Corporate Finance, Module 14: “The Capital Markets”

Homework Assignment

(The attached PDF file has better formatting.)


Jonathan is a consulting actuary who has developed an enterprise risk management (ERM) application that he intends to market to insurance companies. On January 1, 20X2, he invests $100,000 of his own money to develop the application. On January 1, 20X5, he sets up a firm to raise more financing and market the product.

His firm raises $1 million at first-stage financing on July 1, 20X5, from venture capitalists, and a $1.25 million first-stage after-the-money valuation is placed on the firm. The venture capitalists contribute $1 million of the $1.25 million value of the firm, so they receive 80% of the stock of the firm.

The firm succeeds. When additional funds are needed three years later (July 1, 20X8), other venture capitalists contribute $2 million in second-stage financing and the firm is now valued at $4 million. The new venture capitalists contribute half the new value of the firm, so they receive half the new firm’s stock.

A.    What is Jonathan’s (paper) return from original investment to first-stage financing?
B.    What is Jonathan’s (paper) return from first-stage financing to second-stage financing?
C.    What is Jonathan’s (paper) wealth at second-stage financing?

Jacob: How do we determine the value of the firm at first-stage financing and second-stage financing?

Answer: The venture capitalists get a certain percentage of the firm’s stock.

●    At first-stage financing, the venture capitalists contribute $1 million and get 80% of the firm’s stock. The implicit value of the firm is $1 million / 80% = $1.25 million.
●    At second-stage financing, the venture capitalists contribute $2 million and get 50% of the firm’s stock. The implicit value of the firm is $2 million / 50% = $4.00 million.

Question: How do the venture capitalists get 50% of the firm’s stock at second-stage financing? Do Jonathan and the first venture capitalists each sell a certain amount of stock?

Answer: Suppose Jonathan and the first venture capitalists agreed on 1 million shares of stock at first-stage financing. Each share of stock is worth (on paper) $1.25. Jonathan gets 200,000 shares and the venture capitalists get 800,000 shares. At second-stage financing, the firm issues another 1 million share of stock, which are given to the second venture capitalists in exchange for $2 million.

Question: How do we evaluate Jonathan’s (paper) wealth right after first-stage financing and second-stage financing?

Answer: At first-stage financing, Jonathan has 20% of the firm’s stock, so his (paper) wealth is 20% of the firm’s value, or $250,000. At second-stage financing, he has 200,000 of a total 2 million shares, so his portion is 10% of $4 million = $400,000.

Question: Why are these paper returns and paper wealth?

Answer: Until the firm is publicly traded, Jonathan can not exchange his stock for cash.

What is the formula for computing the return?  I cannot find a formular for "paper return."  Can one define what paper wealth is? Can one layout how they solved this problem? I am really confused.

[NEAS: The stock is not publicly traded, so Jonathan can not cash in his shares. His wealth and his return are on paper. If the value of the firm declines, his wealth declines as well, and he has no way to turn it into cash before it declines (unless he finds someone who wants to buy his firm.]

There are two ways to think of this, one as % of ownership and the other as shares of stock. I think % of ownership is easier, so here I go:

January 1, 20X2: Jonathan contributes $100,000, owns 100%
July 1, 20X5: Venture Capatalist A contributes $1M, valued at 80% of company. So, Jonathan owns the remaing 20%, which is .2(1.25M) = $250,000
July 1, 20X8: Venture Capatalist B contributes $2M, valued at 50% of company. So, Venture Capatalist A now owns (.8)(.5) = 40% of the company = $1.6M, and Jonathan now owns (.2)(.5) = 10% of the company = $400,000.

Part A: if X is total return, 100,000(1+X) = 250,000, so X = 150% total return. Or, if you want an annualized return, 100,000(1+X)^3.5 = 250,000, so X = 29.93%. (The problem is very unclear whether we're looking for total return or annual return).
Part B: 250,000(1+X) = 400,000, so X = 60% total return, or 250,000(1+X)^3 = 400,000, so X = 16.96% annualized return

Now for the other method, thinking in shares of stock:
January 1, 20X2: Jonathan buys 100,000 shares of stock for $1 each
July 1, 20X5: Venture Capatalist A buys 400,000 shares of stock for $2.50 each (Jonathan's stock is now worth $250,000)
July 1, 20X8: Venture Capatalist B buys 500,000 shares of stock for $4.00 each (Jonathan's stock is now worth $400,000)

In the stock example, different share amounts/prices could be substituted so long as the ratios remain intact.

Hope that clears the air for anyone confused - feel free to disagree.

[NEAS: Correct]

For Part C, please correct me if I'm wrong...
I do not understand what is the meaning of paper wealth, thus for this part,
I interpret the result based on the findings from Part B

Paper wealth at the 2nd stage financing = 10%* $4M = $400,000

Is this correct? Thank you for answering my doubt.

What is meant by the term paper wealth? i have searched through he textbook and on the internet but I can't find a concrete definition (internet sources say it could relate to Market Value or Book Value).

[NEAS: If an asset is marketable, it can be converted into cash. If an asset is not marketable, it just has a book value, or a paper value.]