### CFA Practice Question

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

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.

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!