FINANCIAL MANAGEMENT

Prof. İlhan Meriç

“Net Present Value Profile”

Andrey Chaplinskiy Anıl Sural

Dorukan TipiciEmre Aykanat

Net Present Value ProfilesThe NPV profile shows the NPV of the

project at different discount rates.

The NPV profile cuts the vertical axis when the

discount rate is 0%.

The NPV of the project at 0% discount rate is the difference between

the some of the future cash inflows and the initial

cash outflow.

NPV PROFILESThe NPV profile cuts the horizontal axis

when the NPV is $0.

Therefore, the horizontal axis intercept of the

NPV profile is the project’s IRR because the IRR

is defined as the discount rate that forces NPV to

become zero, i.e., when the present value of the

future cash inflows is equal to the initial cash

outflow.

NPVA Company is considering two projects with the

following cash flows. The Company's 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

NPV 0 -$100 -$100 0 -$100

-$100 1 $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)

NPV

r

CFt

tn

t

10

IRR: Enter NPV = 0, solve for IRR.

0

10

t

tn

t IRR

CF

01 1

CFIRR

CFt

tn

t

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 % Project Y= 23.6 % *If the projects are mutually exclusive, we should choose Project Y. *If the projects are independent ,we should choose both of them.

-100 10 60 80

-100 70

20

50

NPV ProfilesC) Draw the NPV profiles of the two projects. Show the

values where the NPV profiles intersect the vertical axis and the horizontal

axis.

NPV RULE and IRR RULE

Mutually Exclusive ProjectsWhen you must choose only one project

among several possible projects, the choice is mutually exclusive.

NPV RuleSelect the project with the highest NPV.

IRR RuleSelecting 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

rule cannot be used to compare projects of

different scales.

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 Point

The Crossover point is the discount rate that

yields the same NPV for both projects. The simultaneous solution of the two

NPV equations gives the discount rate at

which the two NPVs will be equal.

The Crossover PointFind 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 PointD) 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.