Joylin, Incorporated, has equity with a market value of $
2
2
.
6
million and debt with a market value of $
1
1
.
3
million. Treasury bills that mature in one year yield
4
percent per year

an

Question

Joylin, Incorporated, has equity with a market value of $
2
2
.
6
 ﻿million and debt with a market value of $
1
1
.
3
 ﻿million. Treasury bills that mature in one year yield 
4
 ﻿percent per year
 
and the expected return on the market portfolio is 
1
0
 ﻿percent. The beta of the company
’
s equity is 
1
.
1
1
.
 ﻿The company pays no taxes.

﻿a
.
What is the company's debt
-
equity ratio? 
(
Do not round intermediate calculations and round your answer to 
2
 ﻿decimal places, e
.
g
.
,
 
3
2
.
1
6
.
)
b
.
What is the company
’
s weighted average cost of capital? 
(
Do not round intermediate calculations and enter your answer as a percent rounded to 
2
 ﻿decimal places, e
.
g
.
,
 
3
2
.
1
6
.
)
c
.
What is the cost of capital for an otherwise identical all
-
equity company?

VIPSolutions · Accepted Answer

Let's break down each part step by step:

**Given:**
- Market value of equity ($E$) = $2.6 million
- Market value of debt ($D$) = $1.3 million
- Risk-free rate ($r_f$) = 4%
- Expected return on market ($r_m$) = 10%
- Beta of equity ($\beta_E$) = 1.11
- No taxes

---

### a. **Debt-Equity Ratio**

$$
\text{Debt-Equity Ratio} = \frac{D}{E} = \frac{1.3}{2.6} = 0.50
$$

**Answer:**  
$$
\boxed{0.50}
$$

---

### b. **Weighted Average Cost of Capital (WACC)**

#### 1. **Cost of Equity ($r_E$) using CAPM:**

$$
r_E = r_f + \beta_E (r_m - r_f)
$$
$$
r_E = 0.04 + 1.11 \times (0.10 - 0.04) = 0.04 + 1.11 \times 0.06 = 0.04 + 0.0666 = 0.1066 \text{ or } 10.66\%
$$

#### 2. **Cost of Debt ($r_D$):**

- Debt is risk-free (T-bills), so $ r_D = r_f = 4\% $

#### 3. **WACC Formula (no taxes):**

$$
\text{WACC} = \frac{E}{D+E} r_E + \frac{D}{D+E} r_D
$$

Calculate weights:
- $ E/(D+E) = 2.6/(1.3+2.6) = 2.6/3.9 = 0.6667 $
- $ D/(D+E) = 1.3/3.9 = 0.3333 $

Plug in values:
$$
\text{WACC} = 0.6667 \times 0.1066 + 0.3333 \times 0.04
$$
$$
= 0.07107 + 0.01333 = 0.0844 \text{ or } 8.44\%
$$

**Answer:**  
$$
\boxed{8.44\%}
$$

---

### c. **Cost of Capital for an All-Equity Company ($r_{A}$)**

This is the unlevered cost of capital. For an all-equity firm with the same business risk as the current firm, the cost of capital would be the cost of equity **if there were no debt**.  
So, use the **unlevered beta** ($\beta_A$) and plug it into CAPM.

#### 1. **Unlevered Beta ($\beta_A$):**
Since debt is risk-free and there are no taxes:
$$
\beta_A = \frac{E}{D+E} \beta_E + \frac{D}{D+E} \beta_D
$$
But $\beta_D = 0$ (risk-free), so:
$$
\beta_A = \frac{2.6}{3.9} \times 1.11 + \frac{1.3}{3.9} \times 0 = 0.6667 \times 1.11 = 0.7400
$$

#### 2. **Cost of Capital for All-Equity Firm ($r_A$):**

$$
r_A = r_f + \beta_A (r_m - r_f)
$$
$$
r_A = 0.04 + 0.74 \times (0.10 - 0.04) = 0.04 + 0.74 \times 0.06 = 0.04 + 0.0444 = 0.0844 \text{ or } 8.44\%
$$

**Answer:**  
$$
\boxed{8.44\%}
$$

---

## **Summary Table**

| Part | Answer         |
|------|---------------|
| a    | 0.50          |
| b    | 8.44%         |
| c    | 8.44%         |

Let me know if you need further explanation on any step!

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