Explanation

To calculate the Weighted Average Cost of Capital (WACC), we use the formula:

$\text{WACC} = \frac{E}{E+D} \times r_e + \frac{D}{E+D} \times r_d \times (1 - t)$

Where:

• $E$ = Market value of equity
• $D$ = Market value of debt
• $r_e$ = Cost of equity
• $r_d$ = Pre-tax cost of debt
• $t$ = Marginal tax rate

Step 1: Calculate total market value of capital E = \`$500` \text{ million} D = \`$1`,000 \text{ million} E + D = \`$500` + \`$1`,000 = \`$1`,500 \text{ million}

Step 2: Calculate weights $w_e = \frac{E}{E+D} = \frac{500}{1,500} = 0.3333$ $w_d = \frac{D}{E+D} = \frac{1,000}{1,500} = 0.6667$

Step 3: Calculate after-tax cost of debt $r_d \times (1 - t) = 4\% \times (1 - 0.30) = 4\% \times 0.70 = 2.8\%$

Step 4: Calculate WACC $\text{WACC} = (0.3333 \times 6\%) + (0.6667 \times 2.8\%)$ $= (0.3333 \times 0.06) + (0.6667 \times 0.028)$ $= 0.02 + 0.018667$ $= 0.038667$ $= 3.8667\%$

Step 5: Compare with options

• 3.6% is too low
• 3.9% is closest to 3.8667%
• 4.7% is too high

Therefore, the WACC is closest to 3.9%.

Key Points:

1. WACC uses market values (not book values) for weights
2. The cost of debt is tax-adjusted since interest is tax-deductible
3. The formula weights each component by its proportion in the capital structure