# The market capitalization rate for Admiral Motors Company is 10%. Its expected ROE is 15% and its...

## Question:

The market capitalization rate for Admiral Motors Company is 10%. Its expected ROE is 15% and its expected EPS is \$7. If the firm's plowback ratio is 50%.

a) Calculate the growth rate.

b) What will be its P/E ratio?

## Sustainable Growth Rate:

The sustainable growth rate of a firm is the maximum rate of growth a firm can sustain without changing its capital structure. In this case, the firm's total assets will grow in proportion to its total equity and total debt.

a) We can use the following formula to compute the growth rate:

• sustainable growth rate = ROE *plowback ratio
• sustainable growth rate = 15% * 50%
• sustainable growth rate = 7.5%

b) We can use the dividend growth model to compute the price of the stock:

• price per share = dividend per share *(1 + growth rate) /(required return - dividend growth rate)
• price per share = 7 * (1 - 50%) * (1 + 7.5%) / (10% - 7.5%)
• price per share = 150.5

The price-earnings (PE ratio) = price per share / earnings per share = 150.5 / 2.7 = 55.74