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Chapter 11VENTURE CAPITAL VALUATION METHODSEXERCISES/PROBLEMS AND ANSWERS[Discount Rates] Calculate the discount rate consistent with a cap rate of 12% and a growth rate of 6%.   Show how your answer would change if the cap rate dropped to 10 percent while the growth rate declined to 5 percent.Cap Rate = (r – g), so r = Cap Rate + gr = 12% + 6% = 18%r = 10% + 5% = 15%2.   [Venture Present Values] A venture investor wants to estimate the value of a venture.  The venture is not expected to produce any free cash flows until the end of year 6 when the cash flow is estimated at \$2,000,000 and is expected to grow at a 7 percent annual rate per year into the future.      A.  Estimate the terminal value of the venture at the end of year 5 if the discount rate at that time is 20 percent.\$2,000,000/(.20 – .07) = \$15,384,615.38 B.  Determine the present value of the venture at the end of year 0 if the venture investor wants a 40 percent annual rate of return on the investment.                          \$15,384,615.38/1.405 = \$2,860,529.723.   [Venture Capital Valuation Method] A venture capitalist wants to estimate the value of a new venture.  The venture is not expected to produce net income or earnings until the end of year 5 when the net income is estimated at \$1,600,000.  A publicly-traded competitor or “comparable firm” has current earnings of \$1,000,000 and a market capitalization value of \$10,000,000.A.  Estimate the value of the new venture at the end of year 5.  Show your answer   using both the direct comparison method and the direct capitalization method.  What assumption are you making when using the current price-to-earning relationship for the comparable firm?                        P/E of comparable firm = \$10,000,000/\$1,000,000 = 10 times                        New Venture Value:  \$1,600,000 net income times 10 = \$16,000,000                Assumptions:            1. The “comparable firm” is really comparable to the new venture.              2. The current price-to-earning relationship of 10 will still be the appropriate multiple to use 5 years from now.                B.  Estimate the present value of the venture at the end of year 0 if the venture capitalist wants a 40 percent annual rate of return on the investment.            \$16,000,000/1.405 = \$2,974,950.914.   [Multiple Financing Rounds] Ratchets.com anticipates that it will need \$15,000,000 in venture capital to achieve a terminal value of \$300,000,000 in five years.

Assuming it is a seed stage firm with no existing investors, what annualized return is embedded in their anticipation?r = (300,000,000/15,000,000)^(1/5)-1 = 82.0564%Suppose the founder wants to have a venture investor inject \$15,000,000 in three rounds of \$5,000,000 at time 0, 1 and 2 with time 5 exit value of \$300,000,000.  If the founder anticipates returns of 70%, 50% and 30% for round 1, 2 and 3, respectively, what percent of ownership is sold during the first round? During the second round? During the third round?  What is the founders’ year-five ownership percentage?First Round FV: 5,000,000 x (1.7)^5 = 70,992,850Second Round FV: 5,000,000 x (1.5)^4 = 25,312,500Third Round FV: = 5,000,000 x (1.3)^3 = 10,985,000Total FV = 107,290,350First Round % of Total FV = 23.66% = 70,992,850/300,000,000Second Round % of Total FV = 8.44% = 25,312,500/300,000,000Third Round % of Total FV = 3.66% = 10,985,000/300,000,000)Founder final ownership = 1 – 23.66% – 8.44% – 3.66% = 64.24%  = 192,709,650/300,000,000Assuming the founder will have 10,000 shares, how many shares will be issued in rounds 1, 2 and 3 (at times 0, 1 and 2)?Founder shares = 10,000Total shares at year 5: =10,000 / .6424 = 15,567Round one shares = .2366 x 15,567 = 3684Round two shares = .0844 x 15,567 = 1313Round three shares = .0366 x 15,567 = 570What is the second round share price derived from the answers in Parts B and C?Second Round Price = 5,000,000 / 1313 =3808/shareHow does the answer to part D change if 10% of the year-five firm is set aside for incentive compensation?  How many total shares are outstanding (including incentive shares) by year 5?Founder final ownership = 1 -23.66% – 8.44% – 3.66% -10% = 54.24%Total shares at year 5 = 10,000 / .54.24 = 18,438Round two shares = .0844 x 18,438 = 1556 Round two price = 5,000,000 / 1556 = 3213/share5.  [Rates of Return] Suppose a venture fund wishes to base its required return (used in discounting future terminal values) on its historical experience and suggests merely averaging the rates on the last three concluded deals.  These deals realized total returns of –67% at the end of 2 years, 50% at the end of 5 years and 70% at the end of three years, respectively.  Assuming no intermediate flows before the terminal payoff, verify that the associated annualized rates are –42.55%, 8.45% and 19.35%.  2 years: (1-.67)^.5 – 1 = -42.55%5 years: (1+.50)^.2 -1 = 8.45%3 years: (1+.7)^(1/3) -1 = 19.35%What is the equally weighted average annualized return?  (-42.55% + 8.45% +19.35%) / 3 = -4.92%Does it make sense to use this as a single discount rate to apply across scenarios involving different durations?The returns have been realized over a total of 10 investment years.  However, the simple average here is only dividing by the three outcomes (not their years).  Consequently, it is open for debate whether this simple project averaging is the best way to calibrate a required return for projects of widely varying known durations.  However, at the time the venture is funded, it is not known what the duration will be and if it is like a small replication of all of the previous funded ventures, it is reasonable to use the hybrid discount rate for all of the venture’s possible outcomes.