Takeovers and short-term behaviour
Stein (1988)
The value of the firm may not be known to outsiders, and
therefore not reflected in current share price.
• The true value of current projects may be difficult to
verify.
A bidder’s offer may be tempting to shareholders, based on
current share price.
Suppose the manager knows that current share price
undervalues the firm. Could he do anything in order to give
the shareholders a better price (or convince them not to sell
yet)?
The manager may choose an action revealing to outsiders
that the firm has valuable projects, but at the same time
reducing the firm’s possibilities to take advantage of the
full, long-term value of those projects.
This way, the position of current shareholders is improved,
but the long-term value of the firm is reduced.
Illustrating case: an oil company whose oil reserves are
unknown to outsiders (including current shareholders).
Tore Nilssen – Economics of the Firm – Lecture 5 – slide 1
The model
Date 1:
The oil company’s manager learns about its oil reserves, x:
The good state: x = x1 barrels of oil, with probability p.
The bad state: x = x2 barrels of oil, with probability (1 – p),
where x2 < x1.
Oil reserves are not observed by shareholders.
Oil sold at date 1 has value 1 per barrel.
Oil sold at date 3 has value (1 + r) per barrel.
No discounting.
The manager decides whether to sell some oil at date 1.
This is bad for the long-term value of the firm.
But it tells outsiders that the firm has oil.
Date 2:
A raider arrives who will enhance the firm’s value by v.
At date 1, v is uncertain, with cumulative distribution F(v).
The raider does not know x.
The raider decides whether to attempt a takeover, at cost c.
In the takeover, the extra value accrues to the raider.
(No free-rider problem.)
Date 3:
The firm sells any oil left and pays out dividends to owners.
Tore Nilssen – Economics of the Firm – Lecture 5 – slide 2
The raider knows what shareholders know.
ƒ uninformed raider
Being able to capture all the extra value, the raider makes a
takeover bid if v ≥ c.
By definition, F(v’) = Prob(v ≤ v’)
→ Seen from date 1, the probability of a takeover bid is
1 – F(c), which is denoted G(c).
Suppose the firm sells oil at date 1 in order to convince
outsiders that it has a lot of oil. For this to be convincing, it
must sell at least x2.
Strictly speaking, an amount x2 + ε is required. But ε can be very small. So let’s assume
that outsiders are convinced if the firm sells x2.
The firm’s value with oil sales of x2 at date 1 is:
x2 + (1 + r)(x1 – x2) = (1 + r)x1 – rx2
ƒ signalling costs: rx2
If the firm sells less than x2, then outsiders are not
convinced, so it might as well sell 0.
But there are two ways the outsiders may respond to a zero
sale of oil at date 0:
• only a low-value firm would sell a zero amount; or:
• while a sale of x2 convinces them that oil reserves are
large, there is nothing in particular to learn from a zero
sale – the firm could still be of either high or low
value.
Tore Nilssen – Economics of the Firm – Lecture 5 – slide 3
“Separating beliefs”
- Only a low-value firm would sell a zero amount
Suppose the firm has large oil reserves: x = x1.
Does it pay to sell oil already at date 1?
If it sells x2 at date 1 and outsiders believe it has a lot of oil,
then shareholders will receive (1 + r)x1 – rx2, either from a
raider at date 2 or as dividends at date 3.
If it does not sell oil at date 1, then outsiders believe it has
little oil, and the outcome is a lottery:
• With probability G(c), the firm is taken over at the
stock price x2(1 + r) (the expected value of a firm that
is believed to have little oil)
• With probability 1 – G(c), the firm survives to date 3,
and it can sell all its oil so that shareholders receive
x1(1 + r).
It pays for a high-value firm to sell early if:
⇔
⇔
(1 + r)x1 – rx2 ≥ G(c) x2(1 + r) + [1 – G(c)] x1(1 + r)
G(c)(1 + r)(x1 – x2) – rx2 ≥ 0
G (c ) ≥
r
x2
1 + r x1 − x2
⇔
c ≤ cs, where cs solves G (cs ) =
r
x2
.
1 + r x1 − x2
Tore Nilssen – Economics of the Firm – Lecture 5 – slide 4
“Pooling beliefs”
- There is nothing to learn from a zero sale.
Interpretation: patient shareholders – even good firms may
have low profits early on.
Now, if the firm does not sell anything at date 1, then the
stock price at which a takeover occurs, with probability
G(c), is:
(1 + r)[px1 + (1 – p)x2]
It pays for a high-value firm not to sell early if:
⇔
⇔
(1 + r)x1 – rx2 ≤
G(c)[px1 + (1 – p)x2](1 + r) + [1 – G(c)] x1(1 + r)
G(c)(1 + r)(1 – p)(x1 – x2) – rx2 ≤ 0
G (c ) ≤
r
x2
1 + r (1 − p )( x1 − x2 )
⇔
c ≥ cp, where cp solves G (c p ) =
r
x2
.
1 + r (1 − p )( x1 − x2 )
Note: cp < cs.
Tore Nilssen – Economics of the Firm – Lecture 5 – slide 5
Conclusion
• If c is low (c < cp), then surely a high-value firm will
sell oil early. (separating equilibrium)
• If c is high (c ≥ cs), then a high-value firm will not sell
early and will instead behave like a low-value firm.
(pooling equilibrium)
• If c is intermediate (cp ≤ c < cs), then there are two
equilibria, one where a high-value firm will sell early
and one where it will not.
• In any case, a low-value firm will not sell early.
Welfare
Normally, lower bidding costs are a good thing.
• Takeover improves firm value. Lower bidding costs
make a takeover more likely.
But here: Lower bidding costs may lead to the firm selling
oil too early.
Takeovers improve firm value, but at the same time make
the firm behave in a more short-sighted way.
The basic welfare trade-off with respect to takeovers:
Efficiency versus short-sightedness.
Regulations: Tighter regulations – higher c.
Extension: Informed raider – lower signalling costs –
shortsightedness more likely, but less damaging.
Tore Nilssen – Economics of the Firm – Lecture 5 – slide 6