 # corporate finance: capital structure

R30P127: q10: I don’t get how it derive current cost of equity from the rate when the company is 100% equity financed: re=r0+(r0-rd)*(1-t)*D/E

D/E = 0 so go figure that re = r0

Say, return on equity with 0 debt, i.e., full equity capital, is r0. As you add debt the equity capital providers demand more return due to the fact that additional leverage increases risk and creates subordination of claims on assets and returns. So re = r0 + x. Required return on equity is always higher than required return on debt since equity is free, i.e., company may or may not pay dividends and in case of bankruptcy equity holders will have only residual claim. From your formula x = (r0-rd)*(1-t) D/E. Now if company is earning r0 with all equity, eventually company is going to earn r0 return irrespective of whats the percentage of equity or debt, but the distribution of the return is not the same. If it distributes r0 return to equity(E%) holders and rd return to debt(D%) holders, there is a residual return r0-rd equal to percentage of debt (D%), meaning (r0-rd)D and you need to pay taxes on this, so net residual claim is (r0-rd)(1-t)D. This is the leverage effect and who gets this residual profit? Its equity holders for taking higher risk with higher debt, so to make it per equity, (r0-rd)(1-t)D/E.

thanks for the good explanation janard, but can you maybe put some numbers on that to illustrate further?

What you need to understand is that r0 is return on assets. Irrespective of how company acquires funds i.e., irrespective of the D and E proportion, r0 is what the company can earn. When we say r0 is return on all equity capital, it is a pure investment return that isolates company’s performance. r0=15% rd=10% E=60% D=40% t=40% If total capital invested is \$1000 ==> \$600 Equity and \$400 debt. Its income would be \$1000 * r0 = \$1000 * .15 ==> \$150. So if company distributes \$600*0.15 = \$90 to Equity holders and \$400*.10 = \$40 to debt holders. Company distributed \$90+\$40 = \$130 to all capital providers and lease a residual profit of \$20. Had \$400 debt been Equity you would have distributed this off as well, but since its debt and its rate is lower you have residual income, this is leverage effect and this belongs to Equity holders because they have residual claim and demand additional return for the risk taken due to leverage. Since this is income (belongs to equity holders) this is subjected to tax, so after tax residual is \$20*.6 = \$12. So re = r0 + x = \$90 + \$12 = \$102. This is obviously higher than 15%. If you calculate the re from above values re = 102/600 = 17% If you use formula, re = r0+(r0-rd)*(1-t)*D/E = 15 + .5 * .6 * .4/.6 = 17% Why are we taking the taxes off only from residual and not from r0? The profits distributed to equity are after tax, however, debt service payments are not taxed. So the leverage effect residual profit runs through the taxes before it is pocketed by Equity holders. What is the risk? What if the company had earned only 5% for the year, meaning r0=5%. Debt holders will still get 10% and Equity holders will receive the rest, it could be loss. Had there been no debt Equity holders would have received 5% at least, but, now due to leverage they may receive less or worse loss.

if r0 is from a capitial stucture that d/e<>0, is the formula still the same? Thanks. janardhanc Wrote: ------------------------------------------------------- > Say, return on equity with 0 debt, i.e., full > equity capital, is r0. As you add debt the equity > capital providers demand more return due to the > fact that additional leverage increases risk and > creates subordination of claims on assets and > returns. So re = r0 + x. > > Required return on equity is always higher than > required return on debt since equity is free, > i.e., company may or may not pay dividends and in > case of bankruptcy equity holders will have only > residual claim. From your formula x = > (r0-rd)*(1-t) D/E. > > Now if company is earning r0 with all equity, > eventually company is going to earn r0 return > irrespective of whats the percentage of equity or > debt, but the distribution of the return is not > the same. If it distributes r0 return to > equity(E%) holders and rd return to debt(D%) > holders, there is a residual return r0-rd equal to > percentage of debt (D%), meaning (r0-rd)D and you > need to pay taxes on this, so net residual claim > is (r0-rd)(1-t)D. This is the leverage effect and > who gets this residual profit? Its equity holders > for taking higher risk with higher debt, so to > make it per equity, (r0-rd)(1-t)D/E.