Based on market values, Gubler's Gym has an equity multiplier of 1.68 times. Shareholders require a return of 11.79 percent on the company's stock and a pretax return of 5.06 percent on the company's debt. The company is evaluating a new project that has the same risk as the company itself. The project will generate annual aftertax cash flows of $321,000 per year for 9 years. The tax rate is 21 percent. What is the most the company would be willing to spend today on the project?

To solve this problem, we need to find the maximum amount Gubler's Gym would be willing to invest in a project that has a given set of cash flows, given its cost of capital. To do that, we'll use the weighted average cost of capital (WACC) to discount the project's cash flows and determine the net present value (NPV). 

### Step-by-Step Breakdown:

1. **Determine the WACC (Weighted Average Cost of Capital):**
   The WACC is the company's overall required rate of return on its investments, which includes both equity and debt. It is given by the formula:

   \[
   WACC = \left(\frac{E}{V} \times r_E\right) + \left(\frac{D}{V} \times r_D \times (1 - T)\right)
   \]
   where:
   - $E$ is the market value of equity,
   - $D$ is the market value of debt,
   - $V = E + D$ is the total value of the firm,
   - $r_E = 11.79\%$ is the required return on equity (shareholders' required return),
   - $r_D = 5.06\%$ is the pretax return on debt,
   - $T = 21\%$ is the tax rate.

2. **Equity Multiplier:**
   The equity multiplier is given by the formula:

   \[
   \text{Equity Multiplier} = \frac{V}{E} = 1.68
   \]

   Therefore, the ratio $ \frac{D}{E} $ is:

   \[
   \frac{D}{E} = \text{Equity Multiplier} - 1 = 1.68 - 1 = 0.68
   \]

   This means for every \$1 of equity, there is \$0.68 of debt. Thus, the ratio $ \frac{D}{V} $ is:

   \[
   \frac{D}{V} = \frac{0.68}{1.68}
   \]
   and $ \frac{E}{V} $ is:

   \[
   \frac{E}{V} = \frac{1}{1.68}
   \]

3. **Calculate WACC:**
   Now, plug in all the values into the WACC formula:

   \[
   WACC = \left(\frac{1}{1.68} \times 0.1179\right) + \left(\frac{0.68}{1.68} \times 0.0506 \times (1 - 0.21)\right)
   \]

   Let me calculate this for you.The company's weighted average cost of capital (WACC) is approximately 8.64%.

### Step 4: Calculate the Present Value (PV) of the project's cash flows

The project generates after-tax cash flows of $ \$321,000 $ per year for 9 years. To find the maximum amount the company would be willing to spend today, we need to calculate the present value of these cash flows using the WACC as the discount rate. The present value of an annuity can be calculated using the formula:

\[
PV = C \times \left(1 - \frac{1}{(1 + r)^{n}}\right) \div r
\]

Where:
- $C = 321,000$ (annual cash flow),
- $r = WACC = 8.64\%$,
- $n = 9$ years.

Let me calculate this next.The present value of the project's cash flows is approximately \$1,953,295.05.

### Conclusion:
The most the company would be willing to spend today on the project is \$1,953,295.05, as this is the present value of the future cash flows generated by the project, discounted at the company's WACC.

Would you like further details on any part of the calculation or have any questions?

### Related Questions:
1. How does the equity multiplier affect the WACC?
2. What happens if the tax rate changes—how would that impact the WACC?
3. What is the difference between pretax and after-tax returns on debt?
4. How would increasing the required return on equity affect the project valuation?
5. How can you calculate the net present value (NPV) if the project's cost is known?

### Tip:
The weighted average cost of capital (WACC) is crucial for evaluating long-term investments as it represents the minimum return the company must earn to satisfy its stakeholders.

Learn how to calculate the maximum investment Gubler's Gym should make on a new project by using the Weighted Average Cost of Capital (WACC) and Present Value of annuity cash flows. This problem involves WACC calculations, equity multiplier concepts, and evaluating project investment decisions, suitable for advanced finance students.

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