Kuhn Co. is considering a new project that will require an initial investment of $45 million. It has a target capital structure of 45% debt, 4% preferred stock, and 51% common equity. Kuhn has noncallable bonds outstanding that mature in five years with a face value of $1,000, an annual coupon rate of 10%, and a market price of $1,050.76. The yield on the company’s current bonds is a good approximation of the yield on any new bonds that it issues. The company can sell shares of preferred stock that pay an annual dividend of $9 at a price of $95.70 per share.

Kuhn does not have any retained earnings available to finance this project, so the firm will have to issue new common stock to help fund it. Its common stock is currently selling for $22.35 per share, and it is expected to pay a dividend of $2.78 at the end of next year. Flotation costs will represent 8% of the funds raised by issuing new common stock. The company is projected to grow at a constant rate of 8.7%, and they face a tax rate of 25%. What will be the WACC for this project?  ****    (**Note**: Round your intermediate calculations to two decimal places.)

To calculate the Weighted Average Cost of Capital (WACC) for Kuhn Co.'s new project, we need to find the cost of each component of capital (debt, preferred stock, and common equity) and then weight these costs by their respective proportions in the target capital structure. Here are the steps involved:

### 1. Cost of Debt (after-tax)
The cost of debt can be found using the yield to maturity (YTM) on the company’s current bonds. The given data indicates that the YTM is the yield on the company’s noncallable bonds which have a market price of $1,050.76, a face value of $1,000, an annual coupon rate of 10%, and a maturity of 5 years.

The formula to calculate the approximate yield to maturity is:
\[ \text{YTM} = \frac{C + \frac{(F - P)}{n}}{\frac{(F + P)}{2}} \]
where:
- $C$ = Annual coupon payment = 10% of $1,000 = $100
- $F$ = Face value of the bond = $1,000
- $P$ = Current price of the bond = $1,050.76
- $n$ = Number of years to maturity = 5

\[ \text{YTM} \approx \frac{100 + \frac{(1,000 - 1,050.76)}{5}}{\frac{(1,000 + 1,050.76)}{2}} = \frac{100 + (-10.15)}{1,025.38} \approx \frac{89.85}{1,025.38} \approx 0.0876 \text{ or } 8.76\% \]

Since we need the after-tax cost of debt:
\[ r_d = \text{YTM} \times (1 - \text{Tax rate}) = 8.76\% \times (1 - 0.25) = 8.76\% \times 0.75 = 6.57\% \]

### 2. Cost of Preferred Stock
The cost of preferred stock is calculated as the dividend divided by the price of the preferred stock:
\[ r_{ps} = \frac{D_{ps}}{P_{ps}} = \frac{9}{95.70} \approx 9.40\% \]

### 3. Cost of Common Equity
The cost of new common equity is calculated using the Gordon Growth Model (also known as the Dividend Discount Model) adjusted for flotation costs:
\[ r_e = \frac{D_1}{P_0 \times (1 - F)} + g \]
where:
- $ D_1 $ = Dividend expected next year = $2.78
- $ P_0 $ = Current price of the stock = $22.35
- $ F $ = Flotation cost percentage = 8\% = 0.08
- $ g $ = Growth rate = 8.7\% = 0.087

\[ r_e = \frac{2.78}{22.35 \times (1 - 0.08)} + 0.087 = \frac{2.78}{22.35 \times 0.92} + 0.087 = \frac{2.78}{20.562} + 0.087 \approx 0.1352 + 0.087 = 0.2222 \text{ or } 22.22\% \]

### 4. Calculate the WACC
Now we will combine the costs using the target capital structure weights:
\[ \text{WACC} = (w_d \times r_d) + (w_{ps} \times r_{ps}) + (w_e \times r_e) \]
where:
- $ w_d $ = Weight of debt = 45\% = 0.45
- $ w_{ps} $ = Weight of preferred stock = 4\% = 0.04
- $ w_e $ = Weight of common equity = 51\% = 0.51

\[ \text{WACC} = (0.45 \times 6.57\%) + (0.04 \times 9.40\%) + (0.51 \times 22.22\%) \]
\[ \text{WACC} = (0.45 \times 0.0657) + (0.04 \times 0.0940) + (0.51 \times 0.2222) \]
\[ \text{WACC} = 0.029565 + 0.00376 + 0.113322 \]
\[ \text{WACC} \approx 0.146647 \text{ or } 14.66\% \]

### Conclusion
The Weighted Average Cost of Capital (WACC) for Kuhn Co.'s new project is approximately **14.66%**.

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Would you like any details or have any questions?

Here are some additional questions for further exploration:

1. How does a change in the target capital structure affect the WACC?
2. What would be the impact on WACC if the flotation costs for issuing new common stock increased?
3. How does the tax rate influence the after-tax cost of debt?
4. What happens to the WACC if the growth rate of common equity increases?
5. How does the cost of new preferred stock issuance affect the overall WACC?
6. What are some strategies Kuhn Co. could use to lower its WACC?
7. How would an increase in the market price of bonds affect the cost of debt?
8. What is the significance of WACC in capital budgeting decisions?

**Tip:** Always consider

Learn how to calculate the Weighted Average Cost of Capital (WACC) for Kuhn Co.'s new project. Includes detailed step-by-step calculations for debt, preferred stock, and common equity costs based on current market conditions and financial data. Suitable for professionals and students studying finance and investment analysis.

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