### CFA Practice Question

There are 534 practice questions for this study session.

### CFA Practice Question

BWT Inc. shows the following data in its financial statements at the end of the year. Assume all securities were outstanding at the beginning of the year:

• 6.125% convertible bond, convertible into 33 shares of common stock. Issue price \$1,000, 100 bonds outstanding.
• 6.25% convertible preferred stock, \$100 par, 2,315 shares outstanding. Convertible into 3.3 shares of common stock, issue price \$100.
• 8% convertible preferred stock, \$100 par, 2,572 shares outstanding. Convertible into 5 common shares, issue price \$80.
• 9,986 warrants are outstanding with an exercise price of \$38. Each warrant is convertible into 1 share of common stock.
• Average market price of common stock is \$52.00 per share. Common shares outstanding at the beginning of the year were 40,045.
• Net income for the period was \$200,000 while the tax rate was 40%.

What were the diluted EPS for the year?
A. 2.95
B. 3.01
C. 3.06
Explanation: (100 bonds)(33 common shares/bond) = 3,300 common shares
(2315 preferred shares)(3.3) = 7640
(2572 preferred shares)(5) = 12860
7640 + 12860 = 20,500 common shares
from preferred [(\$200,000 - \$35,045) + \$35,045 + \$3,675]/(40,045 + 3,300 + 20,500 + 2689) = \$203,675/66534 shares = 3.06

User Comment
kalps Can someone explain what is going on in the numerator please, I do not understand why the \$35,045 is being subtracted and then added again - i am slightly confused especially by the poor workign sgiven without any explanation whatsoever
kalps Why is the working for this question so BAD - it take bloody ages to understand what is going on - i think this is very poor and should be written clearly and explained
pablo kalps: the 35045 = div on pref stock 20576 plus pre-tax div conv pref bond 14469. being subtracted as per basic eps then added back for diluted eps as these securities are both dilutive. NOTE: Conv. pref. bonds have been treated as equity in this solution - can anybody confirm that this is correct - I had expected them to be be deductible debt.
Yuyan I think the correct choice should be D.

Preferred bond is not the same thing as preferred stock. I think it should be treated as convertible bond. The after-tax interest expense on it should be added back to the earnings. Dilluted EPS =(100*1000*6.125%*0.6 + 100*2315*6.25%*0.6 + 200,000) / (3300+2315*3.3+2572*5+2689+40045) = 3.19

Number of common shares from warrants = 9986 - 9986*38/52 = 2689
shasha i may be lacking of knowledge a bit, Yuyan. Is there anything called Preferred Bond? Is it possible the question referred actually to two different Convertible Preferred Stocks? believe the answer is right.
Yuyan After working on other problems, I think shasha is right. Here the preferred bond refers to preferred stocks. Some financial articles do talk about preferred bond. But it's not common.
Gemini I think sasha is right. Answer is C, the convertible preferred bond has to be treated as a convertible preferred stock
turtle what about 6.25% "convertible preferred bond" - why not included in calculation? - answer would be 3,19; are they antidillutive?
annex it is aleady included in the number of 35045
mm05 Where is the 35045 from?
yesficom What about the exercisable warrants?
yesficom Why does it deducts and adds back and not just add the 35045?
yanpz Why the explanation didn't mention Warrents? I treated the 6.25% preferred bond as no-tax-deduction bond, and consider warrant, then got the answer of 3.066, then I picked up C...
Warrant exercise price is \$38, lower than market price \$52, so it should be considered.
Nick2005II The warrants are considered; you use the Treasury method to calculate the impact. The numerator doesn't change, the denominator is affected in the following manner:
9986-[(9986*38)/52]
danlan 6.25% convertible bond means preferred stock and not bond! So we get 200000+(1-40%)*61.25*100 and not 200000+(1-40%)*(61.25*100+6.25*2315)
ljamieson Still no answer on why add 35045 then subtract again? Wouldn't it be easier to just drop it from the solution, and maybe give a reason for either?
ljamieson ok i get it. pablo had it in post 3.
jainrajeshv Anybody can explain what is difference between Preferred Bond and stock? and why net income is calculated before deducting Interest on preferred Bond?
VenkatB Diluted EPS = ((Net Income -Preferred Dividends) + Preferred Dividends + (After-Tax amount of Interest Expense on Bonds Converted)) / (Weighted Average Number of Common Shares Outstanding + Equivalent Number of Potential Common Shares from the Conversion of All Outstanding Dilutive Securities)

OR

Diluted EPS = (Net Income + (After-Tax amount of Interest Expense on Bonds Converted)) / (Weighted Average Number of Common Shares Outstanding + Equivalent Number of Potential Common Shares from the Conversion of All Outstanding Dilutive Securities)

Assuming all of the convertibles are dilutive, below is the explanation.
(Not showing the test for anti-dilutive or dilutive)
- 6.125% convertible bond, convertible into 33 shares of common stock. Issue price \$1,000, 100 bonds outstanding.
Total Interest on the Bond = 6.125 *(100 *10000)= 6125
After tax amount of the Interest on bonds = (1-0.40) * 6125 =3675
Total New Common Stock = 100 *33 = 3300

- 6.25% convertible preferred bond, \$100 par, 2,315 shares outstanding. Convertible into 3.3 shares of common stock, Issue price \$100
Dividends = 6.25% (2315 *100) = 14468.75

Total New Common Stock = 2,315 *3.3 = 7639.5

- 8% convertible preferred stock, \$100 par, 2,572 shares outstanding. Convertible into 5 common shares, Issue price \$80
Dividends = 8% (2572 *100) = 20576

Total New Common Stock = 2572 *5 = 12860

- 9,986 warrants are outstanding with an exercise price of \$38. Each warrant is convertible into 1 share of common. (Average market price of common is \$52.00 per share)
Total New Common Stock = 9986 * 1 - (9986*38)/52 = 2688.54

Diluted EPS Calculation:
Numerator for Basic EPS = 200000- (14468.75 +20576)

(14468.75 +20576) represents the amount that would be available for common stock holders, if preferred dividends are not paid.

Numerator for Diluted EPS = Numerator for Basic EPS + (14468.75 +20576) + 3675 = 203675

Denominator for Diluted EPS = 40,045 +3300+7639.5+12860 + 2688.54 = 66533.04

Diluted PES = 203675 / 66533.04 = 3.061261
Drzewes Respect VenkatB.
vavoev VenkatB you did a great job. Thanks a lot. But is it real exam question? Its take a lot of time. In real exam, i will prefer to gamble this question.
copus I agree with vavoev.....if you get a question like this on the exam, you gamble. The risk return on this question does not make sense.....not even Warren Buffett could get the answer in 90 seconds!
Allen88 Great job VenkatB! Thanks a lot!
jpducros Guys, sorry for the bad news, but this type of question is definitely an expected question on the exam. VenkatB's answer is great for understanding...but you should expect to do this question in, lets say 3 mn. With practice you can do it !
gill15 this question doesnt take long....you dont need to write everything out if you know how to do it....you can do it with ease in two minutes...

just know what to put in the numerator and denominator...
endurance The two preferred stock issues are convertible into common shares (not pref shares), that's why they are added back in the numerator.
RAustin A few issues with this explanation: 1.) Dividends on convertible preferred stock should be added as it is dilutive, the author subtracts from NI and then adds it back, but only preferred dividends should be subtracted, NOT dividends on convertible preferred. 2.) The calculation for warrants was not explained, although someone answered very well in the previous comments. The diluted EPS should be \$3.59 by my figures.
sunnyhui how did the total interest on bond become
6.125*(100*10000)=6125 where did the 10000 come from
ConnerVP1 VenkatB Why does your original formula have (NI + After-tax amount of Interest Expense on Bonds Converted) in the numerator, but later in the calculation you use (Numerator for Basic EPS + After-tax amount of Interest Expense on Bonds Converted) ?
ConnerVP1 Nevermind I see now
Alexeyzz Hi everyone! Why didn't we use tax where added back agter convertation?
we must multiple 35045*(1- tax rate),??