Case 078Event-driven and merger arbitrageWarm up

Samvara Telecom announces a rights issue of 1 new share for every 4 held at Rs 60, with the stock at Rs 100. What is the theoretical ex-rights price, what is each right worth, and what should a holder who does not want to invest do?

The situation

Samvara Telecom needs cash for spectrum payments and announces a rights issue: 1 new share for every 4 held, at Rs 60, while the shares trade at Rs 100. Each holder receives one tradable rights entitlement per 4 shares, and each entitlement lets its owner subscribe for one new share at Rs 60 before the issue closes.

A client of your fund's prime broker holds 400 shares, worth Rs 40,000, and has no spare cash to subscribe. Ignore what the market thinks of the use of the money; assume the new cash is worth exactly what is paid for it.

Your task

What is the theoretical ex-rights price, what is each right worth, and what happens to the holder who does nothing?

Quick check

The 400-share holder lets the rights lapse. What happens to the holder's wealth?

Worked solution

Try it on paper, then open one step at a time.

30-second answerThe answer to give first

The theoretical ex-rights price is Rs 92 and each right is worth Rs 32. Four shares at Rs 100 plus Rs 60 of new cash make five shares worth Rs 460, Rs 92 each, and a right to buy a Rs 92 share for Rs 60 is worth Rs 32, or Rs 8 per old share. A holder who does nothing loses about 8%. A holder who will not invest sells the rights and stays whole.

Step 1Why does the share price fall when the rights go ex?

Picture a family pizza cut into four slices, each worth Rs 100. The family adds a fifth slice that cost only Rs 60 of dough. The pizza is now worth Rs 460 across five slices, Rs 92 a slice. Nobody at the table lost anything, provided each person either paid for a share of the new slice or sold the chance to someone who did. New shares sold below the market price lower the price per share but not the value per holder, as long as the holder takes up or sells the right.

Four shares at Rs 100 plus Rs 60 of new cash, spread over five shares4004 old sharesat Rs 100+60New cashfor 1 share4605 sharestogether460 / 5 sharesEx-rights price Rs 92down Rs 8 from 100, no value lostA right buys one Rs 92 share for Rs 60Right worth Rs 32Rs 8 for each old share held
Four Samvara shares at Rs 100 plus Rs 60 of new cash make five shares worth Rs 460, a theoretical ex-rights price of Rs 92, and the right to buy one of them for Rs 60 is worth Rs 32.
The relationship
TERP=N×P+SN+1=4×100+605=92Right=92−60=32\text{TERP} = \frac{N \times P + S}{N + 1} = \frac{4 \times 100 + 60}{5} = 92 \qquad \text{Right} = 92 - 60 = 32
Nold shares needed for one new share, 4
Pshare price before the issue, Rs 100
Ssubscription price, Rs 60
What it says in wordsThe ex-rights price is the value of the old shares plus the new cash, spread over the larger share count; a right is worth the gap between that price and the subscription price.
Step 2Why do people quote two different values for the right?

Because they count per different things. One entitlement buys one new share and is worth Rs 32; a holder gets one entitlement per four shares, so the rights are worth Rs 8 for each old share held. The textbook formula, (100 minus 60) over (4 plus 1), gives the Rs 8 figure, which is exactly the fall from Rs 100 to Rs 92. Say which one you mean before you use it; mixing them up is how a Rs 8 answer becomes a Rs 32 answer in the same sentence.

Step 3What are the holder's three choices worth?
Choice for 400 sharesCash paid, RsShares afterCash received, RsWealth after, Rs
Take up all 100 rights6,00050046,000 less 6,000 paid = 40,000
Sell all 100 rights at Rs 324003,20036,800 + 3,200 = 40,000
Do nothing, rights lapse40036,800, a loss of 3,200
Taking up the rights or selling them both leave the holder with Rs 40,000 of value; letting them lapse leaves Rs 36,800, a loss of Rs 3,200 or 8%.

So a holder who does not want to put in more money sells the rights, and stays exactly whole. Doing nothing is the only choice that loses, and it loses 8% of the holding for no reason. Companies and brokers remind holders of this for good cause: lapsed rights are a real, avoidable cost.

Step 4Where is the trade for an event-driven fund?

In the gap between the entitlement's market price and its theoretical value. Holders without cash dump their rights, so entitlements often trade below value. If they trade at Rs 28 while the shares sit at Rs 92, buying a right and paying Rs 60 gets a share for Rs 88. Short the shares at Rs 92 against it and the spread is about 4.5%, before borrow costs and the wait for the new shares to be credited. The limitation is the borrow: if the stock is hard to short, the arbitrage is just a long position with a discount.

Where candidates lose it

The common error is reading the fall from Rs 100 to Rs 92 as a loss, or as a cheap entry point, when it is simply the value moving into the rights. The holder is only worse off if the rights are ignored.

The second is confusing the two right values, Rs 32 per entitlement and Rs 8 per old share, and then getting the holder's cash from selling rights wrong by a factor of four.

What the interviewer asks next

  • The market dislikes the use of the money and the stock falls to Rs 85 before the issue closes. What is the right worth now?
  • Why might a company price a rights issue at a deep discount rather than close to the market?
  • The rights trade at Rs 36, above theoretical value. Why might that happen, and what trade does it suggest?

Company names and figures are illustrative.