Question

Stephens Inc. has a current value of $100,000 and is expected to be worth 140,000 in one year based on its current projects.  Stephens also has a potential new project with a cost of $100,000 and will return $125,000.  The appropriate discount rate for Stephens and the new project is 8% annually.  What is the NPV of the project?  Assume Stephens does not have the money to invest and must raise it by selling more equity.  However, potential outside investors mistakenly believe that in one year Stephens will be worth $110,000 without the project and $220,000 with the project.  How much equity (% of the firm) does Stephens need to sell outside investors (at the price they are willing to pay)?  Assuming Stephens sells the equity and engages in the project are existing shareholders better or worse off?

Answer 1

Net present value (NPV) is the difference between the present value of cash inflows and the present value of cash outflows over a period of time.

First we will calculate the present value of cash inflows at 125000 / (1.08) = 115740.74

Present value of outflow = 100,000

Net Present Value of the project = 115740.74 - 100,000 = 15,740.74

Since, the external investors are under the impression that the new project will constitute a 50% (110,000/220,000) of the firm in the next one year, theey will demand atleast 50% ownership equity to fund the said project.

However, in reality, the project is expected to be worth 125,000 in one year and total worth of firm is expected to be 140,000 + 125,000 = 265,000

Which comes out to 125,000/265,000 = 47.17%

Hence, if Stephens sells the equity and engages in the project, the existing shareholders will be worse off because where 47.17% equity should be sold, 50% would be sold and an excess of 50-47.17 = 2.83% ownership interest would need to be let go without any benefit which ultimately represents a loss to the existing shareholders.