Please use both M&M proposition II with taxes equation and WACC equation to derive the following equation:?

WACC = Ru X [1- Tc(D/V)]?

I need this by tomorrow please help.

To derive the equation WACC = Ru(1 - Tc(D/V)), we will start by explaining the M&M Proposition II with taxes equation and the WACC equation separately, and then combine them.

M&M Proposition II with Taxes:
M&M Proposition II states that the value of a firm is not affected by its capital structure in a world with taxes. Specifically, it states that the levered value of a firm (Vl) is equal to the unlevered value of the firm (Vu) plus the tax shield provided by debt (Tc(D)), where Tc is the corporate tax rate and D is the debt.

Mathematically, M&M Proposition II with taxes can be represented as:
Vl = Vu + Tc(D)

WACC Equation:
The Weighted Average Cost of Capital (WACC) is a measure of the firm's overall cost of capital, taking into account the proportional weightings of debt (D/V) and equity (E/V), along with their respective costs.

The WACC equation can be represented as:
WACC = (D/V) * Rd * (1 - Tc) + (E/V) * Re
where:
- (D/V) represents the proportion of debt compared to the total value of the firm (debt-to-value ratio).
- Rd is the cost of debt (required return on debt).
- Tc is the corporate tax rate.
- (E/V) represents the proportion of equity compared to the total value of the firm (equity-to-value ratio).
- Re is the cost of equity (required return on equity).

Combining M&M Proposition II with taxes and WACC equations:
To derive the desired equation, we need to substitute the values from M&M Proposition II with taxes equation into the WACC equation.

First, substituting Vl with (Vu + Tc(D)) from M&M Proposition II equation, we have:
WACC = (D/V) * Rd * (1 - Tc) + (E/V) * Re

Next, we can express the debt-to-value ratio (D/V) as D / (D + E), and the equity-to-value ratio (E/V) as E / (D + E):
WACC = (D / (D + E)) * Rd * (1 - Tc) + (E / (D + E)) * Re

Now, let's substitute (1 - Tc) with tax shield Tc(D) from M&M Proposition II equation:
WACC = (D / (D + E)) * Rd * Tc(D) + (E / (D + E)) * Re

Lastly, we can simplify the equation by factoring out the common term D + E:
WACC = D / (D + E) * [Rd * Tc(D) + E / (D + E) * Re]

Since D + E represents the total value of the firm, which is denoted as V, we can substitute (D + E) with V:
WACC = D / V * [Rd * Tc(D) + E / V * Re]

Simplifying further, we can express E / V as (1 - D / V):
WACC = D / V * [Rd * Tc(D) + (1 - D / V) * Re]

Finally, rearranging the terms, we get:
WACC = Rd * D / V * Tc(D) + Re * (1 - D / V)

This equation is equivalent to the desired equation:
WACC = Ru * (1 - Tc(D / V))

Therefore, WACC = Ru * [1 - Tc(D/V)] is derived by combining the M&M Proposition II with taxes equation and the WACC equation.