Net Present Value ProfilesThe NPV profile shows the NPV of the project atdifferent discount rates.The NPV profile cuts the vertical axis when thediscount rate is 0%.The NPV of the project at 0%discount rate is the difference between the someof the future cash inflows and the initial cashoutflow.
NPV PROFILESThe NPV profile cuts the horizontal axis whenthe NPV is $0.Therefore, the horizontal axis intercept of theNPV profile is the project’s IRR because the IRRis defined as the discount rate that forces NPV tobecome zero, i.e., when the present value of thefuture cash inflows is equal to the initial cashoutflow.
NPVA Company is considering two projects with the following cash flows. The Companys cost of capital is 10 percent. Expected Net Cash Flows (in millions) Year Project X Project Y 0 ($100) ($100) 1 10 70 2 60 50 3 80 20
NPVA) Calculate the NPVs of the projects. Which project would you choose if they are independent projects? Which project would you choose if they are mutually exclusive projects? Why? Project X Project Y Year Cash Flow NPV Year Cash Flow NPV0 -$100 -$100 0 -$100 -$1001 $10 $9.09 1 $70 $63.632 $60 $49.59 2 $50 $41.323 $80 $60.11 3 $20 $15.03 NPV-X= $18.79 NPV-Y= $19.98*If the projects are independent ,we should choose both of them.If the projects are mutually exclusive, we should choose project Y.
Internal Rate of Return(IRR) n CF t t NPV t 0 1 r IRR: Enter NPV = 0, solve for IRR. n n CF t CF t t 0 t CF 0 t 0 1 IRR t 1 1 IRR
Internal Rate of Return(IRR) If L and S are independent, accept both: IRRL > r and IRRS > r. If L and S are mutually exclusive, accept S because IRRS > IRRL. IRR is not dependent on the cost of capital used.
Internal Rate of Return(IRR)B) Calculate the IRRs of the projects. If the projects are independent,which project would you choose? If they are mutually exclusive, whichproject would you choose? Why?- How to find IRR on excel? Project X Project Y fx – internal rate of return Project X= 18.1 % -100 Project Y= 23.6 % -100 10 *If the projects are mutually 70 exclusive, we should choose 60 Project Y. *If the projects are 50 80 independent ,we should 20 choose both of them.
NPV ProfilesC) Draw the NPV profiles of the two projects. Show the values where theNPV profiles intersect the vertical axis and the horizontal axis.
NPV RULE and IRR RULE Mutually Exclusive Projects When you must choose only one project among several possible projects, the choice is mutually exclusive. NPV Rule Select the project with the highest NPV. IRR Rule Selecting the project with the highest IRR may lead to mistakes.
NPV RULE and IRR RULEIf a project’s size is doubled, its NPV will double.This is not the case with IRR. Thus, the IRR rulecannot be used to compare projects of differentscales. NPV assumes reinvest at r (cost of capital). IRR assumes reinvest at IRR. Reinvesting at cost of capital, r, is more realistic, so NPV method is better. NPV should be used to choose between mutually exclusive projects.
The Crossover PointThe Crossover point is the discount rate thatyields the same NPV for both projects.The simultaneous solution of the two NPVequations gives the discount rate at whichthe two NPVs will be equal.
The Crossover Point Find cash flow differences between the projects. Enter these differences in CFLO register, then press IRR. Crossover rate = 8.68%, rounded to 8.7%. Can subtract S from L or vice versa, but easier to have first CF negative. If profiles don’t cross, one project dominates the other.
The Crossover Point D) Calculate the crossover point of the two NPV profiles
AnalyzesE) Analyze the NPV profiles and determine at what cost of capital levels the NPV and IRR methods would rank the projects similarly and differently.