1) Assume a VC firm raised $6B in committed capital for a 10-year investment fund. Each year, 2% of the committed capital will go to management fees, or 20% total. The remaining 80%, or $4.8B, will be invested in start-up firms. The firm also charges 20% carried interest on the profits of the fund. Assume the fund is worth $77.6B at the end of 10 years. What is the annual IRR based on the $6B initial investment? This is what the investors earned, after expenses. Note that you must take out the carried interest to find out the amount that goes to the investors. 2) A firm needs to raise $474.2 million in its IPO to fund its next investment project. The flotation costs (aka underwriting fees) are equal to 7%. How much does the firm need to raise so that they are left with the amount they need after flotation costs? 3)  Determine how many new shares of stock would need to be sold in an IPO with the following characteristics: Pre-IPO valuation: $2 billion Number of existing shares (pre-IPO): 50 million Flotation costs (aka "underwriter spread"): 7% of gross proceeds Percentage of post-IPO value of firm that new investors will own: 14.41%? 2)  You need to replace a machine in your business and you are evaluating a machine with a 5-year life. The machine costs $500,000 and will be depreciated $100,000 each year for the 5 years you own it. The main advantage of this machine is that it will save you $369,000 per year before taxes in operating expenses.  Assume no salvage value, and the purchase will have no impact on your net working capital (NWC). Your tax rate is 21% and your cost of capital for this purchase is 10% per year. What is the NPV of this machine?