The problem provides financial information about Skyworth, including its capital structure, bond details, stock information, and dividend growth. It asks to calculate: 1. The net proceed from issuing common stock.

Applied MathematicsFinancial MathematicsCost of CapitalWeighted Average Cost of CapitalGordon Growth ModelFinance
2025/7/8

1. Problem Description

The problem provides financial information about Skyworth, including its capital structure, bond details, stock information, and dividend growth. It asks to calculate:

1. The net proceed from issuing common stock.

2. The firm's cost of a new issue of common stock.

3. The weighted average cost of capital.

4. The firm's cost of retained earnings.

2. Solution Steps

First, we need to calculate the net proceeds from issuing common stock.
The stock price is $
4

0. The underpricing cost is $3 per share.

The flotation cost is $1.5 per share.
The net proceed from issuing common stock is:
Net Proceed=Stock PriceUnderpricing CostFlotation CostNet\ Proceed = Stock\ Price - Underpricing\ Cost - Flotation\ Cost
Net Proceed=4031.5=35.5Net\ Proceed = 40 - 3 - 1.5 = 35.5
Second, we need to calculate the firm's cost of a new issue of common stock.
We can use the Gordon Growth Model, adjusted for flotation costs and underpricing.
Cost of Equity=D1P0Flotation CostUnderpricing+gCost\ of\ Equity = \frac{D_1}{P_0 - Flotation\ Cost - Underpricing} + g
Cost of Equity=2.4401.53+0.06Cost\ of\ Equity = \frac{2.4}{40 - 1.5 - 3} + 0.06
Cost of Equity=2.435.5+0.06Cost\ of\ Equity = \frac{2.4}{35.5} + 0.06
Cost of Equity=0.0676+0.06Cost\ of\ Equity = 0.0676 + 0.06
Cost of Equity=0.1276Cost\ of\ Equity = 0.1276
Third, we need to calculate the weighted average cost of capital (WACC).
The problem states that 65% of the fund is equity, and the remaining (35%) is debt.
The after-tax cost of debt is 0.
0
7
4

5. The cost of equity is 0.

1
2
7

6. $WACC = (Weight\ of\ Equity \times Cost\ of\ Equity) + (Weight\ of\ Debt \times After-tax\ Cost\ of\ Debt)$

WACC=(0.65×0.1276)+(0.35×0.0745)WACC = (0.65 \times 0.1276) + (0.35 \times 0.0745)
WACC=0.08294+0.026075WACC = 0.08294 + 0.026075
WACC=0.109015WACC = 0.109015
Fourth, we need to calculate the firm's cost of retained earnings.
The cost of retained earnings uses the stock price without adjusting for flotation costs and underpricing.
Cost of Retained Earnings=D1P0+gCost\ of\ Retained\ Earnings = \frac{D_1}{P_0} + g
Cost of Retained Earnings=2.440+0.06Cost\ of\ Retained\ Earnings = \frac{2.4}{40} + 0.06
Cost of Retained Earnings=0.06+0.06Cost\ of\ Retained\ Earnings = 0.06 + 0.06
Cost of Retained Earnings=0.12Cost\ of\ Retained\ Earnings = 0.12

3. Final Answer

1. The net proceed from issuing common stock: 35.5

2. The firm's cost of a new issue of common stock: 0.1276

3. The weighted average cost of capital: 0.109015

4. The firm's cost of retained earnings: 0.12

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