Smith and Jones has two separate divisions. Division X produces custom work on a pre-paid basis only for long-term customers and therefore, is subject to less risk than division Y. The company has assigned a discount rate equal to the firm's WACC minus 2 percent to division X and a rate equal to the firm's WACC plus 3 percent to division Y. The company has a debt-equity ratio of .65 and a tax rate of 35 percent. The cost of equity is 9 percent and the aftertax cost of debt is 5 percent. Presently, each division is considering a new project. Division Y's project provides a 9.5 percent rate of return and division X's project provides a 6.2 percent return. Which projects, if either, should the company accept?
a. accept both X and Y
b. accept X and reject Y
c. reject X and accept Y
d. reject both X and Y
e. The answer cannot be determined without additional information.
To determine which projects the company should accept, we need to compare the returns of the projects to the discount rates assigned to each division.
First, let's calculate the discount rates for each division:
The company's WACC (Weighted Average Cost of Capital) is calculated as follows:
WACC = Cost of Equity * % Equity + Cost of Debt * % Debt * (1 - Tax Rate)
Given that the debt-equity ratio is 0.65, this means the firm's percent equity is 1 - 0.65 = 0.35, and the percent debt is 0.65.
Plugging in the given values, we have:
WACC = 0.09 * 0.35 + 0.05 * 0.65 * (1 - 0.35)
WACC = 0.0585 + 0.021125
WACC = 0.079625 or 7.96%
Now let's calculate the discount rates for each division based on the assigned rates:
Division X discount rate = WACC - 2% = 7.96% - 2% = 5.96%
Division Y discount rate = WACC + 3% = 7.96% + 3% = 10.96%
Next, let's compare the returns of each project to their respective discount rates:
Division X's project return = 6.2%
Division X discount rate = 5.96%
Since the project return (6.2%) is higher than the discount rate (5.96%), the company should accept project X.
Division Y's project return = 9.5%
Division Y discount rate = 10.96%
Since the project return (9.5%) is lower than the discount rate (10.96%), the company should reject project Y.
Therefore, the answer is:
b. accept X and reject Y
To determine whether the company should accept either project, we need to calculate the net present value (NPV) for each project.
First, let's calculate the cost of capital for each division:
- Division X's discount rate = WACC - 2% = Cost of Equity * Equity Weight + Cost of Debt * Debt Weight - 2%
- Division Y's discount rate = WACC + 3% = Cost of Equity * Equity Weight + Cost of Debt * Debt Weight + 3%
Given information:
- Debt-equity ratio = 0.65
- Tax rate = 35%
- Cost of equity = 9%
- Aftertax cost of debt = 5%
To calculate the cost of capital, we need to determine the weights of debt and equity:
- Weight of equity = 1 - Debt-equity ratio = 1 - 0.65 = 0.35
- Weight of debt = Debt-equity ratio = 0.65
Substituting the values in the cost of capital formulas:
- Division X's discount rate = 9% * 0.35 + 5% * 0.65 - 2%
- Division Y's discount rate = 9% * 0.35 + 5% * 0.65 + 3%
Now, let's calculate the NPV for each project, using the discount rates obtained above:
- NPV of Division X's project = Initial investment * (1 + Discount rate)^n - Initial investment
- NPV of Division Y's project = Initial investment * (1 + Discount rate)^n - Initial investment
Given information:
- Division X's project return = 6.2%
- Division Y's project return = 9.5%
Plug in the values to calculate the NPV for each project:
- NPV of Division X's project = Initial investment * (1 + (9% * 0.35 + 5% * 0.65 - 2%))^n - Initial investment
- NPV of Division Y's project = Initial investment * (1 + (9% * 0.35 + 5% * 0.65 + 3%))^n - Initial investment
After calculating the NPV for each project, compare the results to determine which projects, if any, should be accepted. If the NPV is positive, the project should be accepted. Otherwise, if the NPV is negative, the project should be rejected.
Based on the calculations, if the NPV for both Division X's and Division Y's projects are positive, then the answer is option (a) accept both X and Y. If only Division X's project has a positive NPV, then the answer is option (b) accept X and reject Y. If only Division Y's project has a positive NPV, then the answer is option (c) reject X and accept Y. If both projects have a negative NPV, then the answer is option (d) reject both X and Y. If additional information is needed to determine the answer, then the answer is option (e) The answer cannot be determined without additional information.