# Finance 2 Assignment 1 solution

Fall 2014

Vadim di Pietro

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?

= . ૡ%

= . 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.)

. ૢ =

+

= 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?

= 35.68

. ૡ =

ૡ. ૢ +

= .ૡ = ૡ, ૠૡ. ૢ

f) How many shares would be issued at t = 2 to fund Phase 2b? At what price?

= 118.94

. =

ૡ. ૢ +

= 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.

=

ૢ

൰ + . ൬

൰൨...

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