Give step-by-step solution with explanation and final answer:Ee er ned

eR EE Re

to eA et

amo ee es mn mt
p———

EE = 5

Re i i RN
{Corr —

if
Re en re cn
Ee LE
TTT BE ie “a

Question

Give step-by-step solution with explanation and final answer:Ee er ned

eR EE Re

to eA et

amo ee es mn mt
p———

EE = 5

Re i i RN
{Corr —

if
Re en re cn
Ee LE
TTT BE ie “a

VIPSolutions · Accepted Answer

Let's solve each part step by step:

---

## **Given Data**
- **Capital Structure:**
  - Debt: **45%**
  - Preferred stock: **20%**
  - Common equity: **35%** (initially all from retained earnings)
- **Costs:**
  - After-tax cost of debt ($ K_d $): **6.2%**
  - Cost of preferred stock ($ K_{ps} $): **9%**
  - Cost of retained earnings ($ K_{re} $): **9.8%**
  - Cost of new common stock ($ K_{ne} $): **12%**
- **Retained earnings available:** $14 million

---

### **a. Initial Weighted Average Cost of Capital (WACC)**

WACC formula:
$$
\text{WACC} = (w_d \cdot K_d) + (w_{ps} \cdot K_{ps}) + (w_{ce} \cdot K_{re})
$$
Where:
- $ w_d = 0.45 $
- $ K_d = 6.2\% $
- $ w_{ps} = 0.20 $
- $ K_{ps} = 9\% $
- $ w_{ce} = 0.35 $
- $ K_{re} = 9.8\% $

Calculate each component:
- Debt: $ 0.45 \times 6.2 = 2.79 $
- Preferred stock: $ 0.20 \times 9 = 1.80 $
- Common equity: $ 0.35 \times 9.8 = 3.43 $

Sum:
$$
\text{WACC} = 2.79 + 1.80 + 3.43 = 8.02\%
$$

#### **Table:**
| Source           | Weighted Cost |
|------------------|--------------|
| Debt             | 2.79%        |
| Preferred stock  | 1.80%        |
| Common equity    | 3.43%        |
| **WACC**         | **8.02%**    |

---

### **b. Dollar Amount of Capital Supported by Retained Earnings**

Let $ X $ be the total capital raised before exhausting retained earnings.

Since common equity is 35% of capital structure:
$$
0.35X = \$14 \text{ million}
$$
$$
X = \frac{14}{0.35} = \$40 \text{ million}
$$

**Answer:**  
$$
\boxed{40.00 \text{ million}}
$$

---

### **c. Marginal Cost of Capital After Retained Earnings Are Used Up**

After retained earnings are used, new equity must be issued at a cost of **12%**.

So, WACC becomes:
$$
\text{WACC} = (0.45 \times 6.2) + (0.20 \times 9) + (0.35 \times 12)
$$

Calculate:
- Debt: $ 0.45 \times 6.2 = 2.79 $
- Preferred stock: $ 0.20 \times 9 = 1.80 $
- New common equity: $ 0.35 \times 12 = 4.20 $

Sum:
$$
\text{WACC} = 2.79 + 1.80 + 4.20 = 8.79\%
$$

---

## **Final Answers**

**a. Initial WACC:**  
$$
\boxed{8.02\%}
$$

**b. Capital supported by retained earnings:**  
$$
\boxed{40.00 \text{ million}}
$$

**c. Marginal cost of capital after retained earnings:**  
$$
\boxed{8.79\%}
$$

---

Let me know if you need any clarification!

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Give step-by-step solution with explanation and final answer:Ee er ned eR EE Re to eA et amo ee es mn mt p——— EE = 5 Re i i RN {Corr — if Re en re cn Ee LE TTT BE ie “a

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