3. Very Often, it Does Not

3.1. Problem 1: Project Size

Example 4

Let's consider the following 3 mutually exclusive projects E, F, and G. Again, we assume a cost of capital of 10%.

 

Today Year 1 Year 2
Project E -10 5 8
Project F -1'000 500 800
Project G -10'000 5'000 8'000

   

According to the payback rule, all three projects are identical, because they return the investment within 2 years. The NPV rule does not quite agree… Because Project G is much larger, it also has a significantly larger NPV!

 

\(NPV_{E,10\%}=-10+\frac{5}{1.1}+\frac{8}{1.1^2}=1 \)

\(NPV_{F,10\%}=-1'000+\frac{500}{1.1}+\frac{800}{1.1^2}=116 \)

\(NPV_{G,10\%}=-10'000+\frac{5'000}{1.1}+\frac{8'000}{1.1^2}=1'157 \)

 

The NPV rule clearly prefers Project G, as it puts much more money to work in a value-enhancing way than project E. In contrast, the payback rule cannot make that distinction because it ignores the size of the cash flows! We have encountered the same problem already in the context of the IRR rule.

 

Therefore, whenever we are dealing with investment alternatives with different scales, payback and IRR are unreliable investment decision criteria!