Chapter 8Alternative Investments1. Let us compute the terminal value of $1 invested. The share class with the highest terminal value netof all expenses would be the most appropriate, because all classes are based on the same portfolio and thus have the same portfolio risk characteristics.a. Class A. $1 × (1 – 0.05) = $0.95 is the amount available for investment at t= 0, after paying thefront-end sales charge. Because this amount grows at 9% per year, reduced by annual expensesof 0.0125, the terminal value per $1 invested after one year is $0.95 × 1.09 × (1 − 0.0125) = $1.0226.Class B. Ignoring any deferred sales charge, after one year, $1 invested grows to $1 × 1.09 ×(1 – 0.015) = $1.0737. According to the table, the deferred sales charge would be 4%; therefore,the terminal value is $1.0737 × 0.96 = $1.0308.Class C. Ignoring any deferred sales charge, after one year, $1 invested grows to $1 × 1.09 ×(1 − 0.015) = $1.0737. According to the table, the deferred sales charge would be 1%; therefore,the terminal value is $1.0737 × 0.99 = $1.063.Class C is the best.b. Class A. The terminal value per $1 invested after three years is $0.95 × 1.093× (1 − 0.0125)3=$1.1847.Class B. Ignoring any deferred sales charge, after three years, $1 invested grows to $1 × 1.093 ×(1 − 0.015)3= $1.2376. The deferred sales charge would be 2%; therefore, the terminal value is$1.2376 × 0.98 = $1.2128.Class C. There would be no deferred sales charge. Thus, after three years, $1 invested grows to$1 × 1.093× (1 − 0.015)3= $1.2376.Class C is the best.c. Class A. The terminal value per $1 invested after five years is $0.95 × 1.095× (1 − 0.0125)5=$1.3726.Class B. There would be no deferred sales charge. So, the terminal value per $1 invested afterfive years is $1 × 1.095× (1 − 0.015)5= $1.4266.Class C. There would be no deferred sales charge. So, the terminal value per $1 invested afterfive years is $1 × 1.095× (1 − 0.015)5= $1.4266.Classes B and C are the best.d. Class A. The terminal value per $1 invested after 15 years is $0.95 × 1.0915× (1 − 0.0125)15=$2.8653.Class B. There would be no deferred sales charge. So, the terminal value per $1 invested after15 years is $1 × 1.0915× (1 − 0.015)6× (1 − 0.0125)9= $2.9706.Class C. There would be no deferred sales charge. So, the terminal value per $1 invested after15 years is $1 × 1.0915× (1 − 0.015)15= $2.9036.Class B is the best.42 Solnik/McLeavey • Global Investments, Sixth Edition2. Class A performs quite poorly unless the investment horizon is very long. The reason is the high salescharge of 5 percent on purchases. Even though the annual expenses for Class A are low, that is not enough to offset the high sales charge on purchases until a very long investment horizon. One could verify that Class A outperforms Class C for an investment horizon of 21 years or more.Class B performs worse than Class C at very short-term horizons because of its higher deferred sales charges. However, after its deferred sales charges disappear, the relative performance of Class B starts improving. After six years, Class B shares convert to Class A with its lower annual expenses.At longer horizons, Class B starts to outperform Class C due to its annual expenses, which are lower than those of Class C.Class C performs well at shorter investment horizons because it has no initial sales charge and it has a low deferred sales charge.3. The estimated model isHouse value in euros = 140,000 + (210 × Living area) + (10,000 × Number of bathrooms) +(15,000 × Fireplace) − (6,000 × Age)so, the value of the specific house is140,000 + (210 × 500) + (10,000 × 3) + (15,000 × 1) – (6,000 × 5) =€260,0004. a. The net operating income for the office building is gross potential rental income minus estimatedvacancy and collection costs, minus insurance and taxes, minus utilities, minus repairs andmaintenance.NOI = 350,000 − 0.04 × 350,000 − 26,000 − 18,000 − 23,000 = $269,000b. The capitalization rate of the first office building recently sold in the area isNOI/(Transaction price) = 500,000/4,000,000 = 0.125The capitalization rate of the second office building recently sold in the area isNOI/(Transaction price) = 225,000/1,600,000 = 0.141The average of the two capitalization rates is 0.133.Applying this capitalization rate to the office building under consideration, which has an NOI of $269,000, gives an appraisal value of:NOI/(Capitalization rate) = 269,000/0.133 = $2,022,5565. The after-tax cash flow for the property sale year is $126,000 + $710,000 = $836,000. At a cost ofequity of 18%, the present value of the after-tax cash flows in years 1 through 5 is as follows.$60,000/1.18 + $75,000/1.182+ $91,000/1.183+ $108,000/1.184 +36,000/1.185= $581,225 The investment requires equity of 0.15 × $3,000,000 = $450,000. Thus, the NPV = $581,225 −$450,000 = $131,225. The recommendation based on NPV would be to accept the project, because the NPV is positive.Chapter 8 Alternative Investments 43 6. a. The amount borrowed is 80% of $1.5 million, which is $1.2 million. The first year’s interest =9% of $1.2 million = $108,000. So,After-tax net income in year 1 = (NOI − Depreciation − Interest) × (1 − Marginal tax rate) =($170,000 − $37,500 − $108,000) × (1 − 0.30) = $17,150flow= After-tax net income + Depreciation − Principal repaymentcashAfter-taxand,= Mortgage payment − Interest = $120,000 − $108,000 = $12,000 Principalrepaymentso,After-tax cash flow in year 1 = $17,150 + $37,500 − $12,000 = $42,650.New NOI in year 2 = 1.04 × $170,000 = $176,800. We need to calculate the second year’sinterest payment on the mortgage balance after the first year’s payment. This mortgage balanceis the original principal balance minus the first year’s principal repayment, or $1,200,000 –$12,000 = $1,188,000. The interest on this balance is $106,920.So,= ($176,800 − $37,500 − $106,920) × (1 − 0.30) = $22,666incomeAfter-taxnet= $120,000 − $106,920 = $13,080repaymentPrincipalso,After-tax cash flow in year 2 = $22,666 + $37,500 − $13,080 = $47,086New NOI in year 3 = 1.04 × $176,800 = $183,872. We need to calculate the third year’s interestpayment on the mortgage balance after the second year’s payment. This mortgage balance is theoriginal principal balance minus the first two years’ principal repayments, or $1,200,000 −$12,000 − $13,080 = $1,174,920. The interest on this balance is $105,743.So,income= $183,872 − $37,500 − $105,743) × (1 − 0.30) = $28,440netAfter-tax= $120,000 − $105,743 = $14,257repaymentPrincipalso,After-tax cash flow in year 3 = $28,440 + $37,500 − $14,257 = $51,683b. Ending book value = Original purchase price − Total depreciation during three years =$1,500,000 − 3 × $37,500 = $1,387,500.The net sale price = $1,720,000 × (1 − 0.065) = $1,608,200Capital gains tax = 0.20 × ($1,608,200 − $1,387,500) = $44,140After-tax cash flow from property sale = Net sales price − Outstanding mortgage − Capitalgains taxand,= Original mortgage − Three years’ worth of principal repayments,mortgageOutstandingor$1,200,000 − ($12,000 + $13,080 + $14,257) = $1,160,63so,After-tax cash flow from the property sale = $1,608,200 − $1,160,663 − $44,140 = $403,39744 Solnik/McLeavey • Global Investments, Sixth Editionc. The total after-tax cash flow for the property sale year is $51,683 + $403,397 = $455,080. At acost of equity of 19%, the present value of the after-tax cash flows in years 1 through 3 is asfollows:$42,650/1.19 + $47,086/1.192+ $455,080/1.193= $339,142The investment requires equity of 0.20 × $1,500,000 = $300,000. Thus, the NPV = $339,142 −$300,000 = $39,142. The recommendation based on NPV would be to accept the project, because the NPV is positive.7. No, one would not suggest using real estate appraisal-based indexes in a global portfolio optimization.Real estate appraisal values are a smoothed series. One of the reasons for this smoothness is that the appraisals are done quite infrequently. Another reason is that the appraised values typically show relatively few changes. Due to these two reasons, an appraisal-based index understates volatility.This spuriously low volatility would inflate the attractiveness of real estate.8. Clearly, the two real estate indexes have very different price behaviors. Their correlation is almostnull. As expected, the NAREIT index exhibits a strong correlation with U.S. stocks because the REIT share prices are strongly influenced by the stock market. In contrast, the FRC index, which is much less volatile, is not highly correlated with the stock market.9. a. There are three possibilities.Project does not survive until the end of the eighth yearProject survives and the investor exits with a payoff of $25 millionProject survives and the investor exits with a payoff of $35 millionThere is an 80 percent chance that the project will not survive until the end of the eighth year.That is, there is a 20 percent chance that the project will survive, and the investor will exit theproject then. If the project survives, it is equally likely that the payoff at the time of exit will beeither $25 million or $35 million.The project’s NPV is the present value of the expected payoffs minus the required initialinvestment of $1.4 million.= 0.8 × $0 + 0.2 × [(0.5 × $25 million + 0.5 × $35 million)/1.28] − $1.4 million = NPV−$0.004592 million or −$4,592b. Because the expected NPV of the project is negative, the project should be rejected.10. The probability that the venture capital project survives to the end of the first year is (1 − 0.28),1 minus the probability of failure in the first year; the probability that it survives to the end ofsecond year is the product of the probability it survives the first year times the probability it survives the second year, or (1 − 0.28) (1 − 0.25). So, the probability that the project survives to end of the sixth year is (1 − 0.28) (1 − 0.25) (1 − 0.22) (1 − 0.18) (1 − 0.18) (1 − 0.10) = (0.72) (0.75) (0.78)(0.82) (0.82) (0.90) = 0.255, or 25.5%. The probability that the project fails is 1 − 0.255 = 0.745,or 74.5%.The net present value of the project, if it survives to the end of the sixth year and thus earns€60 million, is – €4.5 million +€60 million/1.226=€13.70 million. The net present value of the project if it fails is −€4.5 million. Thus, the project’s expected NPV is a probability-weightedaverage of these two amounts, or (0.255) (€13.70 million) + (0.745) (–€4.5 million) =€141,000.Based on the project’s positive net present value, VenCap should accept the investment.Chapter 8 Alternative Investments 4511. a. Fee = 1.5% + 15% × (35% − 5.5%) = 1.5% + 4.425% = 5.925%.= 35% − 5.925% = 29.1%Netreturnb. Because the gross return is less than the risk-free rate, the incentive fee is zero. The only feeincurred is the base management fee of 1.5%.= 5% − 1.5% = 3.5%.returnNetc. Again, the incentive fee is zero.=−6% − 1.5% =−7.5%.Netreturn12. a. Fixed fee = 1% of $2 billion = $20 million.If the return is 29%, new value of the fund would be $2 billion × 1.29 = $2.58 billion. This newvalue would be $2.58 billion − $2.1 billion = $0.48 billion above the high watermark. So, theincentive fee = 20% × $0.48 billion = $0.096 billion, or $96 million.Total fee = $20 million + $96 million = $116 millionb. Fixed fee = 1% of $2 billion = $20 million.If the return is 4.5%, new value of the fund would be $2 billion × 1.045 = $2.09 billion. Becausethis new value is below the high watermark of $2.1 billion, no incentive fee would be earned.Total fee = $20 millionc. Fixed fee = 1% of $2 billion = $20 million.If the return is −1.8%, no incentive fee would be earned.Total fee = $20 million13. Clearly, the high watermark provision has the positive implication for the investors that they wouldhave to pay the manager an incentive fee only when they make a profit. Further, the hedge fundmanager would need to make up any earlier losses before becoming eligible for the incentive feepayment. However, a negative implication is that the option-like characteristic of the high watermark provision (the incentive fee being zero everywhere below the benchmark and increasing above the benchmark) may induce risk-taking behavior when the fund is below the high watermark. Themanager may take more risky positions when the fund is below the high watermark in order to get to above the high watermark and earn an incentive fee. The worst case for the manager is a zeroincentive fee, regardless of how far below the benchmark the fund turns out to be. Another negative implication is that the incentive fees, if the fund exceeds the high watermark, are set quite high(typically at 20%), which reduces long-run asset growth.14. a. The hedge fund would sell short the overvalued shares and use the proceeds to buy theundervalued shares. The fund has €25 million −€1 million =€24 million to be used toward cashmargin deposit. Because the cash margin deposit requirement is 20%, the fund could take longand short positions totalling €24 million/0.20 =€120 million. So, the fund would do thefollowing:€1 million in cashK eep€24 million in a margin accountDeposit€120 million of overvalued stocks from a brokerBorrowSell the overvalued stocks for €120 millionUse the sale proceeds to purchase undervalued stocks for €120 million46 Solnik/McLeavey • Global Investments, Sixth Editionb. If the performances of both lists of stocks are as expected, there would be a gain of 7% on thelong position of €120 million and a gain of 7% on the short position of €120 million. So, the total gain would be 7%×€120 million × 2 =€16.8 million. Ignoring the return on invested cash of €1 million, and assuming that dividends on the long stocks will offset dividends on the short stocks, this translates to an annual return of (€16.8 million/€25 million) × 100 = 67.2%. The return is so high when the expectations are realized, because the position is highly levered.15. a. The Spanish firm will give two of its shares, which are worth €25, for three of the Italian firm’sshares, which are worth €24. Thus, the shares of the Italian firm are trading at a discount. Thereason for the discount is that there is a possibility that the merger may not go through. If themerger does not go through, the shares of the Italian firm are likely to fall back to the premerger announcement level. An investor currently buying shares of the Italian firm is taking the risk that the merger will not occur.b. The hedge fund will take a hedged position by selling two shares of the Spanish firm short forevery three shares of the Italian firm that it buys. So, the hedge fund will buy 250,000 shares ofthe Italian firm by selling (2/3) × 250,000 = 166,666.67, that is, 166,667 shares of the Spanishfirm. The proceeds from the short sale are 166,667 ×€12.50 =€2,083,338, which is €83,338more than the cost of buying the shares of the Italian firm, which is 250,000 ×€8 =€2,000,000.c. Because the merger did not go through and the stock price of the Italian firm fell, the hedge fundincurs a substantial loss. The loss is 250,000 × (€8 −€6.10) =€475,000.16. a. Net return on Fund A = 50% × (1 − 0.15) = 42.5%Net return on Fund B = 20% × (1 – 0.15) = 17%Net return on Fund C =−10%So, average net return = (42.5% + 17% − 10%)/3 = 16.5%= (50% + 20% − 10%)/3 = 20%.AveragereturngrossThus, the average gross return on the three hedge funds is the same as the percentage increase in the stock market index, and the average net return is lower.b. The publicity campaign launched by Global group illustrates the problem of survivorship bias inperformance measure of hedge funds. Although the average gross return on the three hedge funds is the same as the percentage increase in the stock market index, the performance reported byGlobal group seems much better because it is based on only the funds that survive. That is, theaverage performance reported by Global group is inflated.17. The measurement of the performance of the hedge funds suffers from survivorship bias. The 90 hedgefunds that the analyst has examined include only those funds that have survived during the last 10 years. Thus, any poorly performing funds that have been discontinued due to low return or highvolatility, or both, have been excluded. Accordingly, the average return on hedge funds hasbeen overstated, while the volatility has been understated. Consequently, the Sharpe ratio for the hedge funds has been overstated. Furthermore, the Sharpe ratio may be a misleading measure of risk-adjusted performance for hedge funds because of the optionality in their investment strategies.18. a. The construction of the index is okay in year 10 but not in the earlier years. By using today’sweights in construction of the index in earlier years, the exchange is over-weighing thosecommodities that have become important over the period, and have simultaneously gone up inprice.b. For each year, use the relative economic importance of the commodities in that year as theweights for that year. That is, use year one weights for the index calculated in year one, and so on.Chapter 8 Alternative Investments 4719. a. The expected return on gold, as theoretically derived by the CAPM, isE(Rgold) = 7% +βgold × 4%= 7% − 0.3 (4%) = 5.8%b. Given its negative beta, gold is likely to perform well when the overall market performs poorly.Thus, our investment in gold is likely to offset some of the loss on the rest of the portfolio.Investors should be willing to accept an overall lower expected return on gold because, in periodsof financial distress, gold tends to do well.。
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