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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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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