First determine the payments under the payment system

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1 Corporate Fiace February 5, 2008 Problem Set # -- ANSWERS Klick. You wi a judgmet agaist a defedat worth $20,000,000. Uder state law, the defedat has the right to pay such a judgmet out over a 20 year period, usig a statutory aual discout rate of 5 percet. Your cliet iforms you that she makes 0% i her ivestmet portfolio. You kow that the defedat is a isurace compay that is regulated i such a way that its portfolio oly makes a rate of retur of 7%. a. Will the isurer choose to pay the judgmet i a lump sum or will it elect the 20 year paymet schedule? Why (i.e., show your work)? First determie the paymets uder the paymet system PV=20,000,000 FV=0 N=20 I/Y=5 PMT= $,604,852/year Now examie the isurer s choice. Either it ca pay out $20M ow or it ca pay the paymet laid out above. There are a couple of ways to compare here. First, you could evaluate what the isurer values the loss of,604,852/year for 20 years ad compare that to 20M. FV=0 PMT=,604,852 N=20 I/Y=7 PV= $7,00,825 That is, the isurer would be willig to pay 7,00,825 to avoid these yearly paymets but it would t pay 20,000,000 to avoid them, so it will elect to use the paymet schedule. Aother way to thik of this is to determie what kid of yearly paymets could the isurer geerate from 20,000,000 over the ext 20 years give its ivestmet opportuities. Compare that amout to the PMT required uder the state s schedule. PV=20,000,000 N=20

2 I/Y=7 FV=0 PMT=,887,859 That is, the isurer ca make more from keepig the moey ad ivestig it ad satisfyig its judgmet year to year, so it will ecessarily choose to pay i istallmets. b. Imagie that the post-judgmet bargaiig rules i this state allow a victorious plaitiff to make a sigle couter offer, i the situatio where the defedat chooses the yearly paymet optio, which the defedat either accepts or declies (i.e., the defedat either agrees to pay the couter offer i a lump sum or it chooses the paymet optio but it caot make a subsequet couter offer). What lump sum do you offer to the defedat to satisfy the judgmet? Why? Give that you kow from part a that the isurer is idifferet betwee payig o the istallmet pla ad givig up $7,00, 825, you caot offer more tha that (ad expect the offer to be accepted). So you compare this umber to your cliet s valuatio of the schedule paymets FV=0 N=20 I/Y=0 PMT=,604,852 PV=3,663,00 Therefore, your cliet values this icome stream at $3,663,00 ad is better off with ay lump sum paymet above this. Sice the isurer will accept aythig below $7,00,825, so it makes sese to offer $7,00,825 (perhaps mius a pey to make sure the isurer is strictly better off uder the lump sum paymet).

3 Corporate Fiace February 5, 2008 Problem Set #2 Klick. I the process of valuig the assets of a firm your employer is targetig for takeover, you fid that the target has large real estate holdigs i Tallahassee, FL. You determie that, i the aggregate, these holdigs will geerate before-tax retal icomes of $5,000,000 this year ad that amout is projected to grow by 3% per year. Based o the risk of the market, you determie that the appropriate discout rate is 8%. Curretly, o these properties, property taxes amout to $500,000/year..a What value do you place o these real estate holdigs? Note that while the retal icome is projected to grow, the tax rate is ot, so we eed to do 2 valuatios. The preset discouted value of the i-flows ad the preset discouted value of the outflows: PV = 5,000,000 = 00,000, , 000 PV = = 6,250, So the et preset value of the holdigs is 00,000,000-6,250,000= $93,750,000.b You lear that all retal property taxes are scheduled to go up by 0% (i.e., if taxes ow are x, the ew tax paymet will be.x) after 3 year s time. Does this chage your valuatio of the properties? First, determie what the property will be worth uder the ew tax treatmet, otig that the ret startig i period 4 will be higher tha the preset ret due to the assumed growth. PV PV 5,463,635 = = 09,272, , 000 = = 6,875, So the holdigs, i three years, will be worth 09,272,700-6,875,000= $02,397,700 Now discout that back to the preset FV=02,397,700

4 PMT=0 N=3 I/Y=8 8,286,596 Now you eed to determie what the property is worth for the three years before the tax chage takes place PMT=5,000, ,000 PMT2=5,50, ,000 PMT3=5,304, ,000 Discout each of these accordigly PV=4,66,667 PV2=3,986,626 PV3=3,83,967 So, the total value of these lad holdigs ow is 8,286, ,66, ,986, ,83,967 = $93,253,856.c You further lear that you ca place the property holdigs i a trust. While trusts curretly pay the same property tax as everyoe else, whe the ew taxes go ito effect, property held i trusts becomes tax-free as part of a legislative deal. How much is the property worth ow if it were placed i a trust vehicle? The valuatio of the first three years before the ew tax goes ito effect is the same as above 4,66,667+3,986,626+3,83,967 =,967,260 Now we just eed to value the property after the ew tax rules apply 5,463,635 PV = = 09,272, Ad we eed to discout this back to the preset FV=09,272,700 PMT=0 I/Y=8 N=3

5 86,744,92 Add this to the value of the first three years 86,744,92 +,967,260 = 98,7,452 Note somethig show by this problem: The effect of a tax chage (eve a future oe, as log as it is kow) is immediately capitalized ito the preset value of the property. Thus, it is the curret ower who pays or beefits from a tax icrease or decrease eve if it is the future ower who omially pays the tax bill each year.

6 Corporate Fiace March 3, 2008 Problem Set #3 Klick. You are tasked with valuig a bod with the followig properties ad expectatios. Sice the debt does ot trade i a liquid market, there is o market price agaist which you ca judge your valuatio. The bod has a face value of $,000,000. It pays a aual iterest paymet of $75,000 ad matures i 5 years. Assume that the uderlyig default risk is costat through the life of the bod ad is captured by a 3%/year risk premium (ote that this risk is essetially the same as the risk for the bod fud refereced below). Due to regulatory restrictios o its ivestmets, the bodholder s curret opportuity cost of its fuds is equivalet to the retur o a iflatio idexed bod fud equal to 3%/year (these restrictios were put i place after the etity came ito possessio of the bod you are valuig). Your best estimate of iflatio is a costat aualized rate of 4%/year..a) What is the bod curretly worth? PMT=75,000 FV=,000,000 I/y= 3+3+4=0% N=5 PV=$905,230.b) If market iterest rates icrease such that the bod fud idexed above moves to 4%/year as of the begiig of year 2 (but the uderlyig risk does ot chage; all that chages is geeral productivity levels), what is the bod worth at that time? PMT=75,000 FV=,000,000 I/y=3+4+4= N=4 PV=$89,44.c) Revert to the origial assumptios, but ow assume the ower of the bod pays a 25% tax o all of its ivestmet earigs. PMT=(-.25)*75,000=56,250 FV=,000,000 I/y=3+(-.25)*3+4= =9.25 N=5 PV=$859,90

7 .d) Assume ow that the etity o loger faces the regulatory ivestmet restrictio ad could ivest i higher risk portfolios. I priciple, how does that affect your calculatios i terms of valuig the bod (i.e., do t solve for aythig; describe how this does or does ot chage the iputs i your calculatios)? Basically, for opportuity cost terms, you wat to compare like risks with like risks. So, if the comparable risk is still the bod fud, the you will use that as your opportuity cost. O the other had, if, for some reaso, the regulatory restrictio had previously ruled out aother ivestmet optio/portfolio with equivalet risk but a higher rate of retur (e.g., some kid of mix of bods fuds ad a diversified equity fud), the higher rate of retur is the relevat opportuity cost.

8 Corporate Fiace March 3, 2008 Problem Set #4 Klick. You are asked to review the price estimates ivolved i a iitial public offerig. The ivestmet bak provides you with all of the data o the firm that it used i its ow estimatio. Examiig the data, you fid that over the 5 years the firm has bee i existece, it geerated earigs (i.e., reveues over costs) of $20,000,000 i year, $22,000,000 i year 2, $24,200,000 i year 3, $26,620,000 i year 4, ad $29,282,000 last year. You have every reaso to believe that it will follow the same growth patter for the foreseeable future. Based o your estimates of the uderlyig risk of the firm ad the idustry i which it operates, you determie that a appropriate discout rate is 5%/year. The ivestmet bak has determied it will float 00,000,000 shares i the offerig..a What is your estimate for the iitial share price based o this iformatio? The growth idicated above is 0%/year. This implies the followig valuatio: 29, 282, 000*(.) 32, 20, , 000, , 000, P = = = = $6.44 / share b Now assume that the earigs umbers preseted above are omial umbers (i.e., have ot bee adjusted to accout for iflatio ad thus do ot etirely represet real buyig power growth). Namely, geeral price levels have icreased at a costat rate of 3%/year ad this iflatio is likely to cotiue ito the future. Further, the discout rate idicated above does ot iclude price level cosideratios. What is your ew valuatio of the iitial share price? You are evaluatig the price to be paid ow (ot 5 years ago) so the relevat earigs umber is still.322 per share. What chages is the amout of the growth that is real as opposed to merely iflatioary. This implies: P = = = $4.03/ share.5 (..03).08.c Revert to the origial assumptios laid out i the origial questio. Assume that after the IPO is lauched, the shares actually appreciate to $0/share quite quickly i the market ad this is ot merely a temporary price surge (i.e., the price stays at this level well beyod the time period i which may IPOs surge ad the subsequetly level out at a lower price). What does this imply about the differece betwee your valuatio ad the market s?

9 Note that the market is doig the same calculatio you are so it must suggest a differece of opiio regardig oe of the elemets of your calculatio. Sice the earigs data are what they are, there will be o differece there. The differece must arise from a) the relevat discout rate, b) the relevat growth rate, c) the relevat iflatio expectatio, or d) some combiatio of a-c. Based o the iformatio provided i the questio there is o way to determie where exactly the differece lies.

10 Corporate Fiace March 3, 2008 Problem Set 5 Klick NOTE: See excel worksheet for umerical calculatios. The table below shows the returs for 5 periods for 4 assets Period FSU USC COL PENN a Calculate the mea ad variace for each asset s returs ( ) mea x var(x)= = x = i= i i= 2 ( xi x) Mea(FSU) = 0.5; Var(FSU) = 0.20 Mea(USC) = 0.5; Var(USC) = 0.20 Mea(COL) = 0.5); Var(COL) = 0.20 Mea(PENN) = 0.5; Var(Pe) = 0.20 x.b Calculate the covariace betwee each pair of assets ( ) = ( xi x)( yi y) Cov x,y i = All covariaces are 0 (to 6 decimal places).c Calculate the mea retur ad the variace for a portfolio that has half of its value (at the begiig) i FSU ad the other half i USC. Mea = 0.5 Var = 0..d Calculate the mea retur ad the variace for a portfolio that has /3 of its value (at the begiig) i FSU, /3 i USC, ad /3 i COL. Mea = 0.5 Var = 0.07

11 .e. Calculate the mea retur ad the variace for a portfolio that has /4 of its value (at the begiig) i FSU, /4 i USC, /4 i COL, ad /4 i PENN. Mea = 0.5 Var = 0.05.f Discuss how you could have arrived at your aswers for.c-.e just o the basis of your aswers for.a ad.b. The variace of a costat (b) times a variable with variace v is b^2*v. If two variables are idepedet (i.e., covariace = 0) the variace of the sum is the sum of the variaces. Puttig those two thigs together ad otig that you already kow FSU, USC, COL, ad PENN are all idepedet, the variaces of the portfolios are easy to figure out, amely Var(c) = (.5 *.5 *.2) + (.5 *.5 *.2) Var(d) = (/3*/3*.2) + (/3*/3*.2) + (/3*/3*.2) Var(e) = (.25*.25*.2) + (.25*.25*.2) + (.25*.25*.2) + (.25*.25*.2)

12 Corporate Fiace March 3, 2008 Problem Set 6 Klick Note: see excel sheet for supportig calculatios. The followig table provides the market retur ad the retur o stock FSU for the past 20 periods: Period Market FSU a Assume the risk free rate of retur per period is 0.03 throughout the sample. If the market retur o the 2 st period is 0.035, what does the CAPM predict regardig FSU s retur i the 2 st period? For CAPM, we eed to kow Beta for FSU. Remember: ( ri rm) ( r ) Covariace, βi = Variace m ( ri rm) ( ri r)( ) t i rm r t m Covariace, = = t= ( rm) ( rm r ) t m Variace = = t= βfsu = =

13 Accordig to the CAPM r i = rf + βi( rm rf ) So FSU2 ( ) ( ) r = * = * = 0.036

Chapter 4: Time Value of Money

Chapter 4: Time Value of Money FIN 301 Class Notes Chapter 4: Time Value of Moey The cocept of Time Value of Moey: A amout of moey received today is worth more tha the same dollar value received a year from ow. Why? Do you prefer a