We need the following "theorem", which reduces buying stocks in a leveraged
firm to buying stocks in an all equity-financed firm PLUS a borrowing.
In a 30% leveraged firm (30% debt and 70% stock), buying 1% of the
stock is equivalent to buying 1%
of the stock in an unlevered firm PLUS a borrowing equal to 30% of the
stock value.
In problem #1 we need to convert company A's stock to company B's stock and
debt, and vice versa. The idea is to convert them to the unlevered firm's
stock first. I'll use some symbols.
D(A), D(B) -- debt amount of company A and company B
E(A), E(B), E(U) -- stock amount of company A, company B and unlevered
company
<==> means "is identical to"
(Note that E(U) = asset value of the company.)
(a) Mr. X owns
1% E(A) <==>
1% E(U) + borrowing equal to 30% of (1% E(U)) <==>
1% E(B) + 1% D(B) + borrowing equal to 0.3% E(U) <==>
1% E(B) + 1% D(B) + borrowing equal to 3% of D(B) <==>
1% E(B) + borrowing equal to 2% of D(B)
So Mr. X may buy 1% of B's stock and borrow amount equal to 2% of B's
debt.
(b) Mrs. Y owns
2% E(B) <==>
2% E(U) + borrowing equal to 10% of (2% E(U)) <==>
2% E(A) + 2% D(A) + borrowing equal to 0.2% E(U) <==>
2% E(A) + 2%D(A) + borrowing equal to 0.67% D(A) <==>
2% E(A) + 1.33% D(A)
So Mrs. Y may hold 2% of A's stock and 1.33% of A's debt.
Note. From the above calculation, I believe there is a valuable short cut.
I may come back later.
Kevin
slanglois@proselect.com on 09/03/98 06:48:31 PM
To: studygroup5b@lists.casact.org
cc:
Subject: chapter 17, question and problem #1
Is anyone comfortable enough with this problem to offer the proper
technique
even though the answer is not provided in the back of the book?