Net Present Value and Internal Rate of Return for Actuaries
Master NPV and IRR calculations for capital budgeting on Exam FM.
Net Present Value
The net present value (NPV) of a project is the present value of all cash inflows minus the present value of all cash outflows, discounted at the required rate of return (cost of capital). NPV = sum of CF_t / (1+i)^t for t = 0, 1, ..., n. A positive NPV means the project adds value; a negative NPV means it destroys value. The decision rule: accept if NPV > 0.
Example: An investment costs $10,000 today and generates $3,000 per year for 5 years. At i = 8%, NPV = -10,000 + 3,000 * a-angle-5(0.08) = -10,000 + 3,000 * 3.9927 = $1,978. Accept the project.
Internal Rate of Return
The internal rate of return (IRR) is the discount rate that makes NPV = 0. It is the rate of return earned on the invested capital. The decision rule: accept if IRR > cost of capital. For the example above, solve -10,000 + 3,000 * a-angle-5(IRR) = 0, giving a-angle-5 = 3.333, so IRR is approximately 15.2%.
When cash flows change sign more than once, there may be multiple IRRs. In such cases, NPV is more reliable. On Exam FM, most problems have conventional cash flows (one sign change) where a unique IRR exists.
NPV vs. IRR
NPV and IRR usually agree on accept/reject decisions for independent projects with conventional cash flows. For mutually exclusive projects, they may conflict because IRR ignores the scale of investment. A large project with a lower IRR may have a higher NPV and should be preferred. Exam FM may present scenarios requiring you to choose between NPV and IRR criteria and explain the preference for NPV when they conflict.