1. Net Present Value
The Most Challenging Globally Recognized Finance Training & Certification Programs

2. AGENDA
Time value of money
PV formula
Project / Investment Evaluation example
How to decide between projects?
NPV Exercise

3. Comparing Cash flows - discounting
TIME VALUE OF MONEY
100 $
110 $
10% percent annual
FV – future value
PV – present Value
90.91 $
100 $
10% percent annual
PV – present Value
FV – future value
Comparing Cash flows - discounting

4. Value today of a future cash flow. Discount Factor
TIME VALUE OF MONEY
Present Value
Value today of a future cash flow.
Discount Factor
Present value of a $1 future payment.
Discount Rate
Interest rate used to compute present values of future cash flows.

5. Present Value - Formula
Discount Factor = DF = PV of $1
Discount Factors can be used to compute the present value of any cash flow.
PV = Discount Factor (DF) x Cash Flow (Ct)

6. Project /Investment Evaluation - NPV
+ PV of Future Cash Inflows Income
+ PV of Future Cash Outflows Cost
Net Present Value
What discount rate should we use?
Estimate opportunity cost of capital (2nd best option)
If equally risky investments in the capital market offer a return of 12%, then
Cost of capital = r = 12%
Now we understand that money has a time value. In order to get the Net Present Value of a project we need to have the present value of Future Cash Inflows and Outflows. The next question is what discount rate should we use? In order to estimate the discount rate, we need to know what is our second best option to invest, what return would we get? This is called opportunity cost of capital and this is the rate of return we can use in the discounting process to get the present values. An example: If equally risky investments in the capital market offer a return of 12%, then
The cost of capital = r = 12%

7. A Practical Example

8. Project evaluation How to get a rich guy?
Project evaluation How to get a rich partner?
Project evaluation How to get a rich guy?

9. How to evaluate the financials?
Project evaluation
How to evaluate the financials?
How to evaluate the financials?
Partner 1
Partner 2

10. Project evaluation – best scenarios
Choice between Partner 1 and Partner 2 (supplier A & B, initiative 1 & 2, formula X & Y).
I can expect $10MM from Partner 1, $20MM from Partner 2.
Whom would you choose?
What is the NPV of Partner 2?
NOMINAL REVENUE
Partner 1
$10MM
Partner 2
$20MM
+10

11. Project evaluation – discount factor
Partner 1 gives me the $10MM now, but Partner 2 gives me the $20MM 10 years from now.
Whom would you choose?
Discounted revenue: 20/(1+0.08)^10 = 9
NOMINAL REVENUE
WHEN?
DISCOUNTED REVENUE
Partner 1
$10MM
NOW
Partner 2
$20MM
YEAR 10
$9MM +1

12. Project evaluation – costs
In order to catch Partner 1, there is a need for $2MM immediate investment. Attracting Partner 2 costs $1MM.
Whom would you choose?
DISCOUNTED REVENUE
INVESTMENT
DISCOUNTED CASH FLOW
Partner 1
$10MM
$(2)MM
$8MM
Partner 2
$9MM
$(1)MM

13. Project evaluation – probability
To catch Partner 1, I have 50% chance, while Partner 2 is 99% willing to marry.
Whom would you choose?
What is the NPV?
DISCOUNTED CASH FLOW
PROBABILITY
PROBABILITY ADJUSTED CF
Partner 1
$8MM
50%
$4MM
Partner 2
99% +4

14. Project evaluation – summary
Options need to be gathered.
Evaluation needs to be done vs. 2nd best (Opportunity cost of Capital)
Assumptions need to be collected for both scenarios.
Cash flow needs to be calculated within project life
Cash flows need to be discounted to present to get NPV.
Results need to be risk adjusted

15. Exercise
What is the PV of 400$ at 7% or at 12% cost of capital?

16. Risk and Present Value Learning:
- higher risk projects require a higher rate of return.
- higher required rates of return cause lower PVs.

17. How to decide between projects?

18. Rule 1: Rate of Return Rule
How to decide between projects?
Rule 1: Rate of Return Rule
Accept investments that offer rates of return in excess of their opportunity cost of capital
Example
In the project listed below, the foregone investment opportunity is 12%. Should we do the project?

19. Rule 2: Net Present Value Rule
How to decide between projects?
Rule 2: Net Present Value Rule
Accept investments that have positive net present value
Example
Suppose we can invest $50 today and receive $60 in one year. Should we accept the project given a 10% expected return?

20. NPV Calculation Exercise
You have an option to buy a machine for $3500 that will generate $1000 income for 5 years that will increase by 5% in each year. You use a straight-line depreciation method and you fully depreciate the machine in 5 years. Your corporate tax rate is 25%. You also need to spend on maintenance 5% of the depreciation. You would get 10% return on the market if you invest your money elsewhere.
Does it worth to invest into the machine? How much is the NPV?

21. NPV Calculation Exercise - SOLUTION

22. SUMMARY
Money has a time value
Deciding on investments - compare NPVs.
Accept investments
rates of return > opportunity cost of capital
with positive present values.
Evaluate projects vs. 2nd best option
Cash flows need to be discounted
Results need to be risk adjusted.
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