Van Corp operates in a world with perfect capital markets. It has 100 shares outstanding worth $11 each, no debt, and a cost of capital of 10%. The firm will issue $600 in equity to pay the cost of a new project in its main line of business that generates an additional free cash flow of $50 per year forever.

Upon the announcement of the project, the firm’s stock price (with one decimal) is:

Question

Van Corp operates in a world with perfect capital markets. It has 100 shares outstanding worth $11 each, no debt, and a cost of capital of 10%. The firm will issue $600 in equity to pay the cost of a new project in its main line of business that generates an additional free cash flow of $50 per year forever.

Upon the announcement of the project, the firm’s stock price (with one decimal) is:

BlackTom AI · Accepted Answer

We start by understanding the scenario in a world of perfect capital markets. The firm currently has 100 shares outstanding worth $11 each, so the current total equity value is 100 × 11 = 1100, and there is no debt.

Next, the firm plans to undertake a project requiring $600 in new equity (i.e., it will issue new shares to raise $600) and the project yields a perpetuity of $50 per year in free cash flow.

Compute the value created by the project as an investment: the present value of a perpetual cash flow of $50 at a cost of capital of 10% is 50 / 0.10 = 500. This is the value that the project would add to the firm if it were financed in isolation.

However, the project costs $600 to finance, so the net present value (NPV) of the project is NPV = PV of FCF – cost = 500 – 600 = -100. In a world with perfect capital markets, financing decisions do not affect the overall value except through the project’s own NPV; hence the total firm value changes by -100 due to this project.

Therefore, the firm’s total value after the announcement should be initial value plus the NPV of the project: 1100 + (-100) = 1000.

Now, the firm issues $600 of new equity. Let s be the number of new shares issued, and p be the stock price after the announcement (which is the same price at which new shares are sold in an efficient market). The firm raises 600 by selling new shares, so s × p = 600.

After the issue, total shares outstanding become 100 + s, and the total equity value is 1000 (as established above). Therefore, the share price must satisfy p = total value / total shares = 1000 / (100 + s).

We now solve the two equations together:
- s × p = 600
- p = 1000 / (100 + s)
Substitute p into the first equation: s × [1000 / (100 + s)] = 600.
This yields 1000s = 600(100 + s) = 60000 + 600s, so 400s = 60000, giving s = 150.
Then p = 1000 / (100 + 150) = 1000 / 250 = 4.

Conclusion: upon the announcement, the stock price would be $4.0 per share. The reasoning shows how negative NPV projects reduce firm value and how the mechanics of a new equity issue interact with the updated firm value and share count to determine the post-announcement price.

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