Re: 5B, ch 17-4c and Fall 94, #28

Richard Goldfarb ( (no email) )
Mon, 19 Apr 1999 22:43:17 -0700

There are various ways to do this, but the best way to see what is happening
is as follows. Let's make things simple and assume we have total Earnings
of 100, 100 shares outstanding (earnings per share will be $1) and a stock
price of 10 based on the P/E ratio of 10. If you repurchase half of the
shares, then you will issue $500 of debt and buy back 50 shares at the price
of $10 each. The earnings will then drop by the interest on the debt, so
total earnings will be 100-500*5%=75. This results in an EPS of 75/50=1.50
(remember that there are now only 50 shares outstanding). That's a 50%
increase in EPS. Because we used the new debt to buy back the shares, the
price of the stock should not have changed - remember that the change in
capital structure doesn't affect the total firm value, so if we eliminate
50% of the equity value and reduce the number of shares by 50% too, the
price is the same. So the P/E ratio is now 10/1.5=6.67.

The other way to do this is to note that in this question the rate of return
on equity is the Earnings/Price (remember from Ch 4 that r=E/P if earnings
are constant in perpetuity). So in this case, when the return on equity
becomes 15%, then 15%=E/P and the P/E ratio becomes 1/.15=6.67. And since
15%=E/P, then E=.15P. Before E=.1P when the P/E ratio was 10, so the E has
increased by 50%. I don't recommend thinking about it this way though. The
first way I did it let's you see more clearly what is really happening, and
it is safer in situations in which you are paying a dividend rather than
repurchasing shares.

Ch 20
As I wrote before, for position diagrams the safest and easiest method is to
just plot points. Always plot points like zero, the exercise prices, a
point above and a point below. Then connect the dots - they are always
connected with straight lines. Take your second case. When you lend
someone money today, they will repay you 100 at the end, so that payoff is
always +100. Plot some points. When S=0, the loan payoff is 100, the two
calls are both zero. When S=100, the loan payoff is 100, and both calls are
zero. When S=200, the loan payoff is 100, the call you sold has a payoff
of -100 (negative because you sold the option so someone else has the right
to buy it from you for 100 and it is worth 200), the call you bought has a
payoff of zero, for a net payoff of zero. When S=210, loan payoff is 100,
the call you sold payoff is -110, the call you bought payoff is 10, for a
net of 0. Now connect the dots and you have the diagram you provided in
your original e-mail.

Hope this helps.
----- Original Message -----
From: <Shenaz_Keshwani@mercer.com>
To: <studygroup5b@lists.casact.org> Goldfarb; Richard
<Goldfarb@WESTPORT.MSMAIL.AIGFPC.COM>
Sent: Monday, April 19, 1999 3:55 PM
Subject: 5B, ch 17-4c and Fall 94, #28

> Richard:
>
> Thank you for your all your tips in the past. Here is the question I
> had asked about earlier this morning.
>
>
>
> First problem: chapter 17 Quiz # 4c
>
> Company C is financed entirely by common stock and has a beta of 1.0.
> The stock has a P/E multiple of 10 and is priced to offer a 10%
> expected return. The company decides to repurchase half the common
> stock and substitute an equal value of debt. Assume that the debt
> yields a risk free 5%
>
> (After some calculations we find that the rate of return on the
common
> stock after refinancing is 15% and Beta of equity after refinancing
is
> 2.0)
>
>
> C) Assume that the operating profit of firm C is expected to remain
> constant. Give:
>
> i) The percentage increase in earnings per share
> ii) The new price-earnings multiple.
>
>
> Second Problem Fall 94 #28.
>
> Fall 94 # 28 is from Chapter 20. It has to do w the position
diagrams
> and I tried to create them by using the drawing tools in excel.
> However when I attach the file the drawing is not coming through. I
> could fax you the problem and perhaps you may be able to shed some
> light.
>
> Basically, I am having trouble combining the different position
> diagrams into one diagram. For example how would I represent the
> following:
>
> borrowing the present value of 100 at the risk free rate, buying two
> shares of stock, and selling one call with an exercise price of $100
>
> lending the PV of 100 at the risk free rate, selling a call with an
> exercise price of 100 and buying a call with excercice price of
$200.
>
>
>
>
> ______________________________ Reply Separator
_________________________________
> Subject: RE: 5B, Fall 94, #28
> Author: "Goldfarb; Richard" <Goldfarb@WESTPORT.MSMAIL.AIGFPC.COM> at uucp
> Date: 4/19/99 2:26 PM
>
>
> While I await the full question from you, here's what I think will clear
> things up for you.
>
> In all questions like this, there is rarely any subtle meaning behind it
> all. Simply plot a few points and connect the dots. Take Figure E for
> example. If the stock price is zero, then you have to repay the 100
> that you borrowed, that's -100. The 2 shares of stock are worth zero
> and the call option you sold is zero, so the total is -100. If the
> stock price is 100, then the borrowing is again -100, the two shares are
> 200 and the option payoff is zero, for a total of 100. Then if stock is
> 101, then borrowing is -100, stock is 202 and the option is -1, so
> that's 101. Connect the three dots and you are done.
>
> The only thing to be careful about in these cases is to plot points at,
> above and below the exercise prices of the options. That's where all
> the action will be. So if there are several options involved in a
> particular strategy, be sure to plot points at each exercise price and
> at points in between.
>
> The search for additional meaning is pointless. After a bit of practice
> though, you should be able to start to see some patterns.
>
> > -----Original Message-----
> > From: Shenaz_Keshwani@mercer.com [SMTP:Shenaz_Keshwani@mercer.com]
> > Sent: Monday, April 19, 1999 2:58 PM
> > To: studygroup5b@lists.casact.org; Richard Goldfarb
> > Subject: 5B, Fall 94, #28
> >
> >
> > Chapter 20/21
> >
> > What do figures B and E represent. I have tried to draw the figures
> > in the
> > attached file.
> >
> > Thanks
> >
> >
> > Shenaz << File: MS Excel spreadsheet >>
>