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Chryslar Warrants

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Chrysler¶s Warrants Matt-Harsha-Strong; Murtaza Amil; Vilay Wadhwa; Jayant Das, Mihir Korke; Ravi Prakash 1. Value the Chrysler warrants held by the government on the following five dates: a) September 14, 1979: $5.016 b) January 7, 1980 : $5.748 c) April 8, 1980: $4.070 d) May 12, 1980: $6.256 e) September 1, 1983: $23.442 Table 1 Number of shares Number of warrants Risk-free rate Time (t) Stock Price Adjusted Stock Price Strike Price Historic (30 day) Volatility d1 d2 N(d1) N(d2) Call Value-Historic Volatility Dilution factor Warrant value-Historic Volatility Implied Volatility Warrant value-Implied Volatility Total warrant value-Historic Total warrant value-Implied 9/14/1979 87,106,000 14,400,000 9.3% 10.307 7.875 8.704 13.000 47.5% 1.126 -0.398 0.870 0.345 5.845 85.8% 5.016 39.2% 4.519 72,230,825 65,072,767 1/7/1980 87,106,000 14,400,000 10.6% 9.992 7.500 8.450 13.000 66.8% 1.354 -0.756 0.912 0.225 6.698 85.8% 5.748 40.8% 4.471 82,764,499 64,377,093 4/8/1980 87,106,000 14,400,000 11.0% 9.740 6.625 7.298 13.000 47.4% 1.075 -0.403 0.859 0.344 4.743 85.8% 4.070 57.5% 4.551 58,603,892 65,537,770 5/12/1980 87,106,000 14,400,000 10.5% 9.647 7.500 8.534 13.000 82.6% 1.515 -1.052 0.935 0.146 7.290 85.8% 6.256 59.9% 5.340 90,089,256 76,889,607 9/1/1983 87,106,000 14,400,000 11.9% 6.340 28.375 32.250 13.000 59.4% 1.861 0.365 0.969 0.643 27.318 85.8% 23.442 134.4% 27.196 337,570,746 391,628,173 Assumptions behind inputs Assume all 13.3M bank warrants, 5M other warrants & 320k options Given on case page 1 10-year T-bonds except for 1983 (7-year bond) Assume warrants expire on 1/1/1990 Given in case exhibits =Stock price+(# warrants/# shares)*Warrant value(historic) Given on case page 1 Computed in Gultekin-corrected spreadsheet =(LN(Adj stock price/strike price)+t*(RFR+(Volatility^2/2)))/(Volatility*t^.5) =d1-Volatility*t^.5 =normsdist(d1) =normsdist(d2) =Ad stock price*N(d1)-Strike price*N(d2)*EXP(-RFR*t) =Number of warrants/(Number of shares+warrants) =Call value(historic)*Dilution Factor Computed using Solver based on Exhibit 10 data =Call value(implied)*Dilution Factor =Warrant value(historic)*Number of warrants =Warrant value(implied)*Number of warrants 450,000,000 400,000,000 350,000,000 300,000,000 250,000,000 200,000,000 150,000,000 100,000,000 50,000,000 0 9 14 1979 1 7 1980 4 8 1980 5 12 1980 9 1 1983 o al wa an alue His o ic o al wa an alue plied 2. Why did the warrants¶ value change over this time? Chrysler¶s warrant value has changed over time primarily because of changes in the stock price. Other factors are changes in the estimate of volatility, risk free rate and time remaining on the warrant. 3. Value the government¶s loan guarantee as of May 12, 1980. Remember that it amounts to a put option, which allows the banks to put their risky Chrysler loans to the government. Use the date in Exhibit 11 to estimate the volatility of returns on Chrysler debt. We calculate the value of loan guarantees using 2 methods. 1) Treating the guarantee as a put option and 2) estimating the present value of interest savings Chrysler is getting from the guarantee. We get estimate of $372.5MM from method 1 and estimate of $360.3MM from method 2. Table 2 (Method 1 ± Put Option) B 4 5 6 7 8 9 10 11 12 13 14 15 16 17 C D E Risk-Free Rate Time (t) Guaranteed Bond Price Bond Coupon Rate Strike Price Volatility d1 d2 N(d1) N(d2) B-S Call Value Put Value Total Put Value $500M Bond 10.52% 9.5918 $100.000 10.4% $100.000 86.93% 1.352 -1.340 0.912 0.090 $30.505 $29.905 $149,526,226 $300M Bond 10.52% 9.5096 $100.000 11.4% $100.000 86.93% 1.309 -1.372 0.905 0.085 $27.471 $30.423 $91,269,183 $372,463,756 Total $400M Bond 10.52% 8.9205 $100.000 14.9% $100.000 86.93% 1.148 -1.449 0.874 0.074 $20.263 $32.917 $131,668,346 Assumptions behind inputs 10-Year T-Bond rate at 5/12/1980 - closest date to bond issues Assume that bonds mature on 1/1/1990 Assume that government guarantee is default-free, freezes price at 100% Used in Black-Scholes formulas below Assume that government fully guarantees the face value =(0.002999*252)^0.5; daily deviation from Exhibit 11 =(LN(E7/E9)+E6*(E5-E8+(E10^2/2)))/(E10*E6^0.5) =E11-E10*E6^0.5 =NORMSDIST(E11) =NORMSDIST(E12) =(EXP((0-E8)*E6))*E7*E13-E9*(EXP((0-E5)*E6))*E14 =E15-E7*EXP((-E8)*E6)+E9*(EXP((-E5)*E6)) =E17*400000000 =C17*500000000+D17*300000000+E17*400000000 Alternate approach comparing the above ³total put value´ to the interest savings from a lower debt cost due to the government guarantee, discounted at Chrysler¶s market debt rate: Table 3 (Method 2 ± Interest Savings) Check of Interest Savings vs Put Valuation of Guarantee Interest savings w/ $500M portion Interest savings w/ $300M portion Interest savings w/ $400M portion Total interest savings Less 10% prepayment risk Versus: Total put value $205,951,830 $110,093,406 $84,247,696 $400,292,933 $360,263,640 $372,463,756 1980 33,263,014 15,567,534 1981 57,000,000 31,050,000 24,997,808 1982 57,000,000 31,050,000 27,400,000 1983 57,000,000 31,050,000 27,400,000 1984 57,000,000 31,050,000 27,400,000 1985 57,000,000 31,050,000 27,400,000 1986 57,000,000 31,050,000 27,400,000 1987 57,000,000 31,050,000 27,400,000 1988 57,000,000 31,050,000 27,400,000 1989 57,000,000 31,050,000 27,400,000 4. What is the prospective internal rate of return to the government on the loan guarantee as of May 12, 1980, taking into account the expected fees and current value of the warrants? E Ex-Ante Cost of Gurantee Value of Warrant Fee Net CF IRR 372463756 90089256 10,800,000 -282374500 -15% 10800000 10,800,000 10800000 10,800,000 10800000 10,800,000 10800000 10,800,000 10800000 10,800,000 10800000 10,800,000 10800000 10,800,000 10800000 10,800,000 10800000 10,800,000 10800000 We calculate the ex-ante IRR to be -15%. Explanation: Value of Guarantee: $372.5 MM ± refer Table 2 Value of Warrant on May 12, 1980 = $90.1MM refer Table 1 Fee: 1% of outstanding principal, assuming 10% prepayment risk and 10 year maturity. 5. How does this IRR compare with Chrysler-type risk priced in the open market? Market rate for Chrysler-type risk is in the +20% range. Government IRR is -15%! Government is massively subsidizing Chrysler. 6. What price should Chrysler bid for its warrants in September 1983? Shearson/Amex offered $20.1. We estimate value of call option in Sep 1983 to be $23.44. A price point b/w these 2 numbers make sense ± say, $21.5. Total bid = $21.5*14.4MM = $309.6MM. 7. Based on your bid price, what was the IRR on the government¶s liability after the fact? ³After the fact´ IRR = -3% Ex-Post Cost of Guarantee Value of Warrant 372525983 0 0 11,000,00 0 11000000 0 309600000 Fee Net CF IRR -372525983 -3% 11,000,000 11000000 11,000,000 320600000 8. Was government guarantee overpriced? No, it was massively under-priced. Pricing needs to be based on ex-ante estimates. On the ex-ante basis, value to Chrysler = PV of Guarantee = ~$372MM. Cost to Chrysler = PV_Fee + PV_Warrant on May 12, 1980 = $44+$90.08 = ~$134MM. Government guarantee was under-priced by ~$240MM Even ex-post, when warrants became much more valuable, pay-off to Government was lower than the value of guarantee by ~$30MM Iacocca argument is not sound. Chrysler actually got a good deal, even based on ex-post analysis. While Government did not get the full price from Chrysler commensurate with the benefit Chrysler got from this deal, Government guarantee can still be justified based on positive externalities (such as saved jobs, tax revenue impacts, impacts on suppliers etc.) because the guarantee enabled Chrysler to continue as a going concern.
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