FM for Actuaries

Rates of Return 129
Figure 4.4: NPV versus R R for project in Example 4.15
NPV
8% 15%
R R
−12
The above example shows that the NPV rule avoids the pitfalls of the IRR rule.
A potential pitfall of the NPV rule, however, is to conclude that if the NPV of a
project is positive for a discount rate R, the project is acceptable at any required
rate of return R R <R. Example 4.15 has demonstrated a counter-example.
Example 4.16: You are given two projects to invest. Project A requires an investment
of $1,000 at time 0. You will then receive $100 yearly in arrears for 18
years. Project B requires a capital of $1,200, and you will be paid $70 yearly in
arrears for 15 years, with the return of the capital at the end of the period. Discuss
the choice of the two projects.
Solution: The NPV of Project A is
NPV A = 100a 18⌉ i − 1,000.
Setting the above to zero, we solve for the IRR of Project A to obtain IRR A =