Suppose you are working for a large private venture capital fund that shares control with the owner-founder in Play&Learn, a privately held retailer of educational toys, which is expected to go public through an IPO in 5 years?

Due to unforeseen liquidity needs, the owner-founder is looking to sell his stake to the venture capital fund. You have been provided with the following information:

• Play&Learn generated an after-tax operating income of $30 million on revenues of $150 million in the most recent reporting year.

• The firm is all-equity financed. The owner-founder and the venture capital fund each own 50% of the equity. The book value of the equity (or invested capital) at the start of the most recent year was $100 million. The firm has no excess cash reserves.

• The unlevered beta for publicly traded firms in the sector is 1.2. The correlation of toy retailers with the market is 60% (i.e., the average R2 in the beta regressions for the industry equals 36%).

• The risk free rate is 3.5%, the corporate tax rate is 25% and the market risk premium is 5%.

With this information, please answer the following three questions:

(i) If you expect that the after-tax operating income will grow at a rate of 15% per year for the next 5 years and that the firm will maintain its current Return on Invested Capital, determine the expected Free Cash Flows for each of the next 5 years. Show all your calculations.?

(ii) Assuming that Play&Learn will remain all-equity financed when it goes public, and is then expected to generate an annual growth rate of 3% indefinitely with no change in its Return onInvested Capital, determine the value of Play&Learn to the venture capital fund. Show all your

calculations.?

(iii) Suppose that the venture capital fund applies an illiquidity discount of 10% to the value of the cash flows of private firms while they are private. Based on this information, what would be the maximum premium that the venture capital fund should be willing to pay for the owner-founder's

stake relative to the value of the stake to the owner-founder? Motivate your approach and show your calculations.?