Alexas Corporation reports the following:
$$\begin{array} { l l }
& \mathbf { 2 0 0 5 } \
\text { Earnings per share } & \$ 1.80 \
\text { Dividends per share } & \$ 0.72 \
\text { Book value per share- at the end of the } &\$ 8.62\
\text { year } &
\end{array}$$
-Analysts' expected earnings for Alexas for next two years are:

2006: $2.00
2007: $2.23

Cost of equity is 15%. Return on equity is expected to equal cost of equity from 2008 onwards. Dividend payout ratio is expected to remain the same for 2006 and 2007. Price per share at the end of 2005 would be closest to:

A)$9.45.
B)$9.81.
C)$9.89.
D)Not determinable

Question

Alexas Corporation reports the following:
 $$\begin{array} { l l } 
& \mathbf { 2 0 0 5 } \
\text { Earnings per share } & \$ 1.80 \
\text { Dividends per share } & \$ 0.72 \
\text { Book value per share- at the end of the } &\$ 8.62\
\text { year } & 
\end{array}$$
-Analysts' expected earnings for Alexas for next two years are:

2006: $2.00
2007: $2.23

Cost of equity is 15%. Return on equity is expected to equal cost of equity from 2008 onwards. Dividend payout ratio is expected to remain the same for 2006 and 2007. Price per share at the end of 2005 would be closest to:

A)$9.45.
B)$9.81.
C)$9.89.
D)Not determinable

Quizplus · Accepted Answer

To calculate the price per share at the end of 2005, we use the Dividend Discount Model (DDM) for a multi-stage model since the dividend growth rate changes after 2007. The dividend payout ratio is constant for 2006 and 2007, and it is given by dividends per share in 2005 divided by earnings per share in 2005, which is $0.72 / $1.80 = 0.4 or 40%. For 2006 and 2007, we calculate dividends as follows:- 2006: $2.00 * 0.4 = $0.80- 2007: $2.23 * 0.4 = $0.892The cost of equity is 15%, and from 2008 onwards, the return on equity (ROE) is expected to equal the cost of equity, implying that the growth rate of dividends and earnings will also be 15% from 2008 onwards. To find the price at the end of 2005, we calculate the present value of dividends in 2006 and 2007, plus the present value of the price at the end of 2007. The price at the end of 2007 can be calculated using the Gordon Growth Model since from 2008 onwards, the growth rate is constant at 15%. The Gordon Growth Model formula for the price at the end of 2007 is:$$ P_{2007} = \frac{D_{2008}}{k - g} $$where $D_{2008}$ is the dividend in 2008, $k$ is the cost of equity, and $g$ is the growth rate. Since the dividend payout ratio and ROE are equal from 2008, the dividend in 2008 can be calculated as:$$ D_{2008} = 2.23 * 1.15 * 0.4 = 1.0251 $$Thus, the price at the end of 2007 is:$$ P_{2007} = \frac{1.0251}{0.15 - 0.15} $$However, since the growth rate equals the cost of equity, we adjust our approach to calculate the terminal value using the book value per share and ROE. This approach is necessary because the formula becomes indeterminate when $g = k$. Given the complexities in calculating the terminal value directly due to the growth rate equaling the cost of equity, we focus on the dividends and the information provided to calculate the price per share at the end of 2005 using the present value of future dividends and assuming a constant growth or a model that fits the given data. The correct calculation involves discounting the dividends and the terminal price (which would typically be calculated with a model suitable for when ROE equals the cost of equity) back to the present value at the end of 2005. However, without the terminal price calculation directly provided or a clear method to adjust for the indeterminate form of the Gordon Growth Model under these conditions, the detailed calculation steps are not fully outlined here. Given the information and typical approaches to valuation, the answer involves estimating the present value of future dividends and any terminal value based on the assumptions provided, but the exact value given the scenario described would require additional steps or assumptions not fully detailed in the explanation. The selection of choice B suggests a specific numerical answer, but the explanation provided does not fully detail the terminal value calculation under the scenario where the growth rate equals the cost of equity from 2008 onwards, indicating a need for a model adjustment or additional assumptions for a complete valuation.

Alexas Corporation Reports the Following -Analysts' Expected Earnings for Alexas for Next Two Years Are