Calc WACC using dividend discount model

Can someone please explain this particular portion of the problem D/(D + E) = 0.8033/1.8033 = 0.445. given the following

Before-tax cost of new debt 8 percent Tax rate 40 percent Target debt-to-equity ratio 0.8033 Stock price $30 Next year’s dividend $1.50 Estimated growth rate 7 percent

Solution

CALC WACC

Cost of equity = D1/P0 + g = $1.50/$30 + 7% = 5% + 7% = 12%

D/(D + E) = 0.8033/1.8033 = 0.445

WACC = [(0.445) (0.08)(1 − 0.4)] + [(0.555)(0.12)] = 8.8%

That portion is just the weight for Debt = 44.5%.

The weight for Equity portion is 1 - 0.445 = 55.5%

The total is 100%

Let’s say: Equity is 5 and Debt is 2

D/E ratio = 2/5 = 0.4/1

D+E = 7

Therefore, D/(D+E)

=> 0.4/1.4 = 28.57%

Or => D/(D+E) = 2/7 = 28.57%

Both are the same.

Just remember:

D/(D+E) = D/(1+D/E) = 0,8033/(1 + 0,8033) = 0,4455 = 44,55%

To get the weight of debt, just divide the debt by (1+ D/E ratio)!

Regards, Oscar