**Unformatted text preview: **21‘ Nit. A ﬁrm knows that it will have an opportunity tn invest
$lﬂﬂ- at [:1 in either a safe (5] er risky {R} project. The
bank is aware of the alternatives, but cannet ehserve which
investment will be made. It may either lend at spent at [:1
or alternatively charge a commitment fee, and agree at t=0
to lend $lﬂﬂ at t=1 at a ﬁxed rate. One year market interest
rates are 113% at t=IZl but could be either 5% er 15% at t=l
with equal prnhability. Example — [man Cnmmitrne t Reduces a Metal
Hazard: Greenhaum and r{l995: ®9J Investment nppertunities: [=0 t=i [=2
<$lﬁﬂ
m< R<: $153
'1: 10% i=5‘i'tB er I595 cEtWW
Steps ‘ (D
(1) DO \DQS\$
C If no loan ounnnitment was made. the be [m gait . $MWJS
until the interest rate was known before pricing the l . “\CC tCCd . . brat-RV“
If interest rates were 5%. the hank would price the loan 0“
on the assumption that the safe project 1was undertaken. asg" F i
That is is: i6.ﬁ?% which is determined from: o.9><(1+i5)=1.es <=>q0/ *L3) =
_ l o§ . ~
Lg— 0 q .—\ L9 gnu, \O/
This is a Nash equilibrium in the sense that the Co
assumption that the ﬁrm would undertake the safe \ E C‘C ﬁ
project is correct. This is so because the payoff to the
firm at t=2 is greater for project S:
project 5 — 0.9 :It {15'} — 1115.63): $3ﬂ ")\f
5
project R — ll? x (153 — 11615?) = $23.93
‘PVM M“
m We? \oK
can \ooccd O“ If interest rates were 15%. the bank would price the
loan on the assumption that the safe project was undertaken. That is is: 27.?89’e which is determined
from: U.9:><[1+i3)=l.15 This however is not a Nash Equilibrium in the sense that
the assumption that the firm would undertake the safe
project is incorrect. This is so because the payoff to the
ﬁrm at t=2 is greater for project R: project S — CL? .3: [iii] — 12?.T3) = $2ﬂ project R — (L? s (153 — 12173) = $21.15 If instead the bank prices the loan on the assumption that
the risk},r project was undertaken. That is in: 154.29%
which is detennined from: '\\I ﬂ.7x(l+iﬂ)=l.15 q.) EMQOD >< (W At this interest rate however. the firm wpuld not borrow
since the required repayment would exceed the
maximum pay-off from the project. memes
rm ‘QWM wt“ "in“
\(«Qﬁg WSW 5““ Lr) : 0+ 5’) Condwm - r - (WWW?! Wm WM“ K _ 2-02 x C\S% ’- 63 w‘t \oom w\\ “‘3 tom ow’q *ch " mu.) Q t/r E7- {mesanwséée to; W‘)
fee of $3.95 an then guarantee to lend at 16.67%
irrespective of interest rates at t=1. At this interest rate the
ﬁrm would invest in the safe project (the commitment fee is
a sunk cost to the ﬁrm and does not affect its investment
decision at t=l}. If interest rates were 5%, the bank‘s pay-off at t=1 would he: 10 / 51 Else? 3; us a —=$l[|ﬂ Ltis N. Q07.
If interest rates were 15%, the bank’s pay-off at t=1 .
would he: d-
V‘
\0"- \$'/.
sues? r us _ ﬁ—P—l—
T — $91.31 a ‘ 7'
W. 4;“; to
These interest rate outcomes occur with equal C. u \3‘C
probability, and occur after tlte hank lends $1130 at t=1. Cm Cd Q
The NPV for the bank is therefore: W .
\‘o-S‘a A
NPV : $195 +($lmxﬂ_5+$]91l.l:lxﬂ.5}—$ltltl =$ﬂ ‘lr >.
get IOO
Thus, the bank expects to break-even. /
+Q\3\>< 50/) -—\oo 50.,
, - ‘l l -3\
—\v I01
+——i—
o 10/ I W comwt ‘RZ.
The ﬁrm also beneﬁts 'frent the lean eentmitment since at t=D its expected P'JP‘itIF is greater than without the lean
eemn'iitment. 1'It'il'itzhtmt: the commitment, the firm weuld enlistr horrew
if interest rates were 5%, anti weulti invest in the safe prejeet: NPV = —ﬂ'5 x $30 = $ [2.99 LﬂleJﬂ 1With the ennunitment, the ﬁrm burrows irrespective (if
interest rates and wuuld invest in the safe prujeet: ﬂﬁxﬂiﬂﬂ' + ﬂjxﬁiﬁﬂ NFV = #5335 + — = $2ﬂ.9ﬂ
LUSXIJU 1.15><L1ﬂ
S/
0 / \g/
t ‘ t \
I) t ‘2. 493 news : $30 Crc—i-cr +0
abort.) / ...

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