# How to Determine a Firm's Optimal Capital Structure

“What do you think from below which option better for growing company: 1) Debt Equity ratio 1:1; 2) Debt Equity ratio 2:1 or 3) Only Debt ?”

Recently, I read the above question posted by a fellow in LinkedIn. Without knowing the firm’s specific situations, I don't intent to pin point the specific question, but in general, the two components of every balance sheet debt can be technically framed as:

Cost of Debt = Risk-free rate + default rate

Cost of Equity = Risk-free rate + (beta * market risk premium)

Putting the two together with proportional weights, we will have a “average cost of capital”, WACC (Weighted Average Cost of Capital), as follows:

WACC = Cost of Debt*(Debt/(Debt + Equity)) + Cost of Equity *(Equity/(Debt + Equity)).

Then we need to calculate relationship between cost of funding and firm value, and tax-shelter benefits, etc., including D/(D+E) from 0%, 10%, ….., 100%, corresponding to Cost of equity, After-tax cost of debt (interests on debt can be tax-deducted), Cost of capital, Firm value, etc. We will find the lowest Cost of capital somewhere between 0% and 100%. Although there are some (but few) exceptions to the rule, most firm will find their optimal capital structure somewhere in the ballpark of 30-45% debt (and so 55-70% equity). For example, the results from the calculations are as following Table 3.1. Relationship between cost of funding and firm value (Nijs 2014). As you can see the Cost of capital from 10.50% (at 0% debt ratio), went down to 10.14% (at 40% debt ratio), and then started to go up again. Therefore, we concluded that at 40% debt ratio, the firm had the lowest cost of capital as 10.14%, while the highest firm value as 2,885.

WACC is a function of discount factor to judge the firm’s future cash flows or the firm’s aggregate value (e.g. the implied growth rate, g). One of the key risk control factors is the times interest earned ratio (TIER), as known as the interest coverage ratio (IC Ratio).

TIER = EBIT(DA)/Interest paid

The topics of how to determine default rate, IC ratio related to ratings, and market risk premium, are beyond this essay. If you are interested in those, you can look into CAPM (Capital Asset Pricing Model) and S&P rating, and WSJ daily published spread data, etc. Table 3.2, for example, gives the Relationship between the S&P rating categories and TIER results. (Luc. Nijis, 2014).

Most of the corporate finance beginners often forget about the capital structure's impact on tax implications. Let's look at three basic formulas:

1) ROE and leverage: ROE = (1 - Tax Rate)*(ROA + ROA - Interest rate) *Debt/Equity)

Debt/Equity ratio is positively proportional to ROE, and related to tax implications

2) DuPont Formula: ROE = (Net Profit)/Pretax profit) *(Pretax profit/EBIT)*(EBIT/Sales)*(Sales/Assets)*(Assets/Equity)

Assets/Equity, which is leverage ratio, is also positively proportional to ROE.

3) Conceptually: ROE = Tax Burden * Interest Burden * Margin * Turnover * Leverage

This clearly shows that ROE is a function of Tax, Interest and leverage, and positively proportional to those three debt ratio related factors.

Reference:

Luc Nijs, Mezzanine Financing: Tools, Applications and Total Performance, Published 2014 by John Wiley & Sons Ltd. pp. 91, and pp. 93