Financial Markets

• Laurent Calvet calvet@hec.fr • John Lewis john.lewis04@imperial.ac.uk

Topic 4:

The Internal Rate of Return

HEC – MBA Financial Markets

4-1

IRR Definition
• IRR = The discounting rate that makes the Net Present Value (NPV) equal to zero • IRR is also called the Yield to Maturity • YTM used for securities • IRR used for capital expenditures, Venture Capital and Private Equity.

HEC – MBA Financial Markets

4-2

IRR
• IRR is calculated using the same formula as the NPV except that the rate r is unknown:

Fn ∑ (1 + r ) n =V 0 n =1
Where V0 is the initial investment in the project • The IRR is the rate r where the market value is equal to the present value of the future cash flows from the investment.

N

HEC – MBA Financial Markets

4-3

Computing IRR
• The solution to the IRR formula is found through trial and error • Use a calculator or spreadsheet • Timing of cash flows is very important to calculation • Accurate models very carefully model the cash flows • Implementation shortfall arrives in an optimistic model of cash flows and the reality of actual magnitude and timing

HEC – MBA Financial Markets

4-4

IRR as an Investment Rule
• Many companies have a target return on investment – either through policy or historical results. • In the NPV example, a project was started if the NPV was positive. • In the IRR case, the project is not started unless the return (r) of the project is above a certain threshold.
HEC – MBA Financial Markets 4-5

Limitations of IRR and NPV
• NPV and IRR can give opposing views of a project • Competition among investors and mechanisms of arbitrage theory move NVP towards zero • Therefore exceptional rates of return move towards the required rate of return • Can another investment with IRR = 15.89 be found to replace investment A in year 4?
Year Investment A Investment