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## Management Studies

 Management Theories Operation Management HR Management Project Management Business Management Operation Research Marketing Management Strategic Management Management Information System

PROBLEM SET

Note that for all problems you can use the spreadsheets distributed in class. However, you will need to document all the answers that you provide (diagrams, valuation formulas, etc.) – that is, you cannot solely rely on the spreadsheet to do the work for  you. You have to complete this problem set individually (not in groups). You cannot use any resources outside the class materials.

problem 1: Suppose that EBV is considering a \$5m Series A investment in Newco. EBV proposes to structure the investment as 5m shares of CP with FV of \$5m, one-to one conversion to common, and no dividends. EBV estimates the total valuation of Newco as \$30m. The founders of Newco, who will continue with the firm, currently hold 15m shares of common stock. Thus following the Series A investment, Newco will have 15m common shares outstanding, with another 5m shares upon conversion of the Series A. EBV has lifetime fees of 25% and carried interest of 20%.

a) Compute the LP cost for this investment

b) Compute the partial valuation of this investment

c) Divide this partial valuation into its two components: GP valuation and LP valuation

d) Should EBV make this investment?

e) Perform a sensitivity analysis of this investment recommendation

problem 2: Consider the following four CP investors:

Series A: \$5m FV (and 2X liquidation preference) or converts to 5m shares;
Series B: \$10m FV or converts to 8m shares;
Series C: \$10m FV or converts to 5m shares;
Series D: \$5m FV or converts to 10m shares.

In addition to these investors, the founders hold 10m shares of common. Assume 25% lifetime fees and 20% carry. Assume that the investment equals the face value in each round. Assume the total valuation is \$50m.

a) Find the conversion order for these investors

b) Find the conversion conditions for these investors

problem 3: EBV is considering a \$10m Series A investment in Newco. Three structures are under consideration:

Structure A1: RP (\$8m FV) + 10M shares of common;
Structure A2: CP (\$10m FV and 2X liquidation preference) converting to 10m shares of common;
Structure A3: RP (\$5m FV) + CP (\$5m FV). The CP can convert to 10m shares of common.
The founders of Newco, who will continue with the firm, currently hold 10m shares of common stock. EBV has lifetime fees of 25% and carried interest of 20%.

a) Find the formulas for the partial valuation, GP valuation, and LP valuation for all three structures (A1, A2, and A3). Show all your work, including expiration diagrams and any necessary calculations of conversion conditions and carried interest cutoffs.

b) What remaining information, if any, is necessary to make a choice between the three structures?
Assume that EBV chose structure A1. It is now one year later, and Talltree is considering a \$20m Series B investment in Newco. Two structures are under consideration:

Structure B1: CP (\$20m FV with 2X liquidation preference) converting to Z shares of common;
Structure B2: RP+CS (\$20m FV), with 10m shares of common.

The founders of Newco, who will continue with the firm, still hold 10m shares of common stock. Talltree has lifetime fees of 25% and carried interest of 20% and that, in the event of an exit or liquidation, the Series B investors are redeemed first, followed by
Series A.

c) Find the formulas for the partial valuation, GP valuation, and LP valuation for structures B1 and B2. How would you determine the level of Z for which Talltree is indifferent between the two structures. Show all your work, including expiration diagrams and any necessary calculations of conversion conditions and carried-interest cutoffs.

problem 4: Consider another company, Lateco, which has just received its fifth round  of investment. These rounds have been:

Series A: CP (\$5M FV) or converts to 5M shares of common.
Series B: CP (\$10M FV with 2X liquidation preference) or converts to 5M shares of common.
Series C: RP+CS (\$15M FV) with 5M shares of common.
Series D: CP (\$30M FV) or converts to 5M shares of common.
Series E: RP+CS (\$15M FV) with 5M shares of common.

The FV of each series is equal to the dollars invested in that Series. You can assume that all VC investors have a lifetime fee percentage of 25% and carried interest of 20%, and that, in the event of an exit or liquidation, the Series E investors are redeemed first, followed by Series D, then Series C, Series B, Series A. In addition to the VC investors, the founders of Lateco also have 5M shares of common.

a) Find the formula for the partial valuation of these founder shares following the Series E investment. Show all your work, including expiration diagrams and any necessary calculations of conversion conditions and carried-interest cutoffs.

b) Compute the LP valuation for the series A investors.

problem 5: Suppose that EBV makes a \$6m Series A investment in Newco for 1m shares at \$6 per share. One year later, Newco has fallen on hard times, and receives a \$6m Series B financing from Talltree for 6m shares at \$1 per share. The founders and the stock pool have claims on 3m shares of common stock.
Following the Series B investment, what percentage of Newco (fully diluted) would be controlled by EBV? Consider the following cases:

a) Series A has no anti-dilution protection

b) Series A has full-rachet anti-dilution protection

c) Series A has round-based weighted-average anti-dilution protection

d) Series A has percentage based anti-dilution protection in which the faction of the firm owned by EBV remains constant.

problem 6: Please comment on the following statement. True, False, or Uncertain: If an investor believes that the total valuation of a company is higher than the post- transaction valuation for the transaction, then he should invest.

problem 7: Talltree is considering a \$12m series B investment in Newco for CP with \$12m FV or converting to 5m shares of common. The other investors are the founders, who have 10m shares of common, and the Series A investors, EBV, who have CP with \$6m FV that can convert to 5m shares of common. In both of these structures, the Series B has a liquidation preference to the Series A. Both Talltree and EBV receive carried interest of 20% and charge management fees of 2 percent per year for all ten years. All the parties agree on an estimate of \$30m for the total valuation of Newco, and the expected holding period is four years.

a) After this round with Talltree, what are the pre- and post-money valuations for Newco?

b) What are the pre- and post-transactions valuations?

c) After this round by Talltree, what is the LP transaction valuation for the Series A investment made by EBV?

Management Theories, Management Studies

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