1. “Net Present Value Profile”
Andrey Chaplinskiy
Anıl Sural
Dorukan Tipici
Emre Aykanat

2. Net Present Value Profiles
The 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.

3. NPV PROFILES
The 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.

4. NPV
A 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

5. NPV
A) 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 $63.63
2 $60 $49.59 2 $50 $41.32
3 $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.

6. 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

7. 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.

8. 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, which
project 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.

9. NPV Profiles
C) Draw the NPV profiles of the two projects. Show the values where the
NPV profiles intersect the vertical axis and the horizontal axis.

10. 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.

11. NPV RULE and IRR RULE
If 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.

12. 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.

13. 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.

14. The Crossover Point
D) Calculate the crossover point of the two NPV profiles

15. Analyzes
E) Analyze the NPV profiles and determine at what cost of capital
levels the NPV and IRR methods would rank the projects similarly
and differently.