PMP®
Math Series
Economic Model

PMP is a registered trademark of the Project Management Institute, Inc.

© 2013 iZenBridg...
Present Value
Net Present Value
Internal Rate of Return

Benefit Cost Ratio
Payback Period

© 2013 iZenBridge | CONFIDENTI...
The time value of money.

The money you get in 5 years isn’t worth as money
you get today

© 2013 iZenBridge | CONFIDENTIA...
Present Value

© 2013 iZenBridge | CONFIDENTIAL
Present Value
• Value today of the future cash flow
• Present Value = FV / (1 + i)^ n
• i = Discount rate
• n = Period
• F...
Present Value
Year 2 4000
USD

Now
Year 1

•
•
•
•
•

Discount Rate = 10%
PV = 4000 / (1+10/100) ^2
PV = 4000/ (1.1) ^2
PV...
Which Investment Option is Better ?
Option A :
Returns: 4000 USD after 2
years

Option B:
Returns: 3500 USD after 1
years
...
Usages of Present Value (PV)
• Used as a base for calculating the Net Present Value (NPV)
• Simple investment decisions ca...
Net Present Value (NPV)

© 2013 iZenBridge | CONFIDENTIAL
Net Present Value (NPV)
• NPV is a measure of how much money a project can be
expected to return (in today’s present value...
Net Present Value
NPV = Sum (PV)
= Sum (FV / (1 + i)^ n)
i = Discount rate
n = Period
FV = Future Cash Inflow (+) / Outflo...
Net Present Value
Outflow 1000
USD (Now)

Inflow 4000 USD
(Year 2)
Outflow 1000
USD (Year 1)

• Discount Rate = 10%
• NPV ...
Which Project to Select?
• Project A has a duration of 4 years and an NPV of $40,000,
• Project B has a duration of 3 year...
Usages of Net Present Value (NPV)
•
•
•
•
•

One of the frequently used tools for project selection
Take in account inflow...
Internal Rate of Return (IRR)

© 2013 iZenBridge | CONFIDENTIAL
Internal Rate of Return (IRR)
• IRR is a measure of how quickly the money invested in a
project will increase in value. It...
Internal Rate of Return (IRR)
• The rule is same like NPV, the difference is, now we need to
compute the rate (i) which eq...
Internal Rate Return (IRR)
Outflow 1000
USD (Now)

Inflow 4000 USD
(Year 2)
Outflow 1000
USD (Year 1)

• 0 = -1000-1000 /(...
Internal Rate of Return (IRR)
• Which Project you will select?
Project Name

IRR

Investment

Gold

6%

4,500,000

Silver
...
Usages of Internal Rate of Return (IRR)
•
•
•
•

Frequently used in Project selection
It does not require assumption of di...
NPV vs IRR

NPV represents the
project benefit in
absolute term like
100,000 USD

IRR represents the value
in proportion l...
Benefit Cost Ratio

© 2013 iZenBridge | CONFIDENTIAL
Benefit Cost Ratio
• Money project going to make versus its cost.
• Benefit/Cost OR Revenue/cost
• Remember : Revenue is n...
Benefit Cost Ratio (BCR)
• Greater Benefit<->Greater Ratio <-> Better project

© 2013 iZenBridge | CONFIDENTIAL
Benefit Cost Ratio (BCR)
• Which of the following projects do you select?
• A) Project Gold with a BCR of 0.9
• B) Project...
Usages of Benefit Cost Ratio
•
•
•
•
•

Ratio helps in visualizing the relative value
May calculate considering Time Value...
Payback Period

© 2013 iZenBridge | CONFIDENTIAL
Payback Period
• Time required to get originally invested amount back
• Smaller is better . Earlier we get money, better ...
Payback Period
• Project A requires investment of $500,000. The project is
expected to generate $25K per quarter for the f...
Usages of Payback Period
•
•
•
•

Helps in looking the investment in time dimension
The sooner we get our money back is be...
Present
Value
Net Present
Value

Higher is
Better

Internal Rate
of Return

Higher is
Better

Benefit Cost
Ratio

Higher i...
Stay Connected
Contact Us
Saket.Bansal@iZenBridge.com
www.iZenBridge.com
forum.izenbridge.com

Join Us @

Linkedin:
www.li...
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iZenBridge's PMP® Math Series: Project Selection : PV , NPV, IRR, BCR and Payback Period

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Video of this presentation can be found at :
http://youtu.be/yIMMy8hh0WQ

In this presentation we have introduced some of the techniques used while performing project selection, we have seen people getting questions related to PV, NPV , IRR , BCR and Payback period in their PMP exam.

Project Selection falls under Project Integration Management Knowledge Area and it get executed before Project Charter get prepared.

Published in: Education, Technology, Business

iZenBridge's PMP® Math Series: Project Selection : PV , NPV, IRR, BCR and Payback Period

  1. 1. PMP® Math Series Economic Model PMP is a registered trademark of the Project Management Institute, Inc. © 2013 iZenBridge | CONFIDENTIAL
  2. 2. Present Value Net Present Value Internal Rate of Return Benefit Cost Ratio Payback Period © 2013 iZenBridge | CONFIDENTIAL
  3. 3. The time value of money. The money you get in 5 years isn’t worth as money you get today © 2013 iZenBridge | CONFIDENTIAL
  4. 4. Present Value © 2013 iZenBridge | CONFIDENTIAL
  5. 5. Present Value • Value today of the future cash flow • Present Value = FV / (1 + i)^ n • i = Discount rate • n = Period • FV = Future Cash Inflow/ Outflow Now Year 2 Year 1 © 2013 iZenBridge | CONFIDENTIAL Year 3
  6. 6. Present Value Year 2 4000 USD Now Year 1 • • • • • Discount Rate = 10% PV = 4000 / (1+10/100) ^2 PV = 4000/ (1.1) ^2 PV = 4000 / 1.21 PV = 3305 • It mean 3305 USD earned today is equals to 4000 USD earned after two year © 2013 iZenBridge | CONFIDENTIAL
  7. 7. Which Investment Option is Better ? Option A : Returns: 4000 USD after 2 years Option B: Returns: 3500 USD after 1 years Discount Rate = 10% per annum PV = 4000/(1.1) ^2 = 3305 USD PV = 3500/(1.1) = 3181 USD © 2013 iZenBridge | CONFIDENTIAL
  8. 8. Usages of Present Value (PV) • Used as a base for calculating the Net Present Value (NPV) • Simple investment decisions can be made using this technique • Higher the PV the better the investment © 2013 iZenBridge | CONFIDENTIAL
  9. 9. Net Present Value (NPV) © 2013 iZenBridge | CONFIDENTIAL
  10. 10. Net Present Value (NPV) • NPV is a measure of how much money a project can be expected to return (in today’s present value). • It’s a Sum of Inflow and outflow in present value term (mean discounted based on duration) Now FV 2 (Year 2) FV 1 (Year 1) © 2013 iZenBridge | CONFIDENTIAL
  11. 11. Net Present Value NPV = Sum (PV) = Sum (FV / (1 + i)^ n) i = Discount rate n = Period FV = Future Cash Inflow (+) / Outflow (-) © 2013 iZenBridge | CONFIDENTIAL
  12. 12. Net Present Value Outflow 1000 USD (Now) Inflow 4000 USD (Year 2) Outflow 1000 USD (Year 1) • Discount Rate = 10% • NPV = -1000-1000 /((1+10/100) ^1) • + 4000/((1+10/100)^2) • = -1000 – 909 +3306 • = 1397 (This Project returns 1397 USD in present value term) © 2013 iZenBridge | CONFIDENTIAL
  13. 13. Which Project to Select? • Project A has a duration of 4 years and an NPV of $40,000, • Project B has a duration of 3 years and an NPV of $45,000, • Project C has a duration of 6 years and an NPV of $62,000 Which project will you select? Go with Project C, Time value of money already considered in NPV so years doesn’t matter © 2013 iZenBridge | CONFIDENTIAL
  14. 14. Usages of Net Present Value (NPV) • • • • • One of the frequently used tools for project selection Take in account inflow and outflow of cash Easy to calculate A negative value indicates that we are loosing money Higher the NPV the better the project © 2013 iZenBridge | CONFIDENTIAL
  15. 15. Internal Rate of Return (IRR) © 2013 iZenBridge | CONFIDENTIAL
  16. 16. Internal Rate of Return (IRR) • IRR is a measure of how quickly the money invested in a project will increase in value. It’s a rate of return which calculate based on the inflow and outflow of the project. © 2013 iZenBridge | CONFIDENTIAL
  17. 17. Internal Rate of Return (IRR) • The rule is same like NPV, the difference is, now we need to compute the rate (i) which equalizes the cash inflow and outflow 0 = Sum (FV / (1 + i) ^ n) i = IRR this is what we calculate n = period © 2013 iZenBridge | CONFIDENTIAL
  18. 18. Internal Rate Return (IRR) Outflow 1000 USD (Now) Inflow 4000 USD (Year 2) Outflow 1000 USD (Year 1) • 0 = -1000-1000 /((1+i/100) ^1) + 4000/((1+i/100) ^2) • If we put i = 56, it makes the equation balance, so in this case IRR = 56% © 2013 iZenBridge | CONFIDENTIAL
  19. 19. Internal Rate of Return (IRR) • Which Project you will select? Project Name IRR Investment Gold 6% 4,500,000 Silver 5.8% 1,700,000 Platinum 5.4 % 2,000,000 Copper 3% 1,000,000 © 2013 iZenBridge | CONFIDENTIAL
  20. 20. Usages of Internal Rate of Return (IRR) • • • • Frequently used in Project selection It does not require assumption of discount rate Gives the result in % term rather than absolute Higher the IRR the better the project © 2013 iZenBridge | CONFIDENTIAL
  21. 21. NPV vs IRR NPV represents the project benefit in absolute term like 100,000 USD IRR represents the value in proportion like 10%, 56% We can get contradictory recommendations from NPV and IRR, but in exam you do not get such questions © 2013 iZenBridge | CONFIDENTIAL
  22. 22. Benefit Cost Ratio © 2013 iZenBridge | CONFIDENTIAL
  23. 23. Benefit Cost Ratio • Money project going to make versus its cost. • Benefit/Cost OR Revenue/cost • Remember : Revenue is not equals to Profit © 2013 iZenBridge | CONFIDENTIAL
  24. 24. Benefit Cost Ratio (BCR) • Greater Benefit<->Greater Ratio <-> Better project © 2013 iZenBridge | CONFIDENTIAL
  25. 25. Benefit Cost Ratio (BCR) • Which of the following projects do you select? • A) Project Gold with a BCR of 0.9 • B) Project Silver with a CBR of 0.9 and cost of $100,000 • C) Project Diamond with a cost of $100,000 and benefits of $110,000 • D) Project Platinum with a BCR of 1.2 a) 0.9 b) BCR = 1/0.9 = 1.11 c) 11/10 = 1.1 d) 1.2 • Answer: D © 2013 iZenBridge | CONFIDENTIAL
  26. 26. Usages of Benefit Cost Ratio • • • • • Ratio helps in visualizing the relative value May calculate considering Time Value of Money Simple to calculate and explain Ratio less than 1 indicate we are losing money Higher the value, the better it is. © 2013 iZenBridge | CONFIDENTIAL
  27. 27. Payback Period © 2013 iZenBridge | CONFIDENTIAL
  28. 28. Payback Period • Time required to get originally invested amount back • Smaller is better . Earlier we get money, better it is © 2013 iZenBridge | CONFIDENTIAL
  29. 29. Payback Period • Project A requires investment of $500,000. The project is expected to generate $25K per quarter for the first year and $100K per quarter after that. What is the payback period? By when I get 500,000 Back? First Year = 25K + 25K + 25K + 25K = 100K (still need 400K) Second Year = 100K + 100K+100K+ 100K = 400K (Done) © 2013 iZenBridge | CONFIDENTIAL
  30. 30. Usages of Payback Period • • • • Helps in looking the investment in time dimension The sooner we get our money back is better Usually calculated without considering the time value of money One can calculate discounted payback period © 2013 iZenBridge | CONFIDENTIAL
  31. 31. Present Value Net Present Value Higher is Better Internal Rate of Return Higher is Better Benefit Cost Ratio Higher is Better Payback Period Exam Tip Higher is Better Shorter is Better © 2013 iZenBridge | CONFIDENTIAL
  32. 32. Stay Connected Contact Us Saket.Bansal@iZenBridge.com www.iZenBridge.com forum.izenbridge.com Join Us @ Linkedin: www.linkedin.com/company/izenbridge-consultancy-private-limited Facebook: https://www.facebook.com/izenbridge Google+: https://plus.google.com/+Izenbridge1 © 2013 iZenBridge | CONFIDENTIAL

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