Question

cost of equity 9% 9%
cost of debt 3% 4%
tax rate 35% 35%
based solely on their current weighted average cost of capital, which company should pursue an investment opportunity with an expected return of 6%?
○ both company a and company b
○ only company b
○ neither company a nor company b
○ only company a

Explanation:

Step1: Recall WACC Formula

The Weighted Average Cost of Capital (WACC) formula is \( WACC = w_e \times r_e + w_d \times r_d \times (1 - t) \), where \( w_e \) is weight of equity, \( w_d \) is weight of debt, \( r_e \) is cost of equity, \( r_d \) is cost of debt, and \( t \) is tax rate. However, since the problem likely assumes equal weights (or standard capital structure, but often in such problems, if not given, we assume a simple case or maybe the table had weights, but since the table here shows two companies with same equity cost, different debt cost, same tax. Wait, maybe the table was missing weights? Wait, maybe it's a typo, but likely in the original problem, maybe the weights are 50-50? Wait, no, maybe the table had two companies: let's assume Company A has Cost of Equity 9%, Cost of Debt 3%, Tax 35%. Company B: Cost of Equity 9%, Cost of Debt 4%, Tax 35%. Let's assume equal weights (50% equity, 50% debt) for both.

Step2: Calculate WACC for Company A

For Company A: \( w_e = 0.5 \), \( r_e = 9\% \), \( w_d = 0.5 \), \( r_d = 3\% \), \( t = 35\% = 0.35 \)
\( WACC_A = 0.5 \times 9\% + 0.5 \times 3\% \times (1 - 0.35) \)
\( = 4.5\% + 0.5 \times 3\% \times 0.65 \)
\( = 4.5\% + 0.5 \times 1.95\% \)
\( = 4.5\% + 0.975\% = 5.475\% \)

Step3: Calculate WACC for Company B

For Company B: \( w_e = 0.5 \), \( r_e = 9\% \), \( w_d = 0.5 \), \( r_d = 4\% \), \( t = 0.35 \)
\( WACC_B = 0.5 \times 9\% + 0.5 \times 4\% \times (1 - 0.35) \)
\( = 4.5\% + 0.5 \times 4\% \times 0.65 \)
\( = 4.5\% + 0.5 \times 2.6\% \)
\( = 4.5\% + 1.3\% = 5.8\% \)

Wait, but the expected return is 6%. So if WACC is less than 6%, the company should pursue. Wait, WACC_A is ~5.475%, WACC_B is ~5.8%. Both are less than 6%? Wait, but maybe the weights are different. Wait, maybe the table had weights, but in the given image, the table has two columns (Company A and B) with Cost of Equity (9% each), Cost of Debt (3% and 4%), Tax (35% each). Maybe the weights are 100% debt? No, that doesn't make sense. Wait, maybe the problem is that the original table had weights, but in the user's image, it's cut off. Wait, alternatively, maybe the problem is that the investment return (6%) must be higher than WACC. So let's recalculate with correct weights. Wait, maybe the standard is that if the investment's return is higher than WACC, the company should pursue. So let's assume that for Company A, WACC is calculated as:

Wait, maybe the table was supposed to have weights, but in the given image, it's missing. Wait, maybe it's a mistake, but let's check the options. The options are Both, Only B, Neither, Only A.

Wait, maybe the actual weights are 100% equity? No, that can't be. Wait, maybe the problem is that the cost of debt is after tax? No, WACC uses after-tax cost of debt. Wait, let's re-express:

After-tax cost of debt for A: \( 3\% \times (1 - 0.35) = 1.95\% \)

After-tax cost of debt for B: \( 4\% \times (1 - 0.35) = 2.6\% \)

If we assume the capital structure is 100% debt (unlikely), but no. Wait, maybe the problem is that the company's WACC is less than 6%, so they can pursue. Let's assume that the WACC for A is, say, if equity is 50% and debt 50%:

A: (0.5*9) + (0.5*1.95) = 4.5 + 0.975 = 5.475% < 6%

B: (0.5*9) + (0.5*2.6) = 4.5 + 1.3 = 5.8% < 6%

So both WACCs are less than 6%, so both companies should pursue. But wait, maybe the weights are different. Wait, maybe the original problem had weights, but in the image, it's cut off. Alternatively, maybe the problem is that the cost of equity and debt are the only components, and the company should pursue if the investment return is higher than WACC. So if WACC is less than 6%, then yes.

Wait, but let's check the options. The first option is "Both Company A and Company B". So maybe that's the answer. But let's confirm.

Alternatively, maybe the table had weights, but in the given image, it's missing. But based on the numbers, if we assume equal weights, both WACCs are below 6%, so both should pursue.

Answer:

A. Both Company A and Company B