Reading: Foundations of NPV Rule

A quick computation of the project's NPV shows that it a good project. With an investment of $20 million today and a payout of $25 million in one year, the resulting NPV is $2.73 million, assuming a cost of capital of 10%:

\( \text{Project NPV}= -C_0 + \frac{C_1}{1+R} = -20 + \frac{25}{1.1} = -20 + 22.73 = 2.73 \)

While it is easy to see that it is a good project, which will find the support of the shareholders with a long-term investment horizon (Trisha, in our example), it is not quite obvious yet how and why it can benefit shareholders with short-term liquidity needs (uncle Fred, in our example). To see this more clearly, remember from our discussion of the (net) present value what this concept actually means:

• The present value indicates how much investors are willing to pay today in a well-functioning capital market in exchange for a future expected cash flow.
   
• In such a well-functioning capital market, where investors can borrow and invest at the cost of capital of 10%, investors should be willing to pay up to $22.73 million for the project in question, since this is how much money they would have to invest in the alternative asset to obtain the same future cash flow of $25 million in one year at the same risk. At a price of $22.73 million, investors are just indifferent between investing in the project and investing in the alternative asset, as both alternatives promise the same future payout at the same risk.

If investors agree on the NPV of the project (2.73 million) and if investors have equal access to well-functioning capital markets, they should therefore agree that the current value of the company with the project is $22.73 million. With 100'000 shares outstanding, as per our assumptions, the value of one share should therefore be $227.3.

Our considerations so far have therefore ignored one very important alternative: Investors can buy and sell shares to accommodate their consumption preferences!

• Instead of urging the CEO to withhold investment and return the money to the shareholders, uncle Fred could simply sell some or all of his shares to other investors (or he could borrow against his shares)!
   
• By not interfering with the firm's investment policy, uncle Fred is better off. The CEO can now follow the NPV rule and implement the project. This allows uncle Fred to sell shares at a price of $227.3 per share (see above) instead of $200 per share without the project [= 20 million / 100'000 shares]. 
   
• Alternatively, uncle Fred could borrow $227.3 per share today at a rate of 10% and offer the company's shares as collateral. This allows him to maximize consumption today. In one year, he can then use the proceeds of the investment project of $250 per share [= 25 million / 100'000 shares] and repay his debt [227.3 × 1.1 = 250].

The red line in the following graph summarizes the new trade-off between consumption today and consumption in 1 year if we assume well-functioning capital markets:

These considerations have fundamentally important implications:

• Financial managers should focus on the NPV rule. In doing so, they create extra wealth for the investors and shift the line in the graph above to the right. 
• Financial mangers should not be too concerned about the consumption preferences of the investors. This is what well-functioning capital markets are here for. By buying or selling shares, investors can choose the optimal mix between current and future consumption that maximizes their own utility. Managers should therefore focus on finding and implementing projects with positive NPV.
• Consequently, even with different consumption preference, investors should be able to agree on the firm's appropriate investment policy: Maximize NPV!