More Related Content Similar to iZenBridge's PMP® Math Series: Project Selection : PV , NPV, IRR, BCR and Payback Period (20) More from Saket Bansal (20) iZenBridge's PMP® Math Series: Project Selection : PV , NPV, IRR, BCR and Payback Period2. Present Value
Net Present Value
Internal Rate of Return
Benefit Cost Ratio
Payback Period
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3. The time value of money.
The money you get in 5 years isn’t worth as money
you get today
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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
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Year 3
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
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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
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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
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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)
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11. Net Present Value
NPV = Sum (PV)
= Sum (FV / (1 + i)^ n)
i = Discount rate
n = Period
FV = Future Cash Inflow (+) / Outflow (-)
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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)
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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
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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
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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.
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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
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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%
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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
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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
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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
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23. Benefit Cost Ratio
• Money project going to make versus its cost.
• Benefit/Cost OR Revenue/cost
• Remember : Revenue is not equals to Profit
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24. Benefit Cost Ratio (BCR)
• Greater Benefit<->Greater Ratio <-> Better project
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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
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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.
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28. Payback Period
• Time required to get originally invested amount back
• Smaller is better . Earlier we get money, better it is
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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)
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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
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