BUS326Lecture6example - 21 Nit A rm knows that it will have an opportunity tn invest $l at:1 in either a safe(5 er risky cfw_R project The bank is aware

BUS326Lecture6example - 21 Nit A rm knows that it will have...

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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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