Target Capital Structure (tricky valuation question)

CFA Level I Equities
#1

Attempting to construct the WACC for a firm, but i’m stuck on re-levering beta for CAPM to obtain a target capital structure in the WACC equation. I’m not quite sure where to derive that from … I know my capital structures on the 3 year projections I have are:

Year 1: 1 (Equity is 10 million, Debt is 10 million) Year 2: 0.5 (Equity is 10 million, Debt is 5 million) Year 3: N/A (Equity is 10 million, Debt is 0)

My assumptions given are:

  1. Risk free rate (US) - 3% 2) Country Risk Premium 0.75% 3) Market Risk Premium - 8% 4) Levered Comparable Beta - 1.10 5) Market Debt to Equity - 40% 6) Market Average Tax - 30% 7) Long term growth rate – 3% 8) Interest Rate - 8%

Step 1: Unlever Beta Unlevered Beta = Levered Beta/(1+((1-Tax Rate) x (Total Debt/Equity))) Unlevered Beta = 1.1/(1+((1-30%)x(0.4) Unlevered Beta = 0.86

Step 2: Re-lever Beta Relevered Beta = Unlevered Beta * (1+((1 - Tax Rate) x (Total Debt/Equity))) Okay so here is where my confusion kicks in … what am I supposed to assume for the (Total Debt/Equity))) portion? Also, when computing the (Total Debt/Equity), should I add the retained earnings portion to the equity or just contributed capital and additional paid in capital?

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Ok, so I tried to tackle this again because it has annoyed me. I created an excel sheet with all the assumptions and solved it based on my current debt to equity ratio. I then created a data table for the WACC with the column input cell of Debt/Equity ratio’s ranging from 0.01 to 1, and in an effort to solve find the target capital structure (the lowest WACC), but that came out to be when the debt to equity ratio was 0.01. Not convinced.

#2

While I don’t have an answer, I’m inclined to think that a target capital structure is something a firm maintains over a mid to long-term horizon, in which case you don’t solve for a D/E that yields optimum WACC on a year-to-year basis–that would require a constantly-changing capital structure.

Additionally, while WACC is not the sole nor the most important criteria for a firm’s capital structure decision, we can usually construct a WACC/leverage curve that suggests an appropriate amount of debt across many firms/industries which would minimize WACC.

Perhaps our more knowledgeable members could correct me and provide a better response.

#3

Thanks for the feedback, really good insights. I second your opinion, we need more input!