49.
Firm A and Firm B operate in a perfect capital market environment. Each
generates $5M (M = million) of operating income. Firm A pays $1.8M in interest giving a net
income of $3.2M. Firm B pays no interest and so its net income is $5M. Firm A and Firm B have
respective market values of $30M and $25M. Firm A’s debt is $15M while Firm B’s debt is 0.
You own 1% of Firm A’s equity and can borrow at 12%. What amount can you make through the
arbitrage process without taking on additional risk?
a.
$10,000
b.
$10,250
c.
$11,000
d.
$11,250
[
ANSWER:
You sell your equity ownership at a market value of 0.01($15M) = $0.15M and
borrow $0.15M at 12% per year thereby mimicking Firm’s A capital structure where L = D / V =
$15M / $30M = 0.5 implying you have the same risk. You now use the $0.15M + $0.15M =
$0.3M to buy $0.3M / $25M = 0.012 or
1.2%
of Firm B. In acquiring 1.2% of Firm B, you give
up income of 0.01($3.2M) =
$32,000
. In turn, you now received 0.012($5M) – 0.012($0.15M) =
$0.06M – $0.018 = $0.042M or
$42,000
. Thus, with identical risk, you have received an arbitrage
profit of $42,000 – $32,000 =
$10,000 more per year
.]
c
50.
Firm A and Firm B operate in a perfect capital market environment. Each
generates $5M (M = million) of operating income. Firm A pays $1.8M in interest giving a net
income of $3.2M. Firm B pays no interest and so its net income is $5M. Firm A and Firm B have
respective market values of $30M and $25M. Firm A’s debt is $15M while Firm B’s debt is 0.
You own 2% of Firm A’s equity and can borrow at 12%. What amount can you make through the
arbitrage process without taking on additional risk?
[
borrow $0.3M at 12% per year thereby mimicking Firm’s A capital structure where L = D / V =
$15M / $30M = 0.5 implying you have the same risk. You now use the $0.3M + $0.3M = $0.6M
to buy $0.6M / $25M = 0.024 or
2.4%
of Firm B. In acquiring 2.4% of Firm B, you give up
income of 0.02($3.2M) =
$64,000
. In turn, you now received 0.024($5M) – 0.024($0.15M) =
$0.12M – $0.036 = $0.084M or
$84,000
. Thus, with identical risk, you have received an arbitrage
profit of $84,000 – $64,000 =
$20,000 more per year
.]
a
51.
Firm A and Firm B operate in a perfect capital market environment. Each
generates $10M (M = million) of operating income. Firm A pays $3.6M in interest giving a net
income of $6.4M. Firm B pays no interest and so its net income is $10M. Firm A and Firm B
have respective market values of $60M and $50M. Firm A’s debt is $30M while Firm B’s debt is
0. You own 1% of Firm A’s equity and can borrow at 12%. Assuming you seek to make a riskless
arbitrage profit by selling all of your shares, which of the following will occur in the process of
making this profit?
personal leverage ratio of 0.5, and generate an arbitrage profit of $20,000 more per year.
$20,000 more per year.
interest of $36,000, and generate an arbitrage profit of $20,000 more per year.
Firm A to acquire 1.2% of Firm B, and generate an arbitrage profit of $40,000 more per year.