Question

13-Financial leverage effects

The Neal Company wants to estimate next year's return on equity (ROE) under different financial leverage ratios. Neal's total capital is $16 million, it currently uses only common equity, it has no future plans to use preferred stock in its capital structure, and its federal-plus-state tax rate is 25%. The CFO has estimated next year's EBIT for three possible states of the world: $4.8 million with a 0.2 probability, $3.1 million with a 0.5 probability, and $300,000 with a 0.3 probability. Calculate Neal's expected ROE, standard deviation, and coefficient of variation for each of the following debt-to-capital ratios. Do not round intermediate calculations. Round your answers to two decimal places.

Debt/Capital ratio is 0.

RÔE:	___________ %
σ:	___________ %
CV:	___________

Debt/Capital ratio is 10%, interest rate is 9%.

RÔE:	__________ %
σ:	__________ %
CV:	___________

Debt/Capital ratio is 50%, interest rate is 11%.

RÔE:	________ %
σ:	________ %
CV:	_________

Debt/Capital ratio is 60%, interest rate is 14%.

RÔE:	__________ %
σ:	__________ %
CV:	___________

Answer 1

Solution:

ROE = (0.2*22.50) + (0.5*14.53) + (0.2*1.41)

= 12.19%

Standard Deviation = Square Root [{0.2*(22.50%-12.19%)²} + {0.5*(14.53%-12.19%)²} + {0.3*(1.41%-12.19%)²}

= 7.67%

CV = 7.67% / 12.19%

= 0.63

ROE = (0.2*24.25) + (0.5*15.40) + (0.2*0.81)

= 12.79%

Standard Deviation = Square Root [{0.2*(24.25%-12.79%)²} + {0.5*(15.40%-12.79%)²} + {0.3*(0.81%-12.79%)²}

= 8.53%

CV = 8.53% / 12.79%

= 0.67

ROE = (0.2*36.75%) + (0.5*20.81%) + (0.2*-5.44%)

= 16.13%

Standard Deviation = Square Root [{0.2*(36.75%-16.13%)²} + {0.5*(20.81%-16.13%)²} + {0.3*(-5.44%-16.13%)²}

= 15.35%

CV = 15.35% / 16.13%

= 0.95

ROE = (0.2*40.50%) + (0.5*20.58%) + (0.2*-12.23%)

= 14.72%

Standard Deviation = Square Root [{0.2*(40.50%-14.72%)²} + {0.5*(20.58%-14.72%)²} + {0.3*(-12.23%-14.72%)²}

= 19.18%

CV = 19.18% / 14.72%

= 1.30