Question

Circle Inc. currently uses no debt, but its new CFO is considering changing the capital structure to 77.5% debt (w_d) by issuing bonds and using the proceeds to repurchase and retire some common shares so the percentage of common equity in the capital structure (w_c = 1 – w_d). Given the data shown below, the cost of equity under the new capital structure minus the cost of equity under the old capital structure is _____%. If your answer is 1.23% then input 1.23 in the answer box.

Risk-free rate, rf	5.00%		Tax rate, t	25%
Market risk premium	3.50%		Current wd	0%
Current beta, bu	1.65		Target wd	77.5%

Answer 1

New cost of equity

w_c = 1 – w_d = 1 - 77.5% = 22.5%

levered beta = unlevered beta * (1 + (1 - tax rate)*(debt / equity))

levered beta = 1.65 * (1 + (1 - 25%)*(77.5% / 22.5%))

levered beta = 5.9125

cost of equity = r_f + (beta * Market risk premium)

cost of equity = 5.00% + (5.9125 * 3.50%)

cost of equity = 25.69%

Old cost of equity

cost of equity = r_f + (beta * Market risk premium)

cost of equity = 5.00% + (1.65 * 3.50%)

cost of equity = 10.60%

Difference = 25.69% - 10.60%

Difference = 15.09%

the cost of equity under the new capital structure minus the cost of equity under the old capital structure is 15.09%