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**CFA Practice Question**

TCH Corporation is considering two alternative capital structures with the following characteristics.

Debt/Assets ratio 0.3 | 0.7

kd 10% | 14%

A | B

Debt/Assets ratio 0.3 | 0.7

kd 10% | 14%

The firm will have total assets of $500,000, a tax rate of 40 percent, and book value per share of $10, regardless of capital structure. EBIT is expected to be $200,000 for the coming year. What is the difference in earnings per share (EPS) between the two alternatives?

A. $4.78

B. $2.87

C. $3.03

**Explanation:**Capital structure A: The firm will have debt of $500,000(0.3) = $150,000 and equity of $350,000. We're told the shares have a book value of $10, so the number of shares outstanding is $350,000/$10 = 35,000. Interest expense will be $150,000(10%) = $15,000. We can compute EBT as EBIT - I or $200,000 - $15,000 = $185,000. Also, we can compute NI as EBT(1 -T) or $185,000(1 - 0.4) = $111,000. Finally, EPS = $111,000/35,000 = $3.17.

Capital structure B: The firm will have debt of $500,000(0.7) = $350,000 and equity of $150,000. The number of shares outstanding is $150,000/$10 = 15,000. Interest expense will be $350,000(14%) = $49,000. We can compute EBT as $200,000 - $49,000 = $151,000. Also, we can compute NI as $151,000(1 - 0.4) = $90,600. Finally, EPS = $90,600/15,000 = $6.04. The difference in EPS between capital structure A and capital structure B is $6.04 - $3.17 = $2.87.

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**User Contributed Comments**
22

User |
Comment |
---|---|

garachen |
so 'kd' means "interest on debt" |

Will1868 |
Kd is the "cost of debt" as in the WACC equation, wacc = wd*kd + wde*ke.... k = cost of that type of capital. |

elda |
So, kd is before taking consideration of tax shield? |

Mutizwa |
kd is gross cost of debt i.e before tax considerations! |

eddeb |
Someone spent less than 1.5 min on that question? |

danlan |
Good question, I forgot to reduce the interest expense from EBIT |

mc01 |
wacc= wd*kd(1-t) + we*ke + wp*kp make sure not to forget the tax rate |

steved333 |
It's okay to spend more than 1.5 minutes on a question. There are so many that only take a second to do. As long as you average out to it, you'll be fine. Do the easy ones first. (well, the easiER ones first...) |

Kuki |
aahh...so thats how we find the number of shares...i got stuck there! |

grezavi |
This is the way I got the same answer and it turned out to be right: Debt A=150,000 or B=350,000 EPS= A=200k + 90k (Int Exp Tax Gain)B=200k + 210k Get New earnings numerator, I used 500000/10 to compute denominator 50,000 Calculate EPS for A=5.8 and B=8.2 I got 2.4 which was close enough. HTH ! |

fanfanli |
Ahh...Distinguish between Debt/Asset and Debt/Equity! |

u0302638 |
by digusing interest cost as kd...I totally forget to calculate Interest Exp |

mekc |
shares = EQ/BVper sh |

kellyyang |
who can provide a easy way this problem? |

JeremyMartin |
Total Assets: A = 500,000 B = 500,000 Debt to Assets: A = 0.3 B = 0.7 Debt: (calculated from given D/A ratio) A = 150,000 B = 350,000 KD: (cost of debt, before tax) A = 10% B = 14% Interest: (cost of debt x debt) A = 15,000 B = 49,000 EBIT: A = 200,000 B = 200,000 Interest: (KD x Debt) A = 15,000 B = 49,000 EBT: (EBIT - Interest) A = 185,000 B = 151,000 Tax: (EBT x Tax Rate 40%) A = 74,000 B = 60,400 Net Income: (EBT - Tax) A = 111,000 B = 90,600 ------------------------------ Equity to Assets: (1 - Debt to Assets) A = 0.7 B = 0.3 Equity: (Total Assets x Equity to Assets) A = 350,000 B = 150,000 Book Value per share = $10 (given) Number of shares: (Equity/BV per share) A = 35,000 shares = 350,000/10 B = 15,000 shares = 150,000/10 EPS:(Net Income/number of shares) A = 3.17 = 111,000/35,000 B = 6.04 = 90,600/15,000 Difference in EPS: 6.04 - 3.17 = 2.87! |

MaresaJaden |
Thanks Jeremy!! |

indrayudha |
Wow, Analyst Notes should copy your answer, Jeremy. |

Insipidity |
Great answer, Jeremy! |

tommyguard3 |
Wow...glad I signed up for analyst notes, would have cried if I saw this on the actual exam. Now that I've seen it seems pretty easy if a bit long. |

mary11 |
Don't worry -there will still be questions on the real exam that will make you cry. |

petervinh18 |
Let's me try answer this question in dumb way: A: [($500k x 0.3)x(1+10%)]/($200k) = $0.825 B: [($500k x 0.7)x(1+14%)]/($200k) = $1.995 Difference EPS = A + B => $0.825+$1.995 = $2.82. So if there are number farther than $2.82 then it would right choice to choose; but there are number close or near this number then this method totally incorrect. |

birdperson |
jeremy well done, great answer |