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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%

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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