0273707817_answer_key

Finance in a Nutshell Javier Estrada FT Prentice Hall, 2005

Answer Key to Challenge SectionsChapter 1

Q1Year Price D R1994 $8.50 $0.25 1995 $12.00 $0.27 44.4%1996 $16.48 $0.31 39.9%1997 $24.46 $0.35 50.5%1998 $34.00 $0.40 40.6%1999 $51.58 $0.47 53.1%2000 $47.94 $0.55 -6.0%2001 $40.08 $0.64 -15.1%2002 $24.35 $0.72 -37.5%2003 $30.98 $0.76 30.3%

Q2W0 I CP W1 EI W5 EI5

$100 15% Annual $115.00 15.00% $201.14 101.14%$100 15% Semiannual $115.56 15.56% $206.10 106.10%$100 15% Quarterly $115.87 15.87% $208.82 108.82%$100 15% Monthly $116.08 16.08% $210.72 110.72%$100 15% Continuous $116.18 16.18% $211.70 111.70%

Q3Year Price D r1994 $8.50 $0.25 1995 $12.00 $0.27 36.7%1996 $16.48 $0.31 33.6%1997 $24.46 $0.35 40.9%1998 $34.00 $0.40 34.1%1999 $51.58 $0.47 42.6%2000 $47.94 $0.55 -6.2%2001 $40.08 $0.64 -16.3%2002 $24.35 $0.72 -46.9%2003 $30.98 $0.76 26.5%

Q4Year Price D R r Wealth

The difference between R and r is large when price changes are large, and small when price changes are small

1994 $8.50 $0.25 $100.0 1995 $12.00 $0.27 44.4% 36.7% $144.4 1996 $16.48 $0.31 39.9% 33.6% $202.0 1997 $24.46 $0.35 50.5% 40.9% $304.1 1998 $34.00 $0.40 40.6% 34.1% $427.6 1999 $51.58 $0.47 53.1% 42.6% $654.6 2000 $47.94 $0.55 -6.0% -6.2% $615.4 2001 $40.08 $0.64 -15.1% -16.3% $522.7 2002 $24.35 $0.72 -37.5% -46.9% $327.0 2003 $30.98 $0.76 30.3% 26.5% $426.2

Multiperiod 326.2% 145.0%

is large when price changes are large, and small when price changes are small



Q1Year GM WalMart1994 -22.00% -14.42%1995 28.68% 5.56%1996 8.61% 3.11%1997 19.21% 74.72%1998 21.30% 107.55%1999 25.74% 70.45%2000 -27.84% -22.79%2001 -0.98% 8.94%2002 -20.82% -11.76%2003 52.85% 5.73%AM 8.5% 22.7%GM 5.5% 16.3%

The AM is always larger than or equal to the GM

Q2Year GM-Return GM-Wealth WM-Return WM-Wealth1993 $100.0 $100.01994 -22.00% $78.0 -14.42% $85.61995 28.68% $100.4 5.56% $90.31996 8.61% $109.0 3.11% $93.11997 19.21% $129.9 74.72% $162.71998 21.30% $157.6 107.55% $337.81999 25.74% $198.2 70.45% $575.72000 -27.84% $143.0 -22.79% $444.52001 -0.98% $141.6 8.94% $484.22002 -20.82% $112.1 -11.76% $427.32003 52.85% $171.4 5.73% $451.7

Q3GE At AM $225.6

At GM $171.4WM At AM $773.9

At GM $451.7

The correct terminal wealth is found by compounding at the GM

Q4GE AM-GM 2.9%

AM/GM-1 53.1%WM AM-GM 6.4%

AM/GM-1 39.5%

The differences are larger for WalMart because it has a higher volatility (SD)

Q5Period Price Return Shares-1 CF-1 Wealth-1 Shares-21998 $10.70 50 -$535.0 $535.0 8001999 $38.72 261.9% 100 -$3,872.0 $5,808.0 4002000 $27.88 -28.0% 200 -$5,576.0 $9,758.0 2002001 $12.30 -55.9% 400 -$4,920.0 $9,225.0 1002002 $3.11 -74.7% 800 -$2,488.0 $4,820.5 502003 $4.47 43.7% -1550 $6,928.5 $6,928.5 -1550AM 29.4%GM -16.0%

DWR -30.7%

The DWR is slighthly higher in the first strategy because the timing of the purchases was somewhat better

CF-2 Wealth-2-$8,560.0 $8,560.0-$15,488.0 $46,464.0-$5,576.0 $39,032.0-$1,230.0 $18,450.0-$155.5 $4,820.5$6,928.5 $6,928.5

-32.1%

The DWR is slighthly higher in the first strategy because the timing of the purchases was somewhat better



Q1Year Return1994 0.9%1995 38.4%1996 26.3%1997 28.4%1998 22.4%1999 12.6%2000 10.2%2001 -7.6%2002 -8.9%2003 20.6%

SD (T) 15.0%

Q2Year Return1994 13.5%1995 42.8%1996 39.8%1997 59.9%1998 15.7%1999 63.4%2000 -0.3%2001 -34.5%2002 0.2%2003 37.7%

SD (T) 29.0%SD (T-1) 30.5%

AMEX is riskier than Exxon but less risky than Intel

Q3Year Return1994 13.5%1995 42.8%1996 39.8%1997 59.9%1998 15.7%1999 63.4%2000 -0.3%

2001 -34.5%2002 0.2%2003 37.7%AM 23.8%

R-2*SD -34.1%R+2*SD 81.7%

The 95% confidence interval is wider than that calculated for Exxon but narrower than that calculated for Intel

Q4Year Exxon Intel AMEX1994 0.9% 3.4% 13.5%1995 38.4% 78.2% 42.8%1996 26.3% 131.3% 39.8%1997 28.4% 7.4% 59.9%1998 22.4% 69.0% 15.7%1999 12.6% 39.1% 63.4%2000 10.2% -26.9% -0.3%2001 -7.6% 4.9% -34.5%2002 -8.9% -50.3% 0.2%2003 20.6% 106.6% 37.7%GM 13.3% 23.8% 20.0%

Approx GM 13.4% 25.3% 20.5%

It works well in general, with the approximation improving for series with smaller returns (Exxon) and worsening for those with larger returns (Intel)

The 95% confidence interval is wider than that calculated for Exxon but narrower than that calculated for Intel

It works well in general, with the approximation improving for series with smaller returns (Exxon) and worsening for those with larger returns (Intel)



Q1Year Pepsi HP1994 -9.5% 28.1%1995 56.7% 69.4%1996 6.2% 21.1%1997 36.6% 25.3%1998 14.3% 10.7%1999 -12.5% 67.7%2000 42.6% -28.6%2001 -0.5% -34.0%2002 -12.1% -13.9%2003 12.0% 34.5%AM 13.4% 18.0%SD 23.2% 33.9%Rho 0.13

The correlation between Pepsi and HP is quite low, which is unsurprising given their very different lines of businesses

Q2xP xHP Risk Return

100.0% 0.0% 23.2% 13.4%90.0% 10.0% 21.5% 13.8%80.0% 20.0% 20.5% 14.3%70.0% 30.0% 20.2% 14.8%60.0% 40.0% 20.6% 15.2%50.0% 50.0% 21.7% 15.7%40.0% 60.0% 23.4% 16.2%30.0% 70.0% 25.6% 16.6%20.0% 80.0% 28.1% 17.1%10.0% 90.0% 30.9% 17.6%0.0% 100.0% 33.9% 18.0%

Lowest risk for xP=70% and xHP=30% MVP for xP=70.6% and xHP=29.4%

Q34 assets

18% 20% 22% 24% 26% 28% 30% 32% 34% 36%12%

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5 assets You get the picture by now, you can do this one yourself!

The correlation between Pepsi and HP is quite low, which is unsurprising given their very different lines of businesses

18% 20% 22% 24% 26% 28% 30% 32% 34% 36%12%

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Q1Date NOR SPA1994 24.1% -3.9%1995 6.5% 31.2%1996 29.2% 41.3%1997 6.7% 26.2%1998 -29.7% 50.6%1999 32.4% 5.3%2000 -0.4% -15.5%2001 -11.7% -11.0%2002 -6.7% -14.9%2003 49.6% 59.2%AM 10.0% 16.8%SD 22.6% 26.9%Rho 0.27

The correlation between Spain and Norway is rather low, particularly in the context of the highly-integrated European markets

Q2xN xS Risk Return Ret/Risk

100.0% 0.0% 22.6% 10.0% 44.3990.0% 10.0% 21.2% 10.7% 50.4780.0% 20.0% 20.2% 11.4% 56.3870.0% 30.0% 19.6% 12.1% 61.5860.0% 40.0% 19.4% 12.7% 65.5550.0% 50.0% 19.7% 13.4% 67.9640.0% 60.0% 20.5% 14.1% 68.7830.0% 70.0% 21.6% 14.8% 68.2820.0% 80.0% 23.1% 15.5% 66.8510.0% 90.0% 24.9% 16.1% 64.870.0% 100.0% 26.9% 16.8% 62.62

The MVP consists of xN=61.8% and xS=38.2% The MVP has an expected return of 14.2% and a volatility of 19.43% The MVP has a higher RAR (68.78) than the 100% Norwegian portfolio (44.39) The xN=40%/xS=60% portfolio has the highest RAR (68.78 compared to 44.39 for Norway and 62.61 for Spain)

18% 19% 20% 21% 22% 23% 24% 25% 26% 27% 28%8%

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The correlation between Spain and Norway is rather low, particularly in the context of the highly-integrated European markets

The xN=40%/xS=60% portfolio has the highest RAR (68.78 compared to 44.39 for Norway and 62.61 for Spain)

18% 19% 20% 21% 22% 23% 24% 25% 26% 27% 28%8%

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Q1 - Q6R(i) 10% Stocks Var(p) SD(p)

SD(i) 30% 1 0.0900 30.00%Var(i) 0.09 2 0.0550 23.45%

Cov(i,j) 0.02 3 0.0433 20.82%Rho(i,j) 0.5 4 0.0375 19.36%

5 0.0340 18.44%6 0.0317 17.80%7 0.0300 17.32%8 0.0288 16.96%9 0.0278 16.67%

10 0.0270 16.43%11 0.0264 16.24%12 0.0258 16.07%13 0.0254 15.93%14 0.0250 15.81%15 0.0247 15.71%16 0.0244 15.61%17 0.0241 15.53%18 0.0239 15.46%19 0.0237 15.39%20 0.0235 15.33%21 0.0233 15.28%22 0.0232 15.23%23 0.0230 15.18%24 0.0229 15.14%25 0.0228 15.10%26 0.0227 15.06%27 0.0226 15.03%28 0.0225 15.00%29 0.0224 14.97%30 0.0223 14.94%

As the number of stocks increases risk falls at a decreasing rate After some 20 or so stocks risk decreases are negligible Expectedly, the variance of the 30-stock portfolio (0.0223) is very similar to the average covariance across stocks (0.02)

0 5 10 15 20 25 30 350%

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SD

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Expectedly, the variance of the 30-stock portfolio (0.0223) is very similar to the average covariance across stocks (0.02)



Q1Year BH Cisco MS S&P5001994 25.0% 8.7% -0.8% 1.3%1995 57.4% 112.5% 40.6% 37.6%1996 6.2% 70.5% 43.2% 23.0%1997 34.9% 31.4% 80.7% 33.4%1998 52.2% 149.7% 21.6% 28.6%1999 -19.9% 130.8% 103.1% 21.0%2000 26.6% -28.6% 12.2% -9.1%2001 6.5% -52.7% -28.3% -11.9%2002 -3.8% -27.7% -27.2% -22.1%2003 15.8% 85.0% 47.9% 28.7%AM 20.1% 48.0% 29.3% 13.0%Beta 0.5 2.8 1.5

There does appear to be a positive relationship between risk (beta) and return

Q2BH Cisco MS

RRE 7.2% 19.7% 12.8%



Q1Year Abbott RP ML RP MRP SMB HML1994 5.1% -20.8% -4.1% 0.4% -0.1%1995 24.9% 40.1% 31.0% -6.9% -3.5%1996 18.2% 56.4% 16.3% -1.9% 0.2%1997 25.7% 75.6% 26.1% -3.7% 11.1%1998 47.2% -12.0% 19.4% -23.3% -15.0%1999 -31.2% 20.2% 20.2% 11.7% -39.4%2000 30.7% 60.4% -16.7% -5.7% 21.4%2001 12.0% -27.7% -14.8% 28.4% 27.3%2002 -30.5% -29.9% -22.9% 4.4% 3.7%2003 15.0% 52.5% 30.7% 28.1% 15.1%

Abbott Betas 0.66 -1.03 1.05ML - Betas 1.41 -0.42 1.00

Q2Abbot ML

RRE-CAPM 8.5% 13.3%RRE-3FM 9.1% 15.5%

The RRE estimates between the two models are somewhat different

However, note that if the CAPM is used, betas should be estimated from independently, in which case we would obtain:Abbot ML

Beta 0.37 1.08RRE-CAPM 6.7% 11.2%

Note, then, that the differences between the (properly-estimated) CAPM-RREs and 3FM-RREs widen

However, note that if the CAPM is used, betas should be estimated from independently, in which case we would obtain:



Q1 - Q2Year China Korea1994 -46.4% 23.7%1995 -21.1% -3.3%1996 37.5% -38.1%1997 -25.3% -66.7%1998 -42.4% 141.1%1999 13.3% 92.4%2000 -30.5% -49.6%2001 -24.7% 48.7%2002 -14.0% 8.6%2003 87.6% 35.9%AM -6.6% 19.3%

SSD-AM 20.9% 40.1%SSD-Rf 30.0% 31.7%SSD-0 26.0% 28.9%

VAR-95: -71.4% -81.0%VAR-99: -98.6% -123.3%

According to all three SSDs the Korean market is riskier than the Chinese market Also, according to the VaR the risk of 'extreme' losses is higher in the Korean market Note, however, that any loss higher than -100% is not possible when investing (long) in equities This is one of the problems of using distributions that have no lower bound (like the Normal distribution)

This is one of the problems of using distributions that have no lower bound (like the Normal distribution)



Q1 - Q4Country AM Country Jensen Country Treynor Country

CAN 13.6% USA 4.6% USA 8.3 USAUSA 13.3% CAN 4.5% ITA 8.1 CANITA 12.3% ITA 3.9% CAN 7.9 ITAFRA 11.0% FRA 2.0% FRA 5.6 FRAGER 10.6% UK 1.2% UK 5.2 UKUK 9.1% GER 1.1% GER 4.7 WOR

WOR 8.7% WOR 0.0% WOR 3.7 GERJAP 1.9% JAP -6.3% JAP -3.5 JAP

The rankings based on risk-adjusted returns do differ across the different measures The 'best' country in which to invest depends on the investor's perception of risk (Is it beta? The SD? The SSD?) However, in this case, the US provides the best RARs for all three measures of risk (beta, SD, and SSD)

Sharpe Country RAP Country Sortino52.3 USA 12.8% USA 39.943.8 CAN 11.5% CAN 37.031.1 ITA 9.6% ITA 29.031.0 FRA 9.6% FRA 26.128.9 UK 9.3% GER 22.025.1 WOR 8.7% UK 20.224.5 GER 8.6% WOR 17.8-14.8 JAP 2.8% JAP -11.9

The 'best' country in which to invest depends on the investor's perception of risk (Is it beta? The SD? The SSD?) However, in this case, the US provides the best RARs for all three measures of risk (beta, SD, and SSD)



Q11a 1b 1c 1d 1e 1f

Weights Weights Weights Weights Weights Weights-28.6% 0.0% 10.0% -33.1% -25.7% -25.1%31.5% 14.2% 30.0% 6.1% 48.0% 50.8%34.9% 26.4% 30.0% 91.3% -1.8% -8.1%62.2% 59.4% 30.0% 35.7% 79.5% 82.4%

Ep Ep Ep Ep Ep Ep27.1% 29.9% 31.1% 22.6% 30.0% 30.5%

SDp SDp SDp SDp SDp SDp33.4% 42.4% 48.9% 29.8% 38.9% 40.0%

Sharpe R. Sharpe R. Sharpe R. Sharpe R. Sharpe R. Sharpe R.0.66 0.59 0.53 0.59 0.64 0.64

Q2Date Disney Microsoft 2a 2b 2c1994 8.7% 51.6% Weights Weights Weights1995 29.0% 43.6% 82.9% 79.3% 56.8%1996 19.1% 88.3% 17.1% 20.7% 43.2%1997 42.9% 56.4%1998 -8.5% 114.6% Ep Ep Ep1999 -1.7% 68.4% 13.9% 15.0% 22.0%2000 -0.4% -62.8%2001 -27.7% 52.7% SDp SDp SDp2002 -20.3% -22.0% 21.8% 21.9% 26.0%2003 44.4% 6.8%AM 8.5% 39.8% Sharpe R. Sharpe R. Sharpe R.SD 23.7% 49.8% 0.41 0.46 0.66Rho 0.05

2dWeights25.4%74.6%

Ep31.8%

SDp38.0%

Sharpe R.0.71



Q1P(R>R*) 1 5 10 15 20 25

-5% 82.73% 98.26% 99.86% 99.99% 100.00% 100.00%0% 73.93% 92.42% 97.87% 99.35% 99.79% 99.93%5% 63.82% 78.55% 86.83% 91.46% 94.31% 96.15%10% 53.17% 57.06% 59.93% 62.10% 63.90% 65.46%12% 48.94% 47.62% 46.64% 45.89% 45.26% 44.70%14% 44.79% 38.48% 33.94% 30.60% 27.91% 25.63%16% 40.77% 30.08% 23.02% 18.30% 14.82% 12.16%18% 36.91% 22.74% 14.53% 9.78% 6.75% 4.74%20% 33.24% 16.63% 8.53% 4.67% 2.63% 1.51%25% 25.02% 6.59% 1.66% 0.45% 0.13% 0.04%30% 18.27% 2.15% 0.21% 0.02% 0.00% 0.00%

For T=1, as the target return increases the probability of achieving higher returns than the target plausibly decreases The same is true for T=10 For R*=10%, the probability of achieving returns higher than that is plausibly increasing in T (because R*<GM) For R*=14%, the probability of achieving returns higher than that is plausibly decreasing in T (because R*>GM)

Q22aT 1 5 10 15 20 25

Prob 4.0% 64.3% 89.8% 96.9% 99.0% 99.7%

2bT 1 5 10 15 20 25

Wealth $1,115 $1,723 $2,969 $5,115 $8,812 $15,183

30100.00%99.98%97.36%66.84%44.20%23.66%10.05%3.36%0.88%0.01%0.00%

For T=1, as the target return increases the probability of achieving higher returns than the target plausibly decreases

For R*=10%, the probability of achieving returns higher than that is plausibly increasing in T (because R*<GM) For R*=14%, the probability of achieving returns higher than that is plausibly decreasing in T (because R*>GM)

3099.9%

30$26,159



Q11a 1b - 1c Prices 1dRf 4.3% No growth $14.8 Price

MRP 5.5% 3% growth $30.7Beta 0.30 4% growth $46.9RRE 5.9%

Q2Price $66.9



Q12003

EFCF $2,584CFCF $2,570

Q2CFCF

0 $2,5701 $2,8272 $3,1103 $3,4214 $3,7635 $4,1406 $4,4717 $4,8288 $5,2159 $5,632

10 $6,082TV $78,174

Q3WACC 14.2%

Q4Price $7.9

Q5 Given that Oracle is trading at $11.4 but its intrinsic value is only $7.9, it may not be wise to buy



Q1RRE 14.28%Price $8.0

Q2RRUE 14.26%Price $7.9

Q3 The FTE estimate and the APV estimate are very close to each other and to the WACC estimate calculated before This is the way it should because, when properly applied, all three models should yield the same result In this case, the near equality also follows from the fact that Oracle is a virtually-unlevered company

The FTE estimate and the APV estimate are very close to each other and to the WACC estimate calculated before



Q1Growth 42.3%

Q2Growth 71.6%



Q1 As usual, not all ratios point in the same direction, so the question cannot be answered with certainty In addition, recall that if the multiple of company A is higher than that of company B, it would be incorrect to rush to the conclusion that B is relatively a better buy It may well be the case that B deserves to be cheaper than A (its fundamentals are not as good as those of A)

Q2 Again, we cannot rush to a conclusion without further analysis It may be the case that the fundamentals of Pfizer now are better than they were in the past, in which case it would be expected to be more expensive For example, Pfizer's growth may have increased or its risk may have decreased

Q3 Again, we cannot rush to a conclusion without further analysis It may be the case that the fundamentals of Pfizer are better than those of its peers, in which case it would be expected to be more expensive For example, Pfizer may be expected to grow faster than its peers, or it may be expected to be less risky than its peers

Q4 Pfizer still looks expensive relative to its peers Still, the same caveats mentioned above apply Even after adjusting by growth, if Pfizer is perceived as less risky than its peers, then it would be expected to be more expensive

In addition, recall that if the multiple of company A is higher than that of company B, it would be incorrect to rush to the conclusion that B is relatively a better buy It may well be the case that B deserves to be cheaper than A (its fundamentals are not as good as those of A)

It may be the case that the fundamentals of Pfizer now are better than they were in the past, in which case it would be expected to be more expensive

It may be the case that the fundamentals of Pfizer are better than those of its peers, in which case it would be expected to be more expensive For example, Pfizer may be expected to grow faster than its peers, or it may be expected to be less risky than its peers

Even after adjusting by growth, if Pfizer is perceived as less risky than its peers, then it would be expected to be more expensive



Q1US 5.75% BH Motorola Delta

Price (1a) $1,092.5 $959.0 $1,080.9 $1,044.5Price (1b) $987.6 $864.7 $982.4 $950.8

As expected, when the discount rates increase, bond prices decrease Note that we're actually calculating our estimates of intrinsic value rather than prices (which are the numbers given in the table)


SAy 1.8% 2.1% 2.2% 7.6%Ay 3.6% 4.2% 4.5% 15.1%

EAy 3.7% 4.2% 4.5% 15.7%

The Ay and the EAy are different because the latter (but not the former) takes into account the effect of compounding It is the EAy that properly captures the return delivered by a bond

Note that we're actually calculating our estimates of intrinsic value rather than prices (which are the numbers given in the table)

The Ay and the EAy are different because the latter (but not the former) takes into account the effect of compounding




Price (1a) $1,092.5 $959.0 $1,080.9 $1,044.5Price (1b) $987.6 $864.7 $982.4 $950.8Price (1c) $1,211.0 $1,065.4 $1,191.7 $1,149.8


Change 1-2 -9.6% -9.8% -9.1% -9.0%Change 1-3 10.8% 11.1% 10.3% 10.1%

Their sensitivity to changes in interest rates is similar though the BH bond seems to have slightly higher interest-rate risk

Q3 Interest-rate risk and default risk are not necessarily correlated in theory, and they are not in this case For example, Delta has much higher credit risk and yet it does not have higher interest-rate risk

Their sensitivity to changes in interest rates is similar though the BH bond seems to have slightly higher interest-rate risk




Price (1a) $1,092.5 $959.0 $1,080.9 $1,044.5Price (1b) $1,038.5 $910.4 $1,030.2 $996.2Price (1c) $1,150.0 $1,010.6 $1,134.6 $1,095.6


Duration 5.2 5.3 5.0 4.9

In all cases the durations are longer than the average maturity of 3.5 years because the bonds' cash flows are heavily weighted towards the end of their life


Mod Dur 5.0 5.1 4.7 4.6

These numbers indicate the expected change in the bonds' prices when discount rates increase by 1 percentage point


Change 1-2 -4.9% -5.1% -4.7% -4.6%Change 1-3 5.3% 5.4% 5.0% 4.9%

Average 5.1% 5.2% 4.8% 4.8%

For each bond, the average change (in absolute value) is virtually identical to the bond's modified duration This indicates that the modified duration is a very good approximation to the interest-rate risk of these bonds

In all cases the durations are longer than the average maturity of 3.5 years because the bonds' cash flows are heavily weighted towards the end of their life

These numbers indicate the expected change in the bonds' prices when discount rates increase by 1 percentage point

For each bond, the average change (in absolute value) is virtually identical to the bond's modified duration This indicates that the modified duration is a very good approximation to the interest-rate risk of these bonds



Q1A B C D E E'

0 -100 -100 -100 100 -10 -901 30 100 75 -15 4 26.02 30 100 75 -15 4 26.03 30 100 75 -15 3 27.04 30 75 75 -15 3 27.05 30 -300 -250 -15 3 27.0

NPV $13.7 $13.6 -$17.5 $43.1 $3.1 $10.6IRR 15.2% 5.3% N/A -8.9% 22.4% 14.5%

IRR-2 72.3%

Q2 Yes, because its NPV is positive (and its IRR is higher than the discount rate)

Q3 Yes, because its NPV is positive This is the case although one of the two IRRs is lower than the discount rate When the NPV and the IRR approaches conflict, the NPV gives the more correct answer

Q4 No, because its NPV is negative Note that this project has no IRR

Q5 The company should go for project A because it has a higher NPV This is the case despite the fact that A has a lower IRR than E As "project" E' shows, the NPV of the incremental cash flows of A has a positive NPV ($10.6)

Q6 No, because the project's NPV is negative (-$0.5m)



Q1Time CFs - Low CFs - High E(CFs)

0 -200 -200 -2001 20 40 302 20 40 303 20 40 304 20 40 305 20 40 306 20 40 307 20 40 308 20 40 309 20 40 30

10 20 40 30NPV ($77.1) $45.8 ($15.7)

According to the project's expected CFs, the company should not buy the rights to extract copper That being the case, this is obviously not a good project in the case of low CFs However, when CFs are high, the project does deliver a positive NPV

Q2Time CFs - Low CFs - High

01 -200 -2002 20 403 20 404 20 405 20 406 20 407 20 408 20 409 20 40

10 20 40NPV-1 ($84.8) $30.4 NPV-0 $13.8

RO $29.5

As before, if CFs are low, the company should not invest in this project And also as before, if the CFs are high, the company should invest in this project The NPV of the project, evaluated one period down, the road is $30.4m With 50% probability the company will invest and obtain this NPV, and with 50% probability the company will not invest The weighted-average of this two scenarios, today, is a positive $13.8m Therefore, it pays for the company to invest $5m in the rights to extract copper

The implicit value of the real option is $29.5m (the difference between $13.8m and -$15.7m)

With 50% probability the company will invest and obtain this NPV, and with 50% probability the company will not invest



Q1 - Q4Industry ROC COC Capital NOPAT RI RI-2Cable TV 6.7% 10.3% $189.0 $12.6 ($6.9) ($6.9)

Drugs 28.6% 10.2% $174.1 $49.8 $32.0 $32.0 Life Ins 51.3% 8.4% $126.7 $65.1 $54.4 $54.4

Property Ins 0.3% 8.4% $115.6 $0.3 ($9.4) ($9.4)Tel Equip 4.6% 14.2% $39.8 $1.8 ($3.8) ($3.8)

According to this framework, the drug and life insurance industries created value and the other three destroyed value in 2003

According to this framework, the drug and life insurance industries created value and the other three destroyed value in 2003



Q1 Call price = $3.9

Q2 Put price = $2.3

Q3S X SD

$50.0 $40.0 $50.0 $40.0 25.0% 15.0%Call $7.6 $1.5 $1.9 $7.2 $4.7 $3.2Put $0.9 $4.9 $5.0 $0.7 $3.0 $1.6

Q4 The qualitative relationships discussed in the text do hold in the exhibit above

T Rf1.00 0.5 6.0% 4.0%$4.7 $3.1 $4.1 $3.8$2.5 $2.0 $2.1 $2.4



Q1 - Q2Beta = 0.8 Beta = 0.8 Beta = 1.2 Beta = 1.2

S $10,000 $10,000 $10,000 $10,000c 5.0% 5.0% 5.0% 5.0%y 1.0% 1.0% 1.0% 1.0%T 0.5 0.5 0.5 0.5

F(0) $10,202 $10,202 $10,202 $10,202Dow(0) 10000 10000 10000 10000Dow(1) 9000 11000 9000 11000

Rm -9.5% 10.5% -9.5% 10.5%Beta 0.8 0.8 1.2 1.2

Pfolio (0) $4,000,000 $4,000,000 $4,000,000 $4,000,000Rp -7.1% 8.9% -11.9% 12.1%

Pfolio (1) $3,716,000 $4,356,000 $3,524,000 $4,484,000Gain/Loss -$284,000 $356,000 -$476,000 $484,000

F(0) $10,202.0 $10,202.0 $10,202.0 $10,202.0F(1) 9000 11000 9000 11000

N 32 32 48 48Gain/Loss $384,644.3 -$255,355.7 $576,966.4 -$383,033.6Total G/L $100,644.3 $100,644.3 $100,966.4 $100,966.4

Invest @Rf $4,101,260.5 $4,101,260.5 $4,101,260.5 $4,101,260.5Gain $101,260.5 $101,260.5 $101,260.5 $101,260.5

Difference -$616.2 -$616.2 -$294.0 -$294.0

In both cases the hedges are almost perfect



Q1 1a - For both European and Americans it is the same buying the flat-screen TV in the US or in Europe 1b - In this case the flat-screen TV is cheaper in Europe, and therefore this is not an absolute PPP equilibrium 1c - In this case the flat-screen TV is cheaper in the US, and therefore this is not an absolute PPP equilibrium

Q2 2a- The dollar will depreciate to 1.544 2b- US interest rates will rise to 9% and European interest rates will rise to 6% 2c- The dollar-euro one-year forward exchange rate will be 1.542 2d- At a forward rate of 1.542 Americans would be indifferent between investing in the US or in Europe 2e- At a forward rate of 1.542 Europeans would be indifferent between investing in the US or in Europe 2f- Borrow €100, convert to dollars and invest in the US at 9% for one year, locking a certain profit of €4.5 2g- Borrow $100, convert to euros and invest in Europe at 6% for one year, locking a certain profit of €2.5

1b - In this case the flat-screen TV is cheaper in Europe, and therefore this is not an absolute PPP equilibrium 1c - In this case the flat-screen TV is cheaper in the US, and therefore this is not an absolute PPP equilibrium

2d- At a forward rate of 1.542 Americans would be indifferent between investing in the US or in Europe 2e- At a forward rate of 1.542 Europeans would be indifferent between investing in the US or in Europe 2f- Borrow €100, convert to dollars and invest in the US at 9% for one year, locking a certain profit of €4.5 2g- Borrow $100, convert to euros and invest in Europe at 6% for one year, locking a certain profit of €2.5



Q1 - Q2Year ARG BRA19931994 -23.6% 65.7%1995 12.9% -19.2%1996 20.3% 42.5%1997 24.6% 27.3%1998 -24.3% -39.6%1999 34.3% 67.2%2000 -25.1% -11.4%2001 -18.3% -17.0%2002 -50.5% -30.7%2003 101.3% 115.0%Mean 5.2% 20.0%

Median -2.7% 8.0%Mode N/A N/A

Var (T) 0.1703 0.2392 SD (T) 41.3% 48.9%Covar 0.1577 Correl 0.78

Var (T-1) 18.9% 26.6%SD (T-1) 43.5% 51.6%

The mean and the median are different because these distributions are skewed (asymmetric) The mode does not exist because there is no value that occurs more often than others (all values occur just once in both samples) The covariance indicates a positive linear relationship between the stock markets of Argentina and Brazil The correlation indicates that this positive linear relationship is quite strong

The mode does not exist because there is no value that occurs more often than others (all values occur just once in both samples) The covariance indicates a positive linear relationship between the stock markets of Argentina and Brazil



Q1Range AbsFreq RelFreq(1, 2) 0 0.0%(2, 3) 1 5.0%(3, 4) 2 10.0%(4, 5) 2 10.0%(5, 6) 5 25.0%(6, 7) 2 10.0%(7, 8) 2 10.0%(8, 9) 2 10.0%(9, 10) 1 5.0%

(10, 11) 1 5.0%(11, 12) 1 5.0%(12, 13) 1 5.0%(13, ∞) 0 0.0%

20 1

The distributions of returns does not appear to be normal, it actually appears to have a long right tail (positive skewness)

Q2 - Q3 Prob (R≤12%) = 50.0% Prob (R≤5%) = 36.3% Prob (R≥30%) = 18.4% Prob (5%≤R≤20%) = 29.2%

(1, 2

)(2

, 3)

(3, 4

)(4

, 5)

(5, 6

)(6

, 7)

(7, 8

)(8

, 9)

(9, 1

0)

(10, 1

1)

(11, 1

2)

(12, 1

3)

(13, ∞

)0

1

2

3

4

5

6

Range

Abs

olu

te F

requ

ency

The distributions of returns does not appear to be normal, it actually appears to have a long right tail (positive skewness)

(1, 2

)(2

, 3)

(3, 4

)(4

, 5)

(5, 6

)(6

, 7)

(7, 8

)(8

, 9)

(9, 1

0)

(10, 1

1)

(11, 1

2)

(12, 1

3)

(13, ∞

)0%

5%

10%

15%

20%

25%

30%

Range

Rel

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e F

requ

ency

(1, 2

)(2

, 3)

(3, 4

)(4

, 5)

(5, 6

)(6

, 7)

(7, 8

)(8

, 9)

(9, 1

0)

(10, 1

1)

(11, 1

2)

(12, 1

3)

(13, ∞

)0

1

2

3

4

5

6

Range

Abs

olu

te F

requ

ency

(1, 2

)(2

, 3)

(3, 4

)(4

, 5)

(5, 6

)(6

, 7)

(7, 8

)(8

, 9)

(9, 1

0)

(10, 1

1)

(11, 1

2)

(12, 1

3)

(13, ∞

)0%

5%

10%

15%

20%

25%

30%

Range

Rel

ativ

e F

requ

ency



Q1Skewness 1.05 Sum StatsKurtosis 1.01 Mean 6.9%

Std Error 0.0066Median 5.9%Mode 5.6%SD 3.0%Sample Var 0.0009Kurtosis 1.01Skewness 1.05Range 11.8%Minimum 2.9%Maximum 14.7%Sum 138.5%Count 20

Q2 Prob (R≤10%) = 55.8% Prob (R≥20%) = 24.4% Prob (5%≤R≤25%) = 38.8%



Q1Regression Statistics

R Square 0.05Adj R2 0.02Std Error 0.01Observations 30ANOVA df SS MS F Signif FRegression 1 0.0001 0.0001 1.60 0.22Residual 28 0.0012 0.0000Total 29 0.0012

Coefficients Std Errors t Stat P-valueIntercept 0.001 0.005 0.25 0.80X Variable 1 0.060 0.048 1.26 0.22

The R square is rather low at 5%, indicating that volatility (SD) explains about 5% of the variability in MRs Consistently, the slope coefficient is not significant according to the standard t-test (and, say, a 5% significance level) The slope coefficient indicates that a 1% increase in SD leads to a 0.6% increase in MRs In short, SDs do not seem to be very closely related to MRs



Coefficients Std Errors t Stat P-valueIntercept 0.003 0.002 1.38 0.18X Variable 1 0.004 0.002 1.86 0.07

The R square is still rather low but over twice as high compared to that of the previous regression Beta is not significant at the usual 5% level of significance (but it would be at the 10% level) Beta seems to explain MRs somewhat better than volatility but neither provides a substantial explanation for the variability in MRs



Coefficients Std Errors t Stat P-valueIntercept 0.004 0.005 0.80 0.43X Variable 1 -0.016 0.074 -0.21 0.84X Variable 2 0.004 0.003 1.32 0.20

The R square of this regression is almost identical to that of the previuos regression Neither volatility nor beta seem to explain a substantial part of the variability in MRs The adjusted R squares of this regression and the previous one indicate that it does not pay to add volatility to a regression between MRs and betas

The R square is rather low at 5%, indicating that volatility (SD) explains about 5% of the variability in MRs Consistently, the slope coefficient is not significant according to the standard t-test (and, say, a 5% significance level)

Beta seems to explain MRs somewhat better than volatility but neither provides a substantial explanation for the variability in MRs

The adjusted R squares of this regression and the previous one indicate that it does not pay to add volatility to a regression between MRs and betas

0273707817_answer_key

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