^1}$ $PV(D2) = \frac{2}{(1 +0.15)^2}$ $PV(D3) = \frac{3}{(1 +0.15)^3}$

STEP 9

Calculate the present value of the dividends for the next3 years.

STEP 10

Next, we need to calculate the price of the stock at the end of year3. We can do this using the Gordon Growth Model, which is $3 = \frac{4}{r - g_{long}}$ , where $4$ is the dividend in year4, $r$ is the required return, and $g_{long}$ is the long-term growth rate.

STEP 11

First, calculate the dividend in year4. This is $4 = D3 \times ( + g_{long})$ .

STEP 12

Plug in the given values for the dividend in year and the long-term growth rate to calculate the dividend in year4.
$4 = D \times ( +10\%)$

STEP 13

Convert the percentage to a decimal value.
$10\% =0.$ $= D3 \times ( +0.)$

STEP 14

Calculate the dividend in year4.

STEP 15

Next, calculate the price of the stock at the end of year3. $3 = \frac{4}{r - g_{long}}$

STEP 16

Plug in the given values for the dividend in year4, the required return, and the long-term growth rate to calculate the price of the stock at the end of year3.
$3 = \frac{4}{15\% -10\%}$

STEP 17

Convert the percentages to decimal values.
$15\% =0.15$ $10\% =0.$ $3 = \frac{4}{0.15 -0.}$

STEP 18

Calculate the price of the stock at the end of year3.

STEP 19

Next, calculate the present value of the price of the stock at the end of year3. This is $PV(P3) = \frac{3}{(1 + r)^3}$ .

STEP 20

Plug in the given values for the price of the stock at the end of year3 and the required return to calculate the present value of the price of the stock at the end of year3.
$PV(P3) = \frac{3}{( +15\%)^3}$

STEP 21

Convert the percentage to a decimal value.
$15\% =0.15$ $PV(P3) = \frac{3}{(1 +0.15)^3}$

STEP 22

Calculate the present value of the price of the stock at the end of year.

STEP 23

Finally, calculate the maximum price per share that Newman should pay for Grips. This is the sum of the present value of the dividends for the next3 years and the present value of the price of the stock at the end of year3.
$0 = PV(D1) + PV(D) + PV(D3) + PV(P3)$

STEP 24

Plug in the values for the present value of the dividends and the present value of the price of the stock to calculate the maximum price per share.

STEP 25

Calculate the maximum price per share that Newman should pay for Grips.

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