Upton Umbrellas has a cost of equity of 11.1 percent, the YTM on the company's bonds is 5.7 percent, and the tax rate is 22 percent. The company's bonds sell for 93.1 percent of par. The debt has a book value of $393,000 and total assets have a book value of $947,000. If the market-to-book ratio is 2.59 times, what is the company's WACC?
Question:
Upton Umbrellas has a cost of equity of 11.1 percent, the YTM on the company's bonds is 5.7 percent, and the tax rate is 22 percent. The company's bonds sell for 93.1 percent of par. The debt has a book value of $393,000 and total assets have a book value of $947,000. If the market-to-book ratio is 2.59 times, what is the company's WACC?
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Asked by: Test User 100128
Created at: 2025-05-20 15:13:07
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Let's break down the problem step by step:
**Given:**
- Cost of equity, \( R_e = 11.1\% \)
- YTM on bonds (cost of debt before tax), \( R_d = 5.7\% \)
- Tax rate, \( T = 22\% \)
- Bonds sell for 93.1% of par (market value)
- Book value of debt = \$393,000
- Book value of total assets = \$947,000
- Market-to-book ratio of assets = 2.59
We are to **find the WACC**.
---
## **Step 1: Calculate Market Value of Equity and Debt**
### **Market Value of Assets:**
\[
\text{Market Value of Assets} = \text{Book Value of Assets} \times \text{Market-to-Book Ratio}
\]
\[
= \$947,000 \times 2.59 = \$2,452,730
\]
### **Market Value of Debt:**
\[
\text{Market Value of Debt} = \text{Book Value of Debt} \times \frac{\text{Market Price}}{\text{Par}}
\]
\[
= \$393,000 \times 0.931 = \$365,583
\]
### **Market Value of Equity:**
\[
\text{Market Value of Equity} = \text{Market Value of Assets} - \text{Market Value of Debt}
\]
\[
= \$2,452,730 - \$365,583 = \$2,087,147
\]
---
## **Step 2: Calculate Weights**
\[
\text{Total Market Value} = \text{Market Value of Equity} + \text{Market Value of Debt}
\]
\[
= \$2,087,147 + \$365,583 = \$2,452,730
\]
\[
w_E = \frac{2,087,147}{2,452,730} = 0.8515
\]
\[
w_D = \frac{365,583}{2,452,730} = 0.1491
\]
---
## **Step 3: After-tax Cost of Debt**
\[
\text{After-tax Cost of Debt} = R_d \times (1 - T)
\]
\[
= 5.7\% \times (1 - 0.22) = 5.7\% \times 0.78 = 4.446\%
\]
---
## **Step 4: WACC Calculation**
\[
\text{WACC} = w_E \times R_e + w_D \times R_d \times (1 - T)
\]
\[
= 0.8515 \times 0.111 + 0.1491 \times 0.057 \times 0.78
\]
\[
= 0.09491 + 0.00663
\]
\[
= 0.10154 \text{ or } 10.15\%
\]
---
## **Final Answer**
\[
\boxed{10.15\%}
\]
That's Upton Umbrellas' WACC, rounded to two decimal places.
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