Venture Capital Method: Valuation Problem Set Solutions

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1 REV: OCTOBER 10, 2002 WALTER KUEMMERLE Venture Capital Method: Valuation Problem Set Solutions This note provides detailed solutions to questions 1 through 4 of the Venture Capital Method - Valuation Problem Set HBS Case No The note uses a Socratic approach to presenting the solutions, i.e. the note presents the initial question and subsequent intermediate questions that are intended to guide you towards the solution. The best way to work with these solutions is to quickly compare your own final answer to the answer at the end of each major question (1a, 1b, ). If your answer differs from the one presented here, you can go to the beginning of the solution and work through it step by step. Question 1 The first question to ask with any problem set is: What are the inputs? In this case, the inputs are: - $5 m new money from VC - Value of company in 5 years: 5 20 = $100 m a) Q: What is the rate of return required by the investor? $5 m (1.5) 5 = $37.97 m ~ 38.0% (of $100 m value of Bestafer, Inc.) $5 m (1.3) 5 = $18.56 m ~ 18.6% (of $100m value of Bestafer, Inc.) b) Answering this question requires consideration of eisting pool of shares and consideration of dilution of this pool. Let X be # of shares purchased by VC. (1) Q: How many shares will there be after the VC invests?! VC'sshare! 38% 1,000,000 shares " Solving for This case derives from an earlier case, Venture Capital Method: Valuation Problem Set Solutions, HBS No , prepared by Research Associate Andrew J. Janower under the supervision of Professor William Sahlman. This version was prepared by Professor Walter Kuemmerle. HBS cases are developed solely as the basis for class discussion. Cases are not intended to serve as endorsements, sources of primary data, or illustrations of effective or ineffective management. Copyright 2002 President and Fellows of Harvard College. To order copies or request permission to reproduce materials, call , write Harvard Business School Publishing, Boston, MA 02163, or go to No part of this publication may be reproduced, stored in a retrieval system, used in a spreadsheet, or transmitted in any form or by any means electronic, mechanical, photocopying, recording, or otherwise without the permission of Harvard Business School.

2 Venture Capital Method: Valuation Problem Set Solutions = 0.38 (1,000,000 shares + ) = ,000 shares 0.62 = 380,000 shares = 380,000 shares! 612,903shares 0.62 (2) Q: What price per share should the venture capitalist agree to pay? Assume: -no intermediate dividends -conversion to common stock at 1:1 $5,000,000! $8.16/share 612,903 shares (3) Bonus Question (This question was not asked in the Problem Set): What is the pre-money valuation of the firm? 1,000,000 shares $8.16/share = $8.16m Bonus question : What is the post-money valuation? General Answer: pre-money valuation + new money = post money valuation $8.16m = + $5 m = $13.16m c) Q: What if $12 m was raised in this round, how much would Roger need to give up? - $12 m raised - Required rate of return: 50 % - period: 5 years $12 m (1.5) 5 = $91.13 m Q: What is the value of the company in 5 years? It is still $100 m. - So how much does Roger need to give up? $91.13m $100m! 91.13% This eplains why Roger does not raise all the money in this round. He hopes he can raise some of the money at a higher valuation later as the company makes progress. Question 2 Q: How much of the company does management own at the end of year 5? 15%. This means the share ownership in year 5 will get diluted by 15% Q: What is the value of the company in year 5? Still $100 m (just like in Question 1). Q: So, how much of that value pie do investors own at the end of year 5? $100m-$15m = $85m So, Benedicta now needs to do her analysis based on a value in year 5 of $85m. 2

3 Venture Capital Method: Valuation Problem Set Solutions Q: How much does Benedicta hope to receive in year 5 on her $5m investment? $38 m Q: So, what share of the company does she need to own now? $38m $85m! 44.7% Q: So, how many shares does this translate into? 1,000,000! 44.7% " = 447, = 447, ,000!! ,318 shares Q: So, what is the price per share? $5,000,000! 808,318 $6.19/share Bonus Question: What is the pre-money valuation? $6.19 1,000,000 = $6.19 m Bonus Question: What is the post-money valuation? $ $5 m = $11.19 m Question 3 So, now we have to think about 2 rounds of financing at different valuations. A general approach for this type of problems is as follows:! Step 1: What $ amount and share of the terminal value do round 1 investors epect?! Step 2: What $ amount and share of the terminal value do round 2 investors epect?! Step 3: What share of the terminal value do round 1 investors epect given the dilution by round 2 investors? a) Q: Why would subsequent investors epect/accept a lower return? Because prospects of the company have (presumably) improved. Q: What is the value of the company to investors at the end of year 5? $85m ($15m goes to management) Q: What $ amount of the equity pie does Benedicta require at the end of year 5? $38m (same answer as in question 1 a.) That equals 38% after dilution by management. Q: How much is that before dilution by management? 3

4 Venture Capital Method: Valuation Problem Set Solutions 38% %! before dilution by management (same answer as question 2.) Q: What $ amount of the equity pie does the group of round 2 investors require? (Round 2 investors epect an annual 30% return on their $3m investment for a period of 3 years) $3m (1.3) 3 = $6.59 m. That equals 6.59% after dilution by management. Q: How much is that before dilution by management? 6.59%! 7.75% before dilution by management 0.85 Q: Now, what % of the $85m will stage 1 investors require given the dilution by round 2 investors? (Round 1 investors require 44.7% before management dilutes them (see above) and 44.7%! 48.5% 1# 7.75% before round 2 investors dilute them.) Q: So, how many shares do round 1 investors require?! " 48.5% 1,000,000 " = 485, ,000 =! 941, Q: What is the share price for round 1 investors? $5,000,000! 941,747 $5.30/share Bonus Question: What is the pre-money valuation for round 1? $5.30/share 1,000,000 = $5.3 m Bonus Question: What is the post-money valuation for round 1? $5.3 m $5 m = $10.3 m b) Q: So what # of shares do round 2 investors need to buy? (Remember they need 7.75% of the pie before dilution by management)? Q: How many shares are issued before round 2? 1,000, ,744 = 1,941,767 pre-round 1 issued in round 1 Q: So, how many shares need to be issued to round 2 investors to get to 7.75% ownership (pre-dilution by management)? 1,941,747 "! 7.75% 4

5 Venture Capital Method: Valuation Problem Set Solutions = 150, = 163,128 shares Q: At what share price do shares need to be issued in round 2? $3m 163,178 shares! $18.39/share Bonus Question: What is the pre-money valuation for round 2? 1,941,747 $18.39/share = $35.71 m Bonus Question: What is the post-money valuation for round 2? $35.7 m pre money + $3 m new money = $38.7 m c) Q: Suppose schedule slips 2 years. How do your answers to a) change? Remember: Benedicta has already invested $5 m for a share of 48.5% of company (before dilution by round 2 investors and management) " answer to a) would not change. Benedicta has already made the investment. Q: What would Benedicta s IRR be? Her cash flow: $85m 0.485= $41.2m $3m = $1.455m (her pro-rata share of investment to keep her ownership share constant) " her IRR: 33% (rather than 50% as epended) Note: Benedicta s IRR can be calculated with any standard financial calculator. Q: How do your answers to b) change? Round 2 investors know at the time of their investment that schedule will slip by two years, so they require a larger share than in the original scenario. What share do they require? $3 m (1.3) 5 = $11.14 m. So round 2 investors require 11.14% after dilution by management Q: How much do Round 2 investors require before dilution by management? 11.1%! 13.1% required by stage 2 investors before dilution by management Q: So how many shares do round 2 investors require? 1,941,747! 13.05% " = ,398 = 291,597 shares Q: What is the price per share for round 2? 5

6 Venture Capital Method: Valuation Problem Set Solutions $3m! 291,597 $10.29/share Bonus Question: What is the pre-money valuation of round 2? 1,941,747 shares $10.29/share = $19.9 m (Note: this is lower than the valuation if schedule had not slipped (see question 3b)) Bonus Question: What is the post-money valuation of round 2? $19.9 m $3 m = $22.9 m Question 4 This question is comparable to question 1 a) ecept for the fact that participating preferred stock is used. a) Q: What are the inputs? Investment = $5 m (principal will be repaid) Ownership = $38% Q: What is the terminal value? Terminal value: $100 m - $5 m (principal repaid to Benedicta) = $95 m Q: What is Benedicta s share of the terminal value? Benedicta s share of terminal value: 38% $95 m = $36.1 m Q: What is Benedicta s return (in $ terms) at the end of year 5? Return to Benedicta at the end of year 5: $5m + $36.1m = $41.1 m Q: So, how much of the company does Benedicta own at the end of year 5? Benedicta s de-facto claim on the company at the end of year 5: $41.1m! $100m 41.1% Q: So, what is Benedicta Benedicta s cash flow: " IRR = 53% (note: this is higher than the 50% annual return that Benedicta achieved in the scenario in Question 1) b) Q: What counter offer should Roger propose? If Roger agrees to use the participating preferred stock, he should make a counteroffer which accounts for the fact that Benedicta will receive $5 million first and then participate pro rata in the remaining value of the firm. Under the base-case ($100 m enterprise value - $5 m return of principal = $95 m equity value) this implies that Benedicta would meet her required return with a reduced equity stake. Q: What are the inputs? - Required rate of return: 50% - Horizon: 5 years 6

7 Venture Capital Method: Valuation Problem Set Solutions Q: What payback does Benedicta require in 5 years: 5 (1.5) 5 = 38 m Q: What is the nature of the payback? 1. $5 m cash (payback of principal) 2. $33 m in shares Q: What is the equity value in year 5: $100 m (enterprise value) - $5 m (debt) = $95 m Q: What share of the equity does this require? $33m! $95m 34.7% Q: What number of shares does Benedicta require? 1,000,000! 34.7% " solve for = 531,393 shares Q; What is the share price? $5 m 531,393 shares! $9.41/share " Roger should offer Benedicta 531,393 shares at $9.41/share. Q: What is the pre-money valuation? 1,000,000 shares $9.41 = $9.4 m Q: What is the post-money valuation? $9.41 m + $5 m = $14.41 m c) Q: How does the utilization of participating preferred affect risk and reward for Roger and Benedicta? Utilizing participating preferred enhances the return to the investor and shifts risk from the investor to the founders, particularly if the company is only modestly successful. The effective percentage of the company owned by Benedicta if she uses a participating preferred depends on the total terminal value of the company as illustrated below: Company Value To Investor To Founder $4MM 100% 0% 5 100% 0% 10 69% 31% 20 54% 47% 30 48% 52% 40 46% 54% 50 44% 56% %* 59% % 60% *Scenario under Question 4a. 7

When times are mysterious serious numbers are eager to please. Musician, Paul Simon, in the lyrics to his song When Numbers Get Serious

CASE: E-95 DATE: 03/14/01 (REV D 04/20/06) A NOTE ON VALUATION OF VENTURE CAPITAL DEALS When times are mysterious serious numbers are eager to please. Musician, Paul Simon, in the lyrics to his song When