Chap 7 Solutions

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Chapter 7 TYPES AND COSTS OF FINANCIAL CAPITAL DISCUSSION QUESTIONS AND ANSWERS 1. Describe how the costs of debt and equity differ from the perspective of accounting measures. While accountants recognize that financial capital has a cost and recommend its complete inclusion in performance appraisal and decision making, historical accounting for this cost is incomplete, at least in formal financial statements. Unlike debt, much of equity’s cost is not an expense in a traditional accounting sense (with documentation); only a part of this cost (e.g., dividends) is reflected in historical financial statements. There is virtually no historical accounting for the nondividend component of equity cost, even though it is clear that the nondividend cost component increases with cuts in dividends. 2. How do private and public financial markets differ? Private financial markets are those involving direct two-party negotiations over illiquid non-standardized contracts. Public financial markets are those where transactions involve more liquid securities with standardized contract features. 3. Briefly describe venture debt capital and venture equity capital. In general, early-stage ventures raise debt capital from individuals, venture lenders, and when profitably entering rapid-growth, possibly other financial institutions. The founding entrepreneurial team, business angels, and venture capitalists are the primary sources of early-stage equity capital. In some instances, debt and/or preferred stock convertible into shares of common equity is held by venture investors. 4. What is an interest rate? What is default risk? An interest rate is the rate one must pay to borrow capital. Default risk is risk that a borrower will not pay the interest and/or principal on a loan. 5. What is a nominal interest rate? Describe a risk-free interest rate and a real rate of interest. A nominal interest rate is stated rate of interest. The risk-free interest rate is interest rate for a debt security that is virtually free of default risk. A real rate of interest is rate of return adjusted for the expected inflation. 6. Define inflation. What is meant by an inflation premium?

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Inflation is the general rise in prices that is not due to increases in product quality. An inflation premium is the additional interest required due to the expectation of future inflation 7. Define the term default risk premium. Default risk premium is the additional premium required to compensate for the possibility of the firm’s defaulting on the loan. 8. What is meant by a prime rate? Prime rate: interest rate charged by banks to their highest quality (lowest default risk) business customers 9. What is a bond rating? Bond rating: reflects the default risk of a firm’s bonds as judged by a bond-rating agency 10. What is a liquidity risk premium? What is a maturity risk premium? Liquidity risk premium is the additional rate charged when a debt instrument cannot be sold quickly at a fair price. Maturity risk premium is charged for the inherent increased risk in long-term debt contracts. 11. What is meant by the term structure of interest rates? What is a yield curve? Term structure of interest rates: relationship between nominal interest rates and time to maturity when default risk is held constant Yield curve: graph of the term structure of interest rates 12. Describe the differences between senior debt and subordinated debt. Senior debt: debt secured by a venture’s assets Subordinated debt: debt with an inferior claim (relative to senior debt) to venture assets 13. Explain the meaning of investment risk of loss and describe how risk can be defined relative to an average value.

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Risk is the chance or probability of financial loss from a venture investment. More generally, investment risk is the chance that a security’s future value will differ from what it is expected to be. 14. Describe the following: (a) expected rate of return, (b) standard deviation, and (c) coefficient of variation. (a) Expected rate of return is the probability-weighted average of possible rates of return. (b) Standard deviation is a measure of the dispersion of possible outcomes around the expected return. (c) Coefficient of variation shows the dispersion risk per unit of expected rate of return. 15. Describe the historical average annual return relationships among long-term U.S. government bonds, corporate bonds, small firm common stocks, and large firm common stocks. Small firm common stocks have the highest average annual return followed by large firm common stocks. The third highest return is corporate bonds, and the lowest is long-term U.S. government bonds. 16. What is the difference between private equity investors and publicly traded stock investors? Private equity investors own firms that are typically closely held while investors in publicly traded stocks own firms whose shares trade in a public secondary market. 17. How does an organized securities exchange differ from an over-the-counter market? Organized securities exchanges have a specific place to trade while an over-the-counter market is a network of dealers connected via computer. 18. What is meant by an investment risk premium? What is a market risk premium? An investment risk premium is the additional return above the risk-free rate that investors can expect to earn by investing in a risky common stock. The market risk premium is the additional return above the risk free rate per unit of beta risk that a stock investor can expect. 19. What rates of returns have venture capitalists earned on average in recent years? How do these returns compare against the average venture capitalists returns over the past twenty years?

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During the last few years of the 20th century, VC returns were higher than ever before in history. Returns have been much lower since the “dot com” boom ended. As shown in Table 7.1, for the 20 year period ending during 2014, venture capital holding period returns (all stages) averaged 34.1 percent compared with 9.6 percent for the S&P 500 stock index. However, the 10-year average venture capital holding period return (all stages) was only 10.0 percent compared to 8.1 percent for the S&P 500. Recovery from the financial crisis of 2007-2008 and the great recession of 2008-2009 resulted in five-year venture capital holding period returns for all stages of 14.9 percent versus 15.7 percent for the S&P 500. 20. How do we estimate the cost of equity capital for private ventures? In developing your answer describe the major components that are considered when estimating the rates of return required by venture investors. Equity capital for private ventures is estimated by adding together the risk free rate, an inflation premium, an advisory premium, a liquidity premium, and a hubris projections premium. 21. What discount rates are typically used for development- stage, startup-stage, survivalstage, and early-growth-stage ventures? The discount rate for the development stage is typically above 40%, between 30% and 50% for the startup stage, between 25-45% for the survival stage, and between 25-35% for the early growth-stage. 22. What is meant by the weighted average cost of capital or WACC? Weighted average cost of capital (WACC): weighted average of the cost of the individual components of interest-bearing debt and common equity capital. 23. How is a venture’s WACC likely to change as it moves through a successful life cycle? Most early-stage financing is high-cost equity capital. However, the opportunity to use usually less-costly debt increases as a successful venture progresses through its life cycle. Thus, the WACC is likely to decrease over time for a successful venture. 24. From the Headlines—Ecosphere: You have been retained as a consultant for Ecosphere and tasked with assessing the financial viability of their commercial ventures. What types of  financial ratios would you enlist in your report to Ecosphere? What approach would you  take to determining a relevant cost of capital for those ventures? Answers will vary: Ecosphere has a great deal of variety in the types of products and services it targets. As it grows from tourism and handicrafts toward biofuels and other more capital-intensive operations, it would be beneficial to monitor its inventory turns and

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other operating efficiencies (particularly in its existing handicrafts operations) while taking some notice of trends in overall asset efficiency (as it adds property, plant and equipment) for newer operations (biofuels, etc.). Profit margins should be monitored (overall and line item) as it expands into new areas.

EXERCISES/PROBLEMS AND ANSWERS 1. [Inflation and Risk Premiums] Voice River, Inc. provides media-on-demand services via the Internet. Management has been studying current interest rates. A lender is willing to make a two-year loan to Voice River at a 12 percent annual interest rate. The U.S. government is currently paying 8 percent annual interest on its two-year securities. A.

If the real rate of interest is expected to be 3 percent annually, what is the inflation premium expected at this time? Risk free rate = real rate + inflation premium Inflation premium = risk free rate – real rate = 8% - 3% = 5%

B.

What is the amount of the total risk premium that Voice River will have to pay? Risk premium = nominal interest rate – risk free interest rate = 12% - 8% = 4%

C.

If a 1 percent liquidity premium is built into the 12 percent rate, what is the default risk premium on the loan? Risk premium = liquidity premium + default risk premium Default risk premium = risk premium – liquidity premium = 4% – 1% = 3%

2. [Maturity and Default Risk Premiums] Following is interest rate information currently being observed by the Electronic Publishing Corporation. One-year U.S. government securities One-year bank loans Five-year U.S. government securities Five-year bank loans

4.5% 6.0 7.0 9.5

A. What is the amount of the maturity risk premium on one-year versus five-year U.S. government securities? 7% - 4.5% = 3.5%

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B. What is the amount of the maturity risk premium on one-year versus five-year bank loans? 9.5% - 6% = 3.5% C. What is the default risk premium on one-year bank loans and on five-year bank loans? 1 Year; 6% - 4.5% = 1.5% 5 Year; 9.5% - 7% = 2.5% 3. [Expected Rate of Return and Risk Measures] A venture investor, BKAngel, is considering investing in a software venture opportunity. However, the rate of return to be realized next year is likely to vary with the economic climate that actually occurs. Following are three possible economic outcomes, the probability that each one will occur, and the rate of return projected for each outcome: Economic Climate Recession Normal Rapid Growth A.

Probability of Occurrence .25 .50 .25

Rate of Return -20.0% 15.0 30.0

What is the expected rate of return on the software venture? Expected rate of return = (.25) x (-20%) + (.50) x (15%) + (.25) x (30%) = 10%

B.

Calculate the variance and standard deviation of the rates of return for the software venture? Variance = (.25) x (-20% - 10%)^2 + (.5) x (15% - 10%)^2 +(.25) x (30% - 10%)^2 = 337.5 Standard deviation = (Variance)^(1/2) = (337.5)^(1/2) = 18.37%

C.

Calculate the coefficient of variation of the rates of return for the software venture. If the coefficient of variation of rates of return for BKAngel’s prior venture investments is 1.5, would the software venture be considered as being less or more risky? Coefficient of variation = (standard deviation)/(expected return) = (18.37%)/(10%) = 1.837. The coefficient of variation for this venture would be considered to be more risky since it is above 1.5.

4. [Expected Rate of Return and Risk Measures] A potential venture investment has the following possible outcomes: Performance Rate of

Probability

of

Chapter 7: Types and Costs of Financial Capital Outcome Return Home Run (Success) 500.0% Breakeven 15.0 Strikeout (Failure)

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Occurrence .15 .35 .50

-100.0

A. What is the expected rate of return on the venture? Expected rate of return = (.15)(500.0%) + (.35)(15.0%) + (.50)(-100.0%) = 75% + 5.25% + (-50%) = 30.25% B. Calculate the variance and standard deviation of the rates of return for the venture. Variance = (.15) x (500% - 30.25%)^2 + (.35) x (15% - 30.25%)^2 + (.50) x (-100% 30.25%)^2 = .15 x 220,665.06 + .35 x 232.56 + .50 x 16,965.06 = 33,099.76 + 81.41 + 8,482.53 = 41,663.69 Standard deviation = (Variance)^(1/2) = (41,663.69)^(1/2) = 204.12% C. Calculate the coefficient of variation of the rates of return for the venture. If the coefficient of variation of rates of return for your prior venture investments is 4.0, would the new venture be considered as being less or more risky? Coefficient of variation = (standard deviation)/(expected return) = (204.12%)/(30.25%) = 6.748. The coefficient of variation for this new venture would be considered to be more risky relative to prior venture investments since it is above 4.0. 7. [Loan Present Values] Jerry’s Tree Services is trying to raise debt funds from a prospective venture investors, SureWay LLC. SureWay indicated to Jerry Lau that the annual interest rate on risky venture loans is currently 15 percent. Jerry is seeking a 3-year loan with annual payments. He is willing to pay back $100,000 at the end of 3 years. However, due to cash flow problems, he can afford to pay interest at a 12 percent annual rate. A. Calculate the dollar amount that SureWay venture investors would lend to Jerry’s Tree Services. N=3 I%/Yr = 15% PMT = $12,000 FV = $100,000 PV = ? = $93,150.32 B.

What would be the dollar amount of the loan if the loan was made for only two years?

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N=2 I%/Yr = 15% PMT = $12,000 FV = $100,000 PV = ? = $95,122.87 8. [Loan Present Values] Refer to Problem 7. Show how your answer to Part A of Problem 7 would change if Jerry were willing to pay 16 percent annual interest and a principal payment of $100,000 at the end of three years. N=3 I%/Yr = 16% PMT = $16,000 FV = $100,000 PV = ? = $100,000 9. [Expected Rate of Return and Hubris Premiums] Following is rate of return component information for FirstVenture investors. Rate Return Component Component Liquidity premium 5.5% Risk-free rate 6 Advisory premium 9 Investment risk premium 11.5 Target rate of return 40 A. Calculate the expected rate of return before considering premiums for illiquidity, advisory activities, and hubris projections. Expected rate of return = 6% + 11.5% = 17.5% B. Estimate the hubris projections premium for this FirstVenture investment. Hubris projections premium = 40.0% - 17.5% - 5.5% - 9.0% = 8.0%