Byron Corporation's present capital structure, which is also its target capital structure, is 40 percent debt and 60 percent common equity. Next year's net income is projected to be $21,000, and Byron's payout ratio is 30 percent. The company's earnings and dividends are growing at a constant rate of 5 percent; the last dividend was $2.00; and the current equilibrium stock price is $21.88. Byron can raise all the debt financing it needs at 14 percent. If Byron issues new common stock, a 20 percent flotation cost will be incurred. The firm's marginal tax rate is 40 percent. What is the maximum amount of new capital that can be raised at the lowest component cost of equity?
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BP(RE) = $21,000 x .70/ .60 = $24,500.
To calculate the maximum amount of new capital that can be raised at the lowest component cost of equity, we need to determine the cost of each component of capital (debt and equity) and find the optimal capital structure.
Given information:
Let's calculate the cost of each component of capital:
Cost of debt (rd): The cost of debt is given as 14%.
Cost of equity (re): To calculate the cost of equity, we will use the Dividend Discount Model (DDM). The DDM formula is as follows:
re = (Div1 / P0) + g
Where: Div1 = Dividend expected to be paid next year P0 = Current equilibrium stock price g = Growth rate of earnings and dividends
First, we need to calculate Div1. Since the payout ratio is 30%, the dividend payout would be 30% of the net income:
Div1 = Net income × Payout ratio = $21,000 × 30% = $6,300
Now we can calculate the cost of equity:
re = ($6,300 / $21.88) + 5% = 28.83%
WACC = (wd × rd) + (we × re)
Where: wd = Weight of debt we = Weight of equity
The weights can be calculated based on the target capital structure:
wd = 40% = 0.4 we = 60% = 0.6
Now we can calculate the WACC:
WACC = (0.4 × 14%) + (0.6 × 28.83%) = 21.94%
To find the maximum amount of new capital that can be raised at the lowest component cost of equity, we need to determine the point where the cost of equity (re) is minimized. The lowest cost of equity is obtained when the firm's capital structure consists only of equity (i.e., no debt).
To find the amount of new capital at this point, we use the formula:
Amount of new capital = (Market value of equity / Cost of equity) - Existing equity
The market value of equity is calculated by dividing the current equilibrium stock price by the growth rate:
Market value of equity = P0 / g = $21.88 / 5% = $437.60
Existing equity is the current market value of equity minus the new capital:
Existing equity = Market value of equity - Amount of new capital
Substituting the values, we get:
$437.60 = ($437.60 / re) - Amount of new capital
Rearranging the equation, we find:
Amount of new capital = $437.60 - ($437.60 / re)
Substituting the value of re, we get:
Amount of new capital = $437.60 - ($437.60 / 28.83%) = $437.60 - $1,518.47 = -$1,080.87
The negative amount indicates that no new capital can be raised at the lowest cost of equity. Therefore, the maximum amount of new capital that can be raised at the lowest component cost of equity is $0.