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1. Implied Price of FundingStarware Software was founded last year to develop software for gaming applications. Initially, the founder invested $800,000 and received 8 million shares of stock. Starware now needs to raise a second round of capital, and it has identified an interested venture capitalist. This venture capitalist will invest $1 million and wants to own 20% of the company after the investment is completed.a. How many shares must the venture capitalist receive to end up with 20% of the company? What is the implied price per share of this funding round?Since the venture capitalist wants to own 20%, the founder’s 8 million shares must account for 80% of the company. Therefore the total number of shares after the investment is completed is:Total shares = 8,000,000 shares/80% = 10,000,000 sharesThus the company will issue 2 million shares to the new investor in exchange for $1 million. The implied price per share of this funding round is therefore:Implied price = $1,000,000/2,000,000 shares = $0.50/shareb. What will the value of the whole firm be after this investment (the post–money valuation)?Value = 10,000,000 shares * $0.50/share = $5,000,0002. IRR of Venture CapitalSuppose venture capital firm GSB partners raised $100 million of committed capital. Each year over the 10-year life of the fund, 2% of this committed capital will be used to pay GSB’s management fee.As is typical in the venture capital industry, GSB will only invest $80 million (committed capital less lifetime management fees). At the end of 10 years, the investments made by the fund are worth $400 million. GSB also charges 20% carried interest on the profits of the fund (net of management fees).a. Assuming the $80 million in invested capital is invested immediately and all proceeds were received at the end of 10 years, what is the IRR of the investments GSB partners made? That is, compute IRR ignoring all management fees.The IRR can be found using the formula to find the interest rate for an investment that pays a single cash flow:IRR=FVPV110-1IRR=$400,000,000$80,000,000110-1=17.46%b. Of course, as an investor or limited partner, you are more interested in your own IRR, that is, the IRR including all fees paid. Assuming that investors gave GSB partners the full $100 million up front, what is the IRR for GSB’s limited partners (that is, the IRR net of all fees paid)?The total profit is: $400,000,000 - $100,000,000 = $300,000,000GSB charges 20% carried interest on the profits of the fund: $300,000,000 * 20% = $60,000,000The cash flow to GSB’s limited partners is: $400,000,000 - $60,000,000 = $340,000,000Again, the IRR for GSB’s limited partners can be found using the formula to find the interest rate for an investment that pays a single cash flow:IRR=FVPV110-1IRR=$340,000,000$100,000,000110-1=13.02%3. IPOYour firm has 10 million shares outstanding, and you are about to issue 5 million new shares in an IPO. The IPO price has been set at $20 per share, and the underwriting spread is 7%. The IPO is a big success with investors, and the share price rises to $50 on the first day of trading.a. How much did your firm raise from the IPO?5,000,000 ×(20 – 7% ×20) = $93,000,000b. What is the market value of the firm after the IPO?15,000,000 ×50 = $750,000,000c. Assume that the post–IPO value of your firm is its fair market value. Suppose your firm could have issued shares directly to investors at their fair market values in a perfect market with no underwriting spread and no underpricing. What would the share price have been in this case, if you raise the same amount as in part (a)?Market value of firm assets absent new cash raised = 750 – 93 = $657 million. $657,000,000/(10,000,000 original shares) = $65.70 per share d. Comparing part (b) and part (c), what is the total cost to the firm’s original investors due to market imperfections from the IPO?($65.70 – $50.00) ×10,000,000 = $157,000,000 ................
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