# Finance 2 Assignment 1 solution

Topics: Stock market, Corporate finance, Stock Pages: 9 (3245 words) Published: October 5, 2014
FINE 342: Investment Management
Fall 2014

VA
Assignment 1
Private Equity Issuance
1) Today is t = 0. Vapepsi is a private company that produces high end luxury diet soda. The company’s founder, Vadim, is seeking round 1 financing from 342VC, Montreal’s top Venture Capital firm. In order to begin small scale production (phase 1), Vapepsi needs to raise \$1M at t = 0. Phase 1 will last 2 years and there is a 70% chance phase 1 will be successful.

If phase 1 is successful, the company will proceed to phase 2a, which would require another round of equity financing of \$3M at t = 2. After phase 2a, the company has a 50% chance of being worth \$22M at t = 3 and a 50% chance of being worth \$6.6M at t = 3.

If phase 1 is not successful, the company will proceed to phase 2b, which would require another round of equity financing of \$2M at t = 2 to continue small scale production. After phase 2b, the company has a 50% chance of being worth \$6.6M at t = 3 and a 50% chance of being worth \$2.2M at t = 3. Note that Phase 2 financing will go through Sequoia Capital. Assume that the appropriate discount rate for all expected cash flows is 10%, based on the risk of the luxury diet soda sector.

a) What fractional ownership of Vapepsi will 342VC require in order to raise \$1M at t = 0? ૚=࢞

૟. ૟
૟. ૟
૛. ૛
૛૛
૙. ૠ ቀ૙. ૞ ቀ૚. ૚૙ቁ + ૙. ૞ ቀ૚. ૚૙ቁ − ૜ቁ + ૙. ૜ ቀ૙. ૞ ቀ૚. ૚૙ቁ + ૙. ૞ ቀ૚. ૚૙ቁ − ૛ቁ ૚. ૚૙૛

x = 15.92%
Note:
૛૛

૟.૟

ቂ૙. ૞ ቀ૚.૚૙ቁ + ૙. ૞ ቀ૚.૚૙ቁ − ૜ቃis the premoney value at t = 2 if phase 1 is successful ૟.૟

૛.૛

ቂ૙. ૞ ቀ૚.૚૙ቁ + ૙. ૞ ቀ૚.૚૙ቁ − ૛ቃis the premoney value at t = 2 if phase 1 is unsuccessful

b) What fractional ownership of Vapepsi would Sequoia Capital require to proceed with Phase 2a financing?

࢟૛ࢇ = ૛૜. ૙ૡ%

૜ = ࢟૛ࢇ ൤૙. ૞ ൬

૛૛
૟. ૟
൰ + ૙. ૞ ൬
൰൨
૚. ૚૙
૚. ૚૙

c) What fractional ownership of Vapepsi would Sequoia Capital require to proceed with Phase 2b financing? ૟. ૟
૛. ૛
૛ = ࢟૛࢈ ൤૙. ૞ ൬
൰ + ૙. ૞ ൬
൰൨
૚. ૚૙
૚. ૚૙
࢟૛࢈ = ૞૙%

d) Assume that at t = 0 there are 100 shares outstanding before the private equity issuance. How many shares will be issued at t = 0? (Fractional units are always OK.) ࡺ૚
૙. ૚૞ૢ૛ =
૚૙૙ + ࡺ૚
ࡺ૚ = 18.94
(although not asked here, the issue price is 1M/18.94 = 52,809.92) e) How many shares would be issued at t = 2 to fund Phase 2a? At what price?

ࡺ૛ࢇ = 35.68

૙. ૛૜૙ૡ =

ࡺ૛ࢇ
૚૚ૡ. ૢ૝ + ࡺ૛ࢇ

૜ࡹ

ࡼ૛ࢇ = ૜૞.૟ૡ = ૡ૝, ૙ૠૡ. ૢ૞
f) How many shares would be issued at t = 2 to fund Phase 2b? At what price?

ࡺ૛࢈ = 118.94

૙. ૞૙ =

ࡺ૛࢈
૚૚ૡ. ૢ૝ + ࡺ૛࢈

૛ࡹ

ࡼ૛࢈ = ૚૚ૡ.ૢ૝ = ૚૟, ૡ૚૞. ૠૢ
g) List the percentage ownership of the company for each owner at i) t = 0 before issuance
Founder owns 100%
ii) t = 0 after Phase 1 issuance until t = 2 before Phase 2 issuance 342VC owns 15.92%
Founder owns 84.08%
iii) t = 2 after Phase 2 issuance
case 2a:
Sequoia owns 23.08%
342VC owns 15.92%(1-0.2308) = 12.25%
Founder owns 84.08%(1-0.2308) = 64.67%
case 2b:
Sequoia owns 50%
342VC owns 15.92%(1-0.5) = 7.96%
Founder owns 84.08%(1-0.5) = 42.04%

h) What is the value of the entire company at t = 0 before issuance? 1M/15.92% - 1M = 5,280,992
i) What is the fair value per share at t = 0 before issuance? How does this compare to the t = 0 issue price? 5,280,992/100 = 52,809.92 (same as issue price (see part d))

IPO
2) Today is t = 0. After many years of wildly successful private ownership, Vapepsi is ready to go public. The company is seeking to raise \$50M in an IPO to expand operations internationally. There is a 50% chance the expansion will be very successful, in which case the company will be worth \$195M at t = 1. There is a 50% chance the expansion will be moderately successful, in which case the company will be worth \$135M at t = 1.

At t = 0 there are 1M shares outstanding. How many shares need to be issued, and at what price, in order to raise the required \$50M? Ignore any underwriting costs.
૞૙ࡹ =

૚૜૞
૚ૢ૞
൰ + ૙. ૞ ൬
൰൨...

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