Question

RAK, Inc., has no debt outstanding and a total market value of $150,000. Earnings before interest and taxes, EBIT, are projected to be $36,000 if economic conditions are normal. If there is strong expansion in the economy, then EBIT will be 15 percent higher. If there is a recession, then EBIT will be 25 percent lower. RAK is considering a $95,000 debt issue with an interest rate of 8 percent. The proceeds will be used to repurchase shares of stock. There are currently 6,000 shares outstanding. Ignore taxes for questions a and b. Assume the company has a market-to-book ratio of 1.0. a-1 Calculate return on equity (ROE) under each of the three economic scenarios before any debt is issued. (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) ROE Recession % Normal % Expansion % a-2 Calculate the percentage changes in ROE when the economy expands or enters a recession. (Negative amounts should be indicated by a minus sign. Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) % change in ROE Recession % Expansion % Assume the firm goes through with the proposed recapitalization. b-1 Calculate the return on equity (ROE) under each of the three economic scenarios. (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) ROE Recession % Normal % Expansion % b-2 Calculate the percentage changes in ROE when the economy expands or enters a recession. (Negative amounts should be indicated by a minus sign. Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) % change in ROE Recession % Expansion % Assume the firm has a tax rate of 35 percent. c-1 Calculate return on equity (ROE) under each of the three economic scenarios before any debt is issued. (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) ROE Recession % Normal % Expansion % c-2 Calculate the percentage changes in ROE when the economy expands or enters a recession. (Negative amounts should be indicated by a minus sign. Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) % change in ROE Recession % Expansion % c-3 Calculate the return on equity (ROE) under each of the three economic scenarios assuming the firm goes through with the recapitalization. (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) ROE Recession % Normal % Expansion % c-4 Given the recapitalization, calculate the percentage changes in ROE when the economy expands or enters a recession. (Negative amounts should be indicated by a minus sign. Round your answers to 2 decimal places. (e.g., 32.16)) % change in ROE Recession % Expansion %

Answer #1

Without Taxes

RAK | Expansion | Normal | Recession |

EBIT | 41,400 | 36,000 | 27,000 |

ROE | 27.60% | 24.00% | 18.00% |

% Change | 15.0% | -25.0% | |

With Debt | Boom | Normal | Recession |

EBIT | 41,400 | 36,000 | 27,000 |

Interest | -7,600 | -7,600 | -7,600 |

Profits | 33,800 | 28,400 | 19,400 |

ROE | 61.45% | 51.64% | 35.27% |

% Change | 19.0% | -31.7% |

With Taxes

RAK | Expansion | Normal | Recession |

EBIT | 41,400 | 36,000 | 27,000 |

Taxes (35%) | -14,490 | -12,600 | -9,450 |

Profits | 26,910 | 23,400 | 17,550 |

ROE | 17.94% | 15.60% | 11.70% |

% Change | 15.0% | -25.0% | |

With Debt | Boom | Normal | Recession |

EBIT | 41,400 | 36,000 | 27,000 |

Interest | -7,600 | -7,600 | -7,600 |

EBT | 33,800 | 28,400 | 19,400 |

Taxes (35%) | -11,830 | -9,940 | -6,790 |

Profits | 21,970 | 18,460 | 12,610 |

ROE | 39.95% | 33.56% | 22.93% |

% Change | 19.0% | -31.7% |

Without debt, Equity = 150,000 and with debt, Equity = 150,000 - 95,000 = 55,000

Interest expense = 95,000 x 8% = 7,600

ROE = Profits / Equity

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