Chapter 11 Practice Problems Answers

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1 Chapter 11 Practce Problems Answers 1. Would you be more wllng to lend to a frend f she put all of her lfe savngs nto her busness than you would f she had not done so? Why? Ths problem s ntended to make students thnk of moral hazard. By puttng her lfe savngs nto her busness, the owner s less lkely to take on excessve rsk that endangers your money. The dea s smple, wthout nvestng her money n the busness, f the busness fals the owner does not lose (much) personally and hence does not act n a way to protect aganst busness falure. Possbly, by not havng any money n reserve, the owner would be subject to random proft shocks that makes her busness more rsky. Therefore, some amount of money between no savngs and total lfe savngs may be optmal to requre the owner to nvest. 2. How can the exstence of asymmetrc nformaton provde a ratonale for government regulaton of fnancal markets? In the presence of asymmetrc nformaton, markets wll not functon well or, possbly, wll not functon at all. By requrng publcly traded frms to release nformaton about themselves, the government reduces the asymmetrc nformaton problem and encourages fnancal markets to work better. 3. Imagne that there are twenty of each of two types of people n the world: safe and rsky. Safe people have access to a project that, gven $1000 wll automatcally return $1200. Rsky people can nvest ther $1000 and get a return 30% of the tme of $1400, 50% of the tme of $1000, and 20% of the tme $0. For ease of computaton, assume that you (the banker) do not accept collateral on any loans and the borrowers do not have any money of ther own. Fnally, magne that n the case of default, the borrower ends up wth nether a loss or a gan; n other words the lender loses the amount lent and the borrower pays no bankruptcy costs. a. Plot the demand curve for loans (wth nterest rates on the vertcal axs and quantty of $ on the horzontal axs). The demand curve appears as: 40% 20% 20,000 40,000 Q

2 b. Imagne that you have $40,000 to lend. Plot the supply curve of loans aganst the demand curve. What s the equlbrum nterest rate(s) n ths market? If ths market for loans was perfectly compettve (meanng lenders make zero expected profts), what nterest rate would preval? Too low an nterest rate results n negatve bank profts so banks would not choose to supply funds at these rates. The lowest possble nterest rate a bank would charge and make zero profts s gven by the equaton: ( ) = 0. Solvng for gves = 15.38%. The supply and demand curves are: 40% supply 20% 15.38% 20,000 40,000 Q The equlbrum nterest rate s any nterest rate between 15.38% and 20%. In a zero-proft market, the prevalng nterest rate would be 15.38% and $40,000 worth of loans would be made. c. Wthout takng nto account the nformaton asymmetres, what s the theoretcal mpact on the nterest rate and quantty of funds lent/borrowed gven a decrease n the supply of funds? A decrease n the loanable funds suppled should rase nterest rates and lower the loans traded. d. Imagne that nstead of havng $40,000 to lend, you have only $20,000. Plot the new supply curve of loans aganst the demand curve. What s the equlbrum nterest rate(s) n ths market? Is ths the nterest rate you would charge as a lender? Why or why not? The new pcture would appear as: 40% supply 20% 15.38% 20,000 40,000 Q

3 The equlbrum level of nterest rates s between 20 and 40% where $20,000 of loans wll be made. However, at any of these nterest rates, only rsky borrowers take loans out and, even at 40% nterest, the bank makes negatve profts: 20 ( ) = However, t s possble for a bank to make a postve proft n ths case. By randomly assgnng loans to people (and chargng an <20%), the bank wll, on average, make 10 loans to rsky ndvduals and 10 loans to safe ndvduals. At an nterest rate of 20%, ths would generate profts of: ( ) = 600. Notce, at nterest rate of 20%, 40 ndvduals demand loans and only 20 are made. Thus, we are not n an economc equlbrum but we are n a stuaton that s better for the bank. e. Many poltcans realze the power banks have n stmulatng the economy. For nstance, f, durng recessons, banks were to lend more money then the economy would more quckly expand. One such polcy of rasng lendng s to gve busnesses tax breaks for recevng borrowed funds. The hope s to ncrease demand for loans, rase total borrowng, and ncrease economc output. In the case of credt ratonng presented n part d, do governmental polces of ncreasng demand for loans actually stmulate the economy? Why or why not? By gvng tax breaks, poltcans are ncreasng the demand for loans. In typcal markets, ths ncreases the quantty borrowed and rases the equlbrum prce of loans. In the presence of credt ratonng though, hgher demand for loans may not translate nto lenders actng dfferently f they can make hgher profts at an nterest rate outsde of equlbrum. In other words, governmental polces may not alter lendng behavor and may not stmulate the economy. 4. As a banker, you know that your clents have two opportuntes: borrow $1000 and nvest t nto an opportunty whch guarantees a return of $1200 or borrow $1000 and nvest t nto a rsky opportunty whch returns $ % of the tme, $ % of the tme, or $0 the other 30% of the tme. Fnally, assume the market nterest rate s 15%. a. Calculate the expected returns for your clents f they take the safe opportunty versus the rsky opportunty. From the bank s perspectve, whch opportunty would the bank desre ther customers to undertake (Hnt: Calculate the bank s expected return assumng that the bank receves nothng f the borrower defaults). The expected returns to the borrower for the safe project s = 50 The expected returns to the borrower for the rsky project s.2 ( ) +.5 ( ) = $295. Ths assumes the borrower does not lose anythng n the case of the 0 payback.

4 As long as the borrower s not (extremely) rsk averse, the borrower would choose the rsky actvty to the detrment of the banker. b. As a banker, you have the opportunty to collect collateral whch, f the borrower defaults, you keep. What s the mnmum amount of collateral you need to collect to guarantee the borrower chooses the safe opton and not the rsky opton? Two dfferent ways of answerng ths queston exst. One s to assume that collateral s collected up front, stored n a safe place, and only taken f the borrower defaults. The second case s when the bank requres the borrower to nvest some personal funds n the project. I wll answer n both cases. The expected return to the rsky borrower when collateral s held by the bank s:.2 ( ) +.5 ( ) -.3c where c represents the collateral lost f the borrower does not repay the loan. If the bank pcks c correctly, then the expected returns from the safe project wll be less than the expected returns from the rsky project thus guaranteeng the borrower chooses the safe project. Ths occurs when: 50>.2 ( ) +.5 ( ) -.3c. Solvng for c gves c>$ The second way to answer ths queston s for the bank to requre c dollars to be nvested alongsde the bank s funds. In ths case, the amount borrowed falls from $1000 to $1000 c. The safe project s expected return (meanng the amount earned above the collateral that the borrower started wth) s thus (1000 c) c and the rsky project s s.2 (2500 (1000-c) 1.15 c) +.5 ( (1000-c) 1.15 c) -.3c. Agan, the bank wll choose c such that the expected return from the rsky project s less than the safe project. In ths case c>$ c. What s the relatonshp between the market nterest rate and the mnmum amount of collateral requred to guarantee the safe opton? Replacng 1.15 wth 1+ n the above equatons (the second of the two collateral optons) and dc 333 solvng for c, I fnd c =. Wth a lttle work, one can show that = 1+ d ( 1+ ) 2 whch s always postve for any value of. Thus, hgher nterest rates nduce banks to hold more collateral. 5. Explan how requrng collateral reduces the adverse selecton problem nherent n debt. Adverse selecton s an asymmetrc nformaton problem that occurs pror to the transacton takng place. Wth regards to debt, adverse selecton mples that ndvduals needng debt may be the ones who are most rsky. Ths could be because of pror hstory (ther past rsks ddn t pay off so they need debt now) or could be because there s no downsde rsk for a debtor to undertake excessvely rsky projects whch, when they payoff, enrch the debtor but when they fal only negatvely mpact the lender. In ths second case, collateral can reduce or elmnate the adverse selecton problem. By askng for collateral, a lender changes a debtor s ncentves and makes the debtor less lkely to gamble wth the lender s money (snce, f the gamble does not payoff, the debtor loses the collateral). Hence, borrowers who are less rsky wll be lkely to apply for a loan.

5 6. Rch people often worry that others wll seek to marry them only for ther money. Is ths a problem of adverse selecton? It could be. Adverse selecton occurs before the market s made (n ths case before the weddng takes place) and s caused by ncomplete nformaton about the characterstcs of the product beng purchased (n ths case, a spouse). If I don t know f my grlfrend s pursung me for my money or because she truly recognzes me for the wonderful person I am, then I wll be more hestant to marry (ths s smlar to payng lower amounts for used cars when one doesn t know f they are lemons or not). Rch people may not marry for reasons other than adverse selecton. For nstance, f the nformaton on potental spouses s so mperfect that people can t determne f they are beng pursued for ther money or not, then perhaps these rch people wll act n such a suspcous manner that nobody would want to marry them. 7. What moral hazard ssues arse after a marrage takes place? Incentves change after transactng n the marrage market place. For nstance, upon acqurng a spouse, a husband or wfe may be less lkely to exercse and eat healthy (snce he or she no longer needs to be as attractve to fnd a mate). Spouses lkely buy fewer gfts for each other upon gettng marred as they dd pror to marrage (snce these gfts are sgnals to the worthness of the spouse, they are no longer needed after the spouse has been acqured). Many other examples could be gven. 8. In some ctes, newspapers publsh a weekly lst of restaurants that have been cted for health code volatons by local health nspectors. What nformaton problem s ths feature desgned to solve? How? Ths solves both adverse selecton and moral hazard. People who dne out at restaurants may have a dffcult tme dentfyng restaurants that don t meet certan health standards. Because of ths, some people may not want to eat out at all. Also, restaurants don t have an ncentve to follow health regulatons snce dners can t dstngush restaurants that meet the health standards from those that don t. However, publshng the names of restaurants cted for health code volatons allows people to dentfy unsantary restaurants and thus holds restaurants accountable for followng health regulatons. 9. Indrect fnance s more mportant than drect fnance n most countres n part because of nformaton costs assocated wth lendng. Why are fnancal ntermedares relatvely more effectve at reducng these costs? Fnancal ntermedares are specalsts at screenng and montorng borrowers. For example, they develop expertse n ther credt departments at assessng rsks usng nformaton from loan applcatons and credt scorng agences. They also have unque access to nformaton about potental borrowers from ther depost accounts and debt card usage etc. Ths makes them relatvely effectve at avodng adverse selecton problems. They are also specalsts at montorng borrowers once loans have been extended, allowng them to mtgate moral hazard problems relatvely cheaply. 10. The fnancal sector s heavly regulated. Explan how government regulatons help to solve nformaton problems, ncreasng the effectveness of fnancal markets and nsttutons.

6 The government requres frms to dsclose nformaton. For example, publc fnancal statements prepared accordng to standard accountng practces are requred by the Securtes and Exchange Commsson. Investors can feel more secure n assessng the fnancal health of a frm gven ths government-mandated and standardzed nformaton, thus reducng problems assocated wth adverse selecton. Snce they know they are requred to dsclosure certan nformaton, frms may be less wllng to engage n excessvely rsky behavor, reducng problems assocated wth moral hazard. 11. Suppose two types of frms wsh to borrow n the bond market. Frms of type A are n good fnancal health and are relatvely low rsk. The approprate premum over the rsk-free rate for lendng to these frms s 2%. Frms of type B are n poor fnancal health and are relatvely hgh rsk. The approprate premum over the rsk-free rate for lendng to these frms s 6%. As an nvestor, you have no other nformaton about these frms except that type A and type B frms exst n equal numbers. a. At what nterest rate would you be wllng to lend f the rsk-free rate were 5%? b. Would ths market functon well? What type of asymmetrc nformaton problem does ths example llustrate? a. The approprate nterest rate for type A frms bonds s 7% whle that for type B frms bonds n 11%. As nvestors don t know whch type of frm they are dealng wth and there s an equal probablty of ether type of frm, they wll be only be wllng to lend f they receve at least the average rate of 9%. b. No. The type A frms would not be wllng to pay ths nterest rate and so would wthdraw from the market, leavng only type B frms. Ths s an example of an adverse selecton problem. Only the less desrable frms are wllng to borrow.

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