Part 1
A firm has the current liabilities and equity financing on its balance sheet. The firm has taxable income that puts it in a 38% federal tax bracket, and the state in which it operates levies a 6.5% income tax. Compute the firm’s weighted average cost of capital.
Source Amount Interest/RoR Proportion
Short-term loan $ 5,000,000 7.5% 0.05
Long-term loan $20,000,000 5.8% 0.25
Retained Earnings $25,000,000 17.0% 0.20
Common stock $50,000,000 22.0% 0.50
Part 2
The same firm is considering the following projects to improve its production process. If the firm has a capital budget of $1,400,000, which projects should be accepted by the rate of return criteria? What is the firm’s opportunity cost of capital?
Project First Cost Annual Benefit Life (years)
1 $250,000 $50,000 15
2 $300,000 $70,000 10
3 $125,000 $35,000 5
4 $ 50,000 $12,500 10
5 $250,000 $75,000 5
6 $200,000 $32,000 20
7 $400,000 $125,000 5
Part 3
From your estimates of the WACC in part 1 and the opportunity cost of capital in part 2, what do you estimate the firm’s true MARR to be?
Part 1:
To calculate the firm's weighted average cost of capital (WACC), we need to assign weights to each source of financing and calculate the cost of each source. The formula for WACC is as follows:
WACC = (Weight of Debt * Cost of Debt) + (Weight of Equity * Cost of Equity)
1. Calculate the cost of debt:
The cost of debt is the interest/return rate on each source.
- For the short-term loan, the interest rate is 7.5%.
- For the long-term loan, the interest rate is 5.8%.
2. Calculate the weight of debt:
The weight of debt is the proportion of each source to the total liabilities and equity financing. Given the amounts provided, the weight of debt is:
- Short-term loan: $5,000,000 / ($5,000,000 + $20,000,000 + $25,000,000 + $50,000,000)
- Long-term loan: $20,000,000 / ($5,000,000 + $20,000,000 + $25,000,000 + $50,000,000)
3. Calculate the cost of equity:
The cost of equity is the return on investment expected by shareholders. The percentages provided represent the cost of equity for each source.
- Retained Earnings: 17.0%
- Common Stock: 22.0%
4. Calculate the weight of equity:
The weight of equity is the proportion of each source to the total liabilities and equity financing.
- Retained Earnings: $25,000,000 / ($5,000,000 + $20,000,000 + $25,000,000 + $50,000,000)
- Common Stock: $50,000,000 / ($5,000,000 + $20,000,000 + $25,000,000 + $50,000,000)
5. Substitute the values into the WACC formula and calculate the result.
Part 2:
To determine which projects should be accepted based on the rate of return criteria, we will calculate the Rate of Return (ROR) for each project. The ROR formula is as follows:
ROR = (Annual Benefit / First Cost) * 100
1. Calculate the ROR for each project by dividing the Annual Benefit by the First Cost and multiplying by 100.
2. Compare the ROR of each project to the firm's opportunity cost of capital, which is the minimum ROR required by the firm.
3. Projects with a higher ROR than the opportunity cost of capital should be accepted.
Part 3:
To estimate the firm's true Minimum Acceptable Rate of Return (MARR), we can consider both the WACC from Part 1 and the opportunity cost of capital from Part 2. The MARR is the minimum return rate the firm requires on its investments.
1. Compare the WACC to the opportunity cost of capital from Part 2.
2. If the opportunity cost of capital is higher than the WACC, the firm's true MARR is likely closer to the opportunity cost of capital.
3. If the WACC is higher than the opportunity cost of capital, additional factors should be considered to determine the firm's true MARR. These factors may include industry benchmarks, economic conditions, and specific risk factors impacting the firm's investments.
By considering both the WACC and the opportunity cost of capital, it is possible to estimate the firm's true MARR. Note that this estimation may not capture all the complexities of the firm's investment decisions, and further analysis may be required.
Part 1:
To calculate the firm's weighted average cost of capital (WACC), we need to calculate the weighted average of the cost of each source of financing, taking into account the proportions and interest rates.
Step 1: Calculate the after-tax cost of debt:
After-tax cost of debt = Interest rate * (1 - Tax rate)
After-tax cost of short-term loan = 7.5% * (1 - 0.38) = 4.65%
After-tax cost of long-term loan = 5.8% * (1 - 0.38) = 3.61%
Step 2: Calculate the weighted average cost of debt:
Weighted average cost of debt = Proportion of short-term loan * After-tax cost of short-term loan + Proportion of long-term loan * After-tax cost of long-term loan
Weighted average cost of debt = 0.05 * 4.65% + 0.25 * 3.61% = 0.4075% + 0.9025% = 1.31%
Step 3: Calculate the weighted average cost of equity:
Weighted average cost of equity = Proportion of retained earnings * Return on retained earnings + Proportion of common stock * Return on common stock
Weighted average cost of equity = 0.20 * 17.0% + 0.50 * 22.0% = 3.40% + 11.00% = 14.40%
Step 4: Calculate the firm's WACC:
WACC = Weighted average cost of debt + Weighted average cost of equity
WACC = 1.31% + 14.40% = 15.71%
Therefore, the firm's weighted average cost of capital (WACC) is 15.71%.
Part 2:
To determine which projects should be accepted by the rate of return criteria, we need to calculate the rate of return for each project and compare it to the firm's opportunity cost of capital.
Step 1: Calculate the rate of return for each project:
Rate of return = (Annual Benefit - First Cost) / First Cost
For Project 1: (50,000 - 250,000) / 250,000 = -0.6 or -60%
For Project 2: (70,000 - 300,000) / 300,000 = -0.1 or -10%
For Project 3: (35,000 - 125,000) / 125,000 = -0.72 or -72%
For Project 4: (12,500 - 50,000) / 50,000 = -0.75 or -75%
For Project 5: (75,000 - 250,000) / 250,000 = -0.7 or -70%
For Project 6: (32,000 - 200,000) / 200,000 = -0.84 or -84%
For Project 7: (125,000 - 400,000) / 400,000 = -0.6875 or -68.75%
Step 2: Compare the rate of return for each project to the firm's opportunity cost of capital (WACC):
Opportunity cost of capital = WACC = 15.71%
Projects with a rate of return greater than the opportunity cost of capital (WACC) should be accepted.
Based on the calculations:
Project 2 and Project 7 have rate of returns greater than the opportunity cost of capital (WACC).
Part 3:
To estimate the firm's true Minimum Acceptable Rate of Return (MARR), we need to consider both the WACC and the opportunity cost of capital from different perspectives.
Given that the WACC represents the overall cost of financing for the firm and the opportunity cost of capital represents the return required by the firm's investors, the true MARR can be estimated as somewhere between these two figures.
In this case, the estimated true MARR would likely be around the average of the WACC and the opportunity cost of capital. Therefore, the estimated true MARR would be around 15.71% (WACC) + 15.71% (Opportunity cost of capital) / 2 = 15.71%.
Therefore, the firm's estimated true Minimum Acceptable Rate of Return (MARR) would be around 15.71%.