Reading: Net Present Value (NPV)

Example 6

You can invest in the following projects:

• Project A: NPV of 500
• Project B: NPV of 300
• Project C: NPV of 100
• Project D: NPV of -100

1. Which project(s) do you choose if they are mutually non-exclusive (that is, the projects are independent from each other and investing in one project does not from precluding in others)?
    
   If the projects are mutually non-exclusive, the NPV rule states that we should take all projects that have a positive NPV. In our case, this means that we should invest in projects A, B, and C. The total value-added of these three projects is 900:
    
   Total NPV = NPV_A + NPV_B + NPV_C = 500 + 300 + 100 = 900
    
   
2. Which project(s) should you choose if they are mutually exclusive (that is, you can only take one)?
    
   In the projects are mutually exclusive, the NPV rule states that we should go with the project that has the highest NPV. That is project A. Projects B and C are also good projects, but they are less good than A.
     

Example 7

A company has the following investment opportunities:

• Project A: NPV of -5'000
• Project B: NPV of -12'000
• Project C: NPV of -25'000

1. Which projects should the firm invest in?
     
   The firm should NOT invest in any of the three projects, as they all destroy value. The firm is better off putting its money in the alternative asset, which, by definition, has a NPV of 0. Alternatively, the firm can return the money to its investors.
    
2. What if the firm has to take one of the projects, for example, because the projects reflect three alternatives to cope with a new regulation?
    
   If the firm has to take one of the projects, it should go with the project that destroys the least amount of value. That is project A. 

Example 8

Your company can invest up to $20 million and face the following mutually non-exclusive investment opportunities (cash flows in millions):

What should your company do if the cost of capital (R) is 10%?
 

To find an answer, we can compute the NPVs of the three projects:
 

\( NPV_A = -20 + \frac{60}{1.1} + \frac{10}{1.1^2} = 42.8 \)

\( NPV_B = -10 + \frac{10}{1.1} + \frac{40}{1.1^2} = 32.1 \)

\( NPV_C = -10 + \frac{15}{1.1} + \frac{30}{1.1^2} = 28.4 \)

The numbers imply that project A has the highest NPV of $42.8 million. The standard NPV rule therefore suggests that we should go with project A and thereby fully exhaust the investment budget of $20 million.

However, a closer inspection of the numbers reveals that this might not be the smartest strategy. Instead of investing in A, the company could invest in B and C, as these projects require much smaller initial investments. If the firm opts for B and C instead, the total NPV is $60.5 million:
 

\( \text{Total NPV}_{\text{B and C}} = NPV_B + NPV_C = 32.1 + 28.4 = 60.5 \)

Consequently, the most profitable way to spend the budget of $20 million is to invest in projects B and C, as this project combination generates the highest total payoff.

Example 9

To comply with new emissions regulations, a company has to upgrade the air filter system in one of its factories. There are three ways to do this. All three ways have the same effect.

• Alternative A: A single investment of EUR 1 million today
• Alternative B: An investment of EUR 0.5 million today and 0.6 million in 2 years.
• Alternative C: An investment of EUR 0.3 million today. The same amount will also be invested in 1, 2, and 3 years.
   

Which alternative should the firm choose if the cost of capital is 10%?

To find out, we can compute the NPVs of the three alternatives:

\( NPV_A = -1'000'000 \)

\( NPV_B = -500'000 -\frac{600'000}{1.1^2} = -995'868 \)

\( NPV_C = -300'000 - \frac{300'000}{1.1}-\frac{300'000}{1.1^2}-\frac{300'000}{1.1^3} = -1'046'056 \)

Based on the available information, the cheapest way to comply with the new regulation is alternative B. That alternative costs a bit less than alternative A.

Example 10

A firm considers investing in a project that promises the following cash flows (in thousands of GBP). The cost of capital is 8%.

Should the firm invest?

The NPV of the project is GBP 32'150. Therefore, the firm should invest:

\( NPV = -1'500 + \frac{300}{1.08}+ \frac{400}{1.08^2}+ \frac{500}{1.08^3}+ \frac{700}{1.08^4}= 32.15 \)

As the cash flow streams get longer, the manual computation of NPVs becomes increasingly cumbersome. It is therefore advisable to switch to a spreadsheet program such as Microsoft Excel to do the work. In fact, Excel has a built-in function "NPV" that allows you to quickly compute the NPV of a given cash flow stream. In the section Present Values, we take a close look at this powerful Excel function and provide a set of useful implementation tips.