I usually understand arbitrage issues (buy low, sell high).

However, I completely don’t understand the detailed solution for this problem, and I’m also unsure why one can borrow $60 without having to repay it?

Sorry, I would appreciate a detailed explanation. Thanks, everyone.

14-6. Suppose Alpha Industries and Omega Technology have identical assets that generate
identical cash flows. Alpha Industries is an all-equity firm, with 10 million shares
outstanding that trade for a price of $22 per share. Omega Technology has 20 million
shares outstanding as well as debt of $60 million.

a. According to MM Proposition I, what is the stock price for Omega Technology?

b. Suppose Omega Technology stock currently trades for $11 per share. What arbitrage
opportunity is available? What assumptions are necessary to exploit this opportunity?

a. V(Alpha) = 10*22 = 220m = V(Omega) = D + E E = 220 – 60 = 160m p = $8 per
share.

b. Omega is overpriced. Sell 20 Omega, buy 10 Alpha, and borrow 60. Initial = 220 – 220 +
60 = 60. Assumes we can trade shares at current prices and that we can borrow at the same
terms as Omega (or own Omega debt and can sell at same price

If no one else is going to have a go, I’ll take a shot, and hopefully someone will clean the answer up.

Alpha is currently trading for $22 per share and Omega for $11 per share

In part (a), they calculate that (based on the valuation of Alpha), Omega should be worth $8 per share, so they claim it is overpriced by $3 per share.

I would have given a different answer for (b).
Because Omega is overvalued, I would have sold 20 shares of Omega and brought 10 shares of Alpha. That would have a net cost of $0, because Alpha currently trades for twice the price per share of Omega.
When (if?) the market corrects the overpricing, I can close out the position and realize a profit of $60, because Omega is overpriced by $3 a share
The answer you gave takes that $60 out right at the start (by borrowing $60), so that the initial position has a net cost of minus $60. Again, when the market corrects the overpricing, I can close out the position and once again realize a profit of $60

Omega falls to 8
Buy back 20 @ 8 = 160
Sell 10 Alplha @22 = 220 cash
Gain = 60m

Think about timong how long it take for Omega to revalue.
1 day then gain is now.
Takes 1 year then present value of gain (say 10% cost) = 60/1.1 = 54.54

Now back to suggested answer.

Sell 20 Omega @ 11 = 220 cash raised
Buy 10 Alpha @ 22 = 220 cash spent
Borrow 60m cash and play with it.
When arb closes you can use gain to pay off the loan.
But you will have interest costs inbetween.

The idea of the arb is your are replicate the exposure
We aumme
Value of business = A = 220
Value of Alpha = A
Value Omega = A - 60
Re-arrange A = Omega + 60
Shorting A then would be sell Omega and borrow money

To be precise of the arb
We are long A via Alpha
And short A via Omega and loan

Theoretically no matter how arbitrage closes we should be covered.