Chapter 8:

1.      Why are the hurdle rates that venture capital firms use to value investment
        opportunities gene...
5.      For valuing investments made by public companies, why is it common to use
        the Risk Adjusted Discount Rate ...
False. Even if the future is highly uncertain, valuing the opportunity still is important.
Furthermore, it can be of consi...
Answer:
Total Capital Cash Flow = $180,000 - $70,000 = $110,000

13.    Compute the venture’s cash flow to creditors for t...
Answer:
The risk-averse investor’s portfolio will have lower risk and a lower expected return. In
addition, the willingnes...
24.    Compute the weighted average cost of capital (WACC).

Answer:
WACC = .4(1.0 – 0.1)6.5% + .6 x 10.34% = 8.58%




25...
Method                        Advantages                            Disadvantages
RADR                          Based on C...
The tax deductibility of interest payments is a complicating factor because taxes may
affect both the cash flows and the d...
4.567
                              2.345

                           Beta Risk =              1.947548

  30.     Given t...
Answer:
          Return

          rm = 12%


           rf = 7%


                     1.0   Beta
Appendix 8A

1.      A company is expected to pay a $4 dividend until infinity. Assuming that the
        firm’s cost of c...
PV = $7,436,110.87


6.      What would be the present value of future cash flows for an accountant who
        earns a st...
Appendix 8B

Use the data below to answer the following four questions.
                                           Individ...
4.     Calculate the regressions if Stock B is the dependent variable.

       Answer:
                             CovA,B...
7.   What are the covariance and correlation between the returns of the two
     stocks?

     Answer:

               Sto...
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Chapter 8

  1. 1. Chapter 8: 1. Why are the hurdle rates that venture capital firms use to value investment opportunities generally higher than cost of capital of the investment opportunities? Answer: Venture capital firms normally base their valuations on cash flow projections that are optimistic (positively biased). To compensate for the optimism in the projections, they discount the projected cash flows at hurdle rates that are positively biased. 2. Hurdle rates used by venture capital firms are higher than cost of capital because: A) the venture capitalist does not know the true cost of capital and wants to make sure to use a rate that is no less than cost of capital. B) the hurdle rate compensates for positive bias in the cash flow projections of the investment opportunity. C) the venture capitalist can do better by only accepting projects that have positive NPVs when expected cash flows are discounted at rates higher than cost of capital. D) opportunity cost of capital is not relevant to the value of a venture capital investment. Answer: B 3. Why are realized returns (IRRs) to venture capital investments generally lower than the hurdle rates that venture capital firms use to value investment opportunities? Answer: On average, the cash flows that are valued by discounting at the hurdle rate are higher than the expected cash flows of the investments. When the true cash flows are realized, they imply an IRR that is below the hurdle rate. On average, the IRRs should be above opportunity cost of capital. 4. Why is it appropriate to use the CAPM, an approach that bases valuation on undiversifiable risk, to value investments by underdiversified venture capital funds? Answer: The investors in venture capital funds are well-diversified investors. It is their diversification that is relevant to the justification for using the CAPM.
  2. 2. 5. For valuing investments made by public companies, why is it common to use the Risk Adjusted Discount Rate (RADR) form of the CAPM rather than the CEQ form? Answer: The RADR form is easy to use if investors can be assumed to be well diversified and there are public companies that are comparable to project in which the company plans to invest. In that case, the CAPM beta can be inferred from the stock price data of the comparable public firms. 6. Why might it difficult to use the RADR form of the CAPM to value investments by venture capital funds? A) Comparable public firms may not be available for projects that have the high total risk of venture capital fund investments. B) Beta risk is not relevant to valuing investments by venture capital funds. C) The market risk premium is not relevant to venture capital fund investments. D) Comparable public firms may not be available for projects that have the market risk of venture capital fund investments. Answer: D 7. Why might it be difficult to use the RADR form of the CAPM to value investments by underdiversified entrepreneurs, even if comparable public firm data on beta risk and total risk are available? Answer: The comparable firm data on beta and total risk is based on equilibrium holding period returns for well-diversified investors. Consequently, the public data understates the equilibrium beta and total risk for an underdiversified entrepreneur. 8. “The value of an investment in a new venture is qualitative, based on the preferences of the investor, rather than on the potential of the venture to generate future cash flows.” True, false, or uncertain? Explain. Answer: False. Investors may disagree about the value of the venture based on their own subjective perceptions, but even in this case, value depends on the venture’s potential to generate cash flows in the future. 9. “For ventures that are extremely risky, there is no point in trying to forecast future cash flows.” True, false, or uncertain? Explain. Answer:
  3. 3. False. Even if the future is highly uncertain, valuing the opportunity still is important. Furthermore, it can be of considerable value to develop estimates of how uncertain the cash flows are. When uncertainty is high, forecasts can aid in structuring investment agreements and in assessing performance after the initial investment is made. 10. “The reason hurdle rates tend to be higher for earlier stage investment is that total risk is higher and therefore the return the investor hopes to realize is higher.” True, false, or uncertain. Explain. Answer: Uncertain. The investor must be compensated for diversifiable risk, which may be no higher for an early-stage venture than a later stage one. The hurdle rates are higher because the optimism built into the “success scenario” forecast of cash flows is higher. In problems 11 through 16, use the following financial information for one year of operation. Assume that the debt is riskless. Income Statement Revenue $1,000,000 Cost of Goods Sold 450,000 Gross Profit 550,000 Depreciation Expense 100,000 Other Operating Expenses 200,000 Operating Profit 250,000 Interest Expense 75,000 Net Taxable Income 175,000 Taxes (40%) 70,000 Net Income 105,000 Selected Items from Sources and Uses of Funds Statement Change in Current Assets $ 180,000 Change in Current Liabilities 100,000 Debt Repayment 20,000 New Debt Issued 35,000 Capital Expenditures 90,000 11. Compute the venture’s operating cash flow for the year. Answer: Operating Cash Flow = $250,000 + $100,000 - $90,000 – ($180,000 - $100,000) = $180,000 12. Compute the venture’s cash flow to all investors for the year.
  4. 4. Answer: Total Capital Cash Flow = $180,000 - $70,000 = $110,000 13. Compute the venture’s cash flow to creditors for the year. Answer: Debt Cash Flow = $75,000 + ($20,000 – $35,000) = $60,000 14. Compute the venture’s cash flow to stockholders for the year. Answer: Equity Cash Flow = $180,000 - $75,000 – ($20,000 - $35,000) - $70,000 = $50,000 15. Compute the venture’s unlevered free cash flow for the year. Answer: Unlevered Free Cash Flow = $180,000 – 40% x $250,000 = $80,000 16. Compute the venture’s EBITDA for the year. Answer: EBITDA = $250,000 + $100,000 = $350,000 17. What is the difference between Cash Flow to Creditors and Contractual Cash Flow to Creditors. Answer: If the debt is riskless, there is no difference. If it is risky, the firm might default on interest payments or principal repayments, which would make Cash Flow to Creditors (which is based on expected performance) less than Contractual Cash Flow. 18. In the context of portfolio theory, with only risky assets, what is the meaning of the term “feasible set” and what is the meaning of the term “efficient frontier?” Answer: The feasible set is the set of achievable risk and expected return combinations that investors can get by forming portfolios of the risky assets. The efficient frontier is the set of portfolios that yield the highest expected return for a given level of risk. 19. In a world with only risky assets, if all investors agree about the expected returns and the underlying risk of the assets and their correlations with each other, how will the portfolio choice of a highly risk-averse investor differ from the portfolio choice of a risk-tolerant investor?
  5. 5. Answer: The risk-averse investor’s portfolio will have lower risk and a lower expected return. In addition, the willingness of the investor to accept additional risk in exchange for a higher expected return (the investor’s price of risk) will be low compared to that of the risk- tolerant investor. 20. In the CAPM world, where investor can hold combinations of risky assets and a riskless asset, why, if investors agree on the risk characteristics and expected returns of the risky assets, do they all hold the same risky portfolio, and how do the portfolios of risk-averse and risk-tolerant investors differ? Answer: They all hold the risky portfolio that, when combined with investment in the riskless asset, gives them the ability to achieve the highest return for a given level of risk. A risk- averse investor will put more wealth into the riskless asset, and will have lower portfolio risk and a lower expected return. All investors will trade off risk and return at the price, the market price of risk. Use the following information in questions 21 through 24. Risk-free rate 4.0% Market rate 10.0% Beta of Assets 0.8 Beta of Debt 0.2 Debt/Value 0.4 Debt interest rate 6.5% Net tax advantage of debt 0.1 21. Compute the required return on assets. Answer: rA = 4.0% + .8(10.0% - 4.0%) = 8.8% 22. Compute the cost of capital for debt. Answer: rD = 4.0% + .2(10.0% - 4.0%) = 5.2% 23. Compute the equity beta and cost of capital for equity. Answer: BetaE = .8 x (1/.7) - .2 x (.3/.7) = 1.057 rE = 4.0% + 1.057(10.0% - 4.0%) = 10.34%
  6. 6. 24. Compute the weighted average cost of capital (WACC). Answer: WACC = .4(1.0 – 0.1)6.5% + .6 x 10.34% = 8.58% 25. The expected cash flow in two years of an investment made today is $1200, correlation between venture cash flows and the market is 0.2, the standard deviation of future cash flows is $300, the market risk premium is 6.0 percent, the two-year standard deviation of the market is 22.0%, and the risk-free rate is 4.0%. What is the risk adjustment to the expected cash flow, certainty equivalent cash flow, and what is the present value of the cash flow? Answer: Risk adjustment = - 0.2 x $300 x 6.0% / 22.0% = $16.36 Certainty Equivalent Cash Flow = $1200 - $16.36 = $1183.64 Present Value = $1183.64/(1.04)2 = $1094.34. 26. Describe in words the RADR and CEQ methods of valuing a venture. What are the advantages and disadvantages of each? Answer: The RADR approach converts an expected future cash flow to present value by applying a discount rate that reflects both the time value of money and the riskiness of the expected future cash flow. Instead of adjusting the discount rate for the riskiness of a future cash flow, the CEQ approach makes the risk adjustment directly to the cash flow. Then the risk-adjusted cash flow is converted to present value by discounting at the risk- free rate.
  7. 7. Method Advantages Disadvantages RADR Based on CAPM The discount rate depends on the standard deviation of the holding- period return; the holding period return depends on the value of the project (endogeneity problem) Requires making repeated guesses about the value by computing the resulting holding-period returns and cost of capital, valuing the cash flow, and checking to see if the estimate is the same as the value computed using the PV equation Based on the CAPM (models does not fully explain required rates of return; based on historical evidence; anomalies; assumptions may not hold CEQ Based on CAPM Based on the CAPM (models does Uses the standard deviation of cash not fully explain required rates of flow to calculate the project risk return; based on historical evidence; instead of holding-period return. anomalies; assumptions may not hold The standard deviation of cash flow does not require estimating project value. 27. “In valuing financial claims, correct valuation depends on matching the cash flows with the discount rate. Tax deductibility is a complicating factor in the valuation.” Explain. Answer:
  8. 8. The tax deductibility of interest payments is a complicating factor because taxes may affect both the cash flows and the discount rate. The discount rate and expected cash flows must be consistent with respect to their treatment of taxes. One way to achieve consistency is to estimate the expected after-tax-cash flow given the target capital structure of the venture and to discount those flows at a rate that is not adjusted for the tax deductibility of interest expense. This way, any tax benefit of debt financing is reflected in the cash flow. The alternative way is to estimate theoretical cash flow as if the venture is not leveraged and then discount those flows using a discount rate that is based on the benefit of the debt tax shelter at the target capital structure. 28. Because new ventures are, in fact, portfolios of options, can we use standard option pricing models (OPM), like the Black-Scholes model, to value new venture? Answer: Standard OPMs are derived assuming market completeness and continuous trading of assets. A complete market means that the underlying asset, matched pairs of puts and calls (with the same exercise price and the expiration date), and the riskless debt are all continuously available and it is possible to take long or short positions in each. Those conditions hold reasonably well for publicly traded options on publicly traded common stocks. They also may provide reasonable approximations for options on nonpublic assets such as gold mines, whose value are closely tied to the value of the gold, which is publicly traded asset. Because there rarely are publicly traded assets that underlie new ventures, an OPM approach would tend to over-estimate the value of a new venture’s real options. Also, the conditions described above do not characterize new ventures, although it does make sense to think of new ventures as bundles of options. There also are practical difficulties of valuing the many interrelated options that characterize new ventures. 29. Compute the beta risk of an investment if: its covariance with the market is: 4.567 the variance of market returns 2.345 Answer: its covariance with the market is: 4.567 the variance of market returns 2.345 covariance(returns on asset, returns from market) Variance of market returns
  9. 9. 4.567 2.345 Beta Risk = 1.947548 30. Given the answer above, if the risk premium is 5% and risk free rate is 6%, what would the expected rate of return be using the CAPM model? Answer: Discount Rate = risk free rate + beta*(risk premium) 6% + 1.948(5%) Discount Rate 15.74% 31. If the correlation coefficient of holding period returns is 0.45 and standard deviations of the asset and the market are 30% and 15% respectively, what is the beta risk of the asset? Answer: Beta Risk = (Corr. Betw. asset returns and mkt. returns)*(Standard Deviation of the asset returns) Standard Deviation of market returns (.45*.30) .15 Beta Risk = 0.9 32. In the following, what is the return for the market? What is the risk free rate? Beta Expected Return Stock A 1.6 10.4% Stock B 0.9 7.6% Answer: RPM = (rA – rB)/(BetaA – BetaB) = 0.028/.7 = 4.0% 10.4% = rF + 1.6 x 4.0% rf = 4%, rm = 8% 33. If the market risk-premium is 5% and the risk-free rate is 7%, draw the appropriate security market line.
  10. 10. Answer: Return rm = 12% rf = 7% 1.0 Beta
  11. 11. Appendix 8A 1. A company is expected to pay a $4 dividend until infinity. Assuming that the firm’s cost of capital is 10%, what is its share price? Answer: $4/.10 = $40 / share 2. Suppose that the expected dividend increases to $4.50 per share, how would this affect the stock price? Answer: $4.50/.10 = $45/share 3. A company has a cash flow for this year of $2 million and expects it to grow at a rate of 3% per year for 5 years and then 6% annually after that. If its cost of capital is 10 percent, what is its value? Answer: Year Cash Flow PV 0 $2,000,000 $2,000,000 1 $2,060,000 $1,872,727 2 $2,121,800 $1,753,554 3 $2,185,454 $1,641,964 4 $2,251,018 $1,537,475 5 $2,318,548 $1,439,636 6 Years + $38,150,350 PV of all Future Cash Flows $48,395,706 4. Assume a family takes out a $300,000 dollar 30-year fully-amortizing mortgage with annual payments on January 1, 2004 that is paid annually. What is the annual payments at the beginning of each year be if the interest rate is 6%? Answer: PV = (C/r)(1-(1/(1+r)t)) $300,000 = C/.06(1-(1/1.06)30) C = $21,794.67 5. What is the present value of a Lottery jackpot that pays out as $750,000 annual payments for the next 50 years? Assume the stated annual interest rate is 10%? Answer: PV = C/r(1-(1/(1+r)t)) PV = $750,000/.1(1-(1/1.1)50)
  12. 12. PV = $7,436,110.87 6. What would be the present value of future cash flows for an accountant who earns a starting (year 1) salary of $30,000 at the age of 21 and expects regular 3% salary increases until the retirement age of 65? Assume the discount rate to be 10%. Answer: PV = (C1/(r – g))(1 – ((1 + g)/(1 + r))t) PV = (30,000/.07)(1 - .936430) PV = $368,886
  13. 13. Appendix 8B Use the data below to answer the following four questions. Individual Returns State Stock A Stock B Bear 6.30% -3.70% Normal 10.50% 6.40% Bull 15.60% 25.30% 1. What are the individual means returns of Stock A and Stock B? Answer: Stock A Stock B Mean: 10.80% 9.33% 2. What are the variance and standard deviations for each of the stocks? Answer: Stock A Stock B Variance 0.002169 0.02167 STD DEV 0.046573 0.147208 3. What are the covariance and correlation between the returns of the two stocks? Answer: Covariance 0.004539 Correlation 0.993091
  14. 14. 4. Calculate the regressions if Stock B is the dependent variable. Answer: CovA,B /VarA 0.004539/.02167 = .21 Use the data in the table below to answer the following questions. Individual Returns State Probability Stock A Stock B Depression 10.00% -10.00% 5.00% Recession 20.00% -5.00% 0.00% Normal 50.00% 15.00% -2.00% Boom 20.00% 40.00% 15.00% 5. What are the individual mean returns of Stock A and Stock B? Answer: Stock A Stock B Mean 4.00% 1.80% 6. What are the variance and standard deviations for each of the stocks? Answer: Mean Dev Dev^2 Prob Prob Sq Dev -10.00% -14.00% 0.0196 10.00% 0.00196 -5.00% -9.00% 0.0081 20.00% 0.00162 15.00% 11.00% 0.0121 50.00% 0.00605 40.00% 36.00% 0.1296 20.00% 0.02592 Variance A 0.03555 Mean Dev Dev^2 Prob Prob Sq Dev 5.00% 3.20% 0.001024 10.00% 0.0001024 0.00% -1.80% 0.000324 20.00% 0.0000648 -2.00% -3.80% 0.001444 50.00% 0.000722 15.00% 13.20% 0.017424 20.00% 0.0034848 Variance B 0.004374
  15. 15. 7. What are the covariance and correlation between the returns of the two stocks? Answer: Stock A Stock B Mean Dev Mean Dev Prod DEV Prob Prob DEV -14.00% 3.20% (0.00448) 10.00% -0.00045 -9.00% -1.80% 0.00162 20.00% 0.000324 11.00% -3.80% (0.00418) 50.00% -0.00209 36.00% 13.20% 0.04752 20.00% 0.009504 Covariance 0.00729 Correlation = CovA,B / σA, σB = 0.00729 / (.035550.5 x .0043740.5) = 0.00729/(.18855 x .06614) = 0.5846

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