Questions:
My company's debt cost of capital of 5% and an equity cost of capital of 8%. Let's say our debt-to-equity ratio is 0.7. What is our pre tax WACC?

Now let's say the corporate tax rate is 40%. What is the impact of the interest rate tax shield on our WACC?

Reference answers:
The WACC, or weight average cost of capital,

WACC = (E / (E + D)) * r_e + (D / (E + D)) * r_d

Where:
E = equity
D = debt
r_e = cost of equity
r_d = cost of debt

SInce the debt to equity ratio is 0.7, we know that:
D / E = 0.7
D = 0,7 E
E = 1.428 D

Which means that:

E / (E + D) = E / (E + 0.7 E) = 1 / 1.7 = 0.588
D / (E + D) = 0.7 E / (E + 0.7 E) = 0.411

Filling this in then gives us:

WACC = 0.588 * 0.08 + 0.411 * 0.05 = 0.06759

Therefore, our pre-tax WACC is approximately 6.759%.

The interest rate tax shield reduces our tax burden which in turn reduces our WACC. The post tax WACC can be computed as,

WACC = (E / (E + D)) * r_e + (D / (E + D)) * r_d * (1 - t)  = pre-tax WACC - ((D / (E + D)) * r_d * t

Where t is the tax rate. 

Plugging in our values:
((D / (E + D)) * r_d * t = 0.411 * 0.08 * 0.4 = 0.013152

Therefore, accounting for tax will reduce the WACC by approximately 1.31% to 5.44%.