Prada has 10 million shares outstanding, generates free cash flows of $50 million each year and has a cost of capital of 10%. It also has $50 million of cash on hand. Prada wants to decide whether to repurchase shares or invest the cash in a project that generates free cash flows of $5 million each year. Should Prada invest or repurchase the shares?

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BlackTom AI · Accepted Answer

To analyze Prada's choice, we first lay out the numbers: Prada has 50 million in cash and a project that, if undertaken, would generate 5 million in free cash flow every year. The company’s hurdle rate (cost of capital) is 10%.

Consider investing the cash in the project: If the project yields a perpetual 5 million per year, its value today (present value) at a 10% discount rate is 5,000,000 / 0.10 = 50,000,000. This means the project has a net present value (NPV) of +50,000,000 minus the 50,000,000 cash outlay, which is 0. In other words, the project’s value equals the cash it costs, so it’s a break-even, zero-NPV opportunity.

Now consider repurchasing shares: using the 50 million cash to repurchase shares reduces the number of shares outstanding. If nothing else changes (e.g., the stock price reflects this cash return appropriately and there are no taxes or transaction costs), the total firm value remains the same, but value is distributed to shareholders as higher per-share value. The absence of a positive NPV from the project suggests there is no additional value created by tying up cash in the project.

Putting these perspectives together: since the perpetuity project offers exactly a 50 million PV at the 10% cost of capital, its NPV is zero, meaning it does not add value relative to returning cash to shareholders. Therefore, neither option creates additional value beyond what returning cash would accomplish. In this sense, Prada should be indifferent between investing and repurchasing from a pure NPV standpoint.

One might wonder about other considerations (risk, flexibility, signaling effects), but with the information given and under standard NPV logic, there is no clear value advantage to either choice. Hence, the conclusion is that Prada is indifferent between the two options.

Option-by-option check:
- a. invest: This would lock up 50 million in a project with perpetual 5 million annual cash flow, which has zero NPV at 10%—not adding value relative to simply returning the cash. 
- b. repurchase: Returning the cash via buyback transfers value to shareholders and typically increases per-share value; with zero NPV from the project, this is not worse than investing.
- c. indifferent between options: Correct, since the project’s PV equals the cash outlay, yielding zero incremental value versus returning cash.
- d. cannot say for sure: Not supported, given the perpetual cash-flow assumption and discount rate provided yield a clear NPV of zero for the project, allowing a definite comparison.

FINS2615-Intermediate Business Finance - T2 2025

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