1. Capital Budgeting Decision Rules
NPV
IRR
MIRR
Profitability Index
Payback
Discounted Payback

2. Net Present Value A. Calculation B. Decision Rule C. Interpretation
Forecast the incremental cash flow generated by the project
Determine the discount rate; which represents the opportunity cost of capital
Calculate the present value of all cash flows
Add discounted values and subtract the investments initial costs
B. Decision Rule
Accept projects with NPV > 0
C. Interpretation
The NPV of an investment is the difference between its market value and its cost.

3. The Internal Rate of Return (IRR)
A. Calculation
IRR is the discount rate which makes NPV = 0.
Is calculated by iterations or computer.
B. Decision Rule
Accept projects with IRR greater than the opportunity cost of capital.
C. Interpretation
The IRR is the discount rate that makes the estimated NPV of an investment equal to zero.
Why might people prefer to think about the capital budgeting decision in terms of an interest rate rather than a present value?

4. NPV Illustrated (Calculation)1 2
Initial outlay
($1,100)
Revenues $1,000
Expenses 500
Cash flow $500
Revenues $2,000
Expenses 1,000
Cash flow $1,000
– $1,100.00
+$180.99 1
$500 x
1.10 1
$1,000 x
NPV

5. Internal Rate of Return Illustrated
Initial outlay = -$1100
Year Cash flow
1 500
2 1000
Find the IRR such that NPV = 0
0 =
(1+IRR) (1+IRR)2
1100 =
(1+IRR) (1+IRR)2

6. NPV Illustrated (concluded)1 2
Initial outlay
($1,100)
Revenues $1,000
Expenses 500
Cash flow $500
Revenues $2,000
Expenses 1,000
Cash flow $1,000
– $1,100.00
$0.00 1
$500 x 1
$1,000 x
NPV

7. NPV using a Financial CalculatorCF
2nd CLR Work
CF0 = ENTER
C01 = 500 ENTER
F01 = 1 ENTER
C02 = ENTER
F02 = 1 ENTER
NPV
I = 10 ENTER
CPT
$180.99
The cash flow registers have the same information as the NPV analysis.
IRR
CPT
20.74 %

8. Excel Calculations (double click on Excel Sheet)

9. Modified Internal Rate of Return (MIRR)
MIRR is the discount rate which causes the PV of a project’s terminal value (TV) to equal the PV of costs.
TV is found by compounding inflows at cost of capital.
Thus, MIRR assumes cash inflows are reinvested at cost of capital.

10. MIRR Illustrated (I require to earn at least 10 percent on my investment, do the cash flows provide at least this much in return?) 1 2
Initial outlay
($1,100)
Revenues $1,000
Expenses 500
Cash flow $500
Revenues $2,000
Expenses 1,000
Cash flow $1,000
Terminal Value:
Positive Cash Flows
$500 x
550
1550
PV outflows
TV inflows TV
PV =
(1 + MIRR) 2
1550
1100 =
(1 + MIRR) 2

11. Excel Calculations (double click on Excel Sheet)

12. It measures the “bang for the buck.”
Profitability Index
The profitability index (PI) is the present value of future cash flows divided by the initial cost.
It measures the “bang for the buck.”
PV future CF
PI =
Initial Cost

13. PI Illustrated (Calculation)1 2
Initial outlay
($1,100)
Revenues $1,000
Expenses 500
Cash flow $500
Revenues $2,000
Expenses 1,000
Cash flow $1,000
Initial Cost +$ 1
$500 x
1.10 1
$1,000 x
PV of future CF
1,280.99
PV future CF
PI = = =
Initial Cost
1,100.00

14. Payback Rule
A. Calculation: The number of years for the project to return its investment.
B. Decision rule
Accept projects with payback less than some specified period
C. Interpretation
The payback period is the length of time until the sum of an investment’s cash flows equals its cost. (This does not imply that additional flows are profit.)
D. Advantages
Simple to calculate
E. Disadvantages
Does not allow for time value of money
Ignores cash flows after cutoff date
Does not consider the risk of the project

15. Payback Rule Illustrated
1 year and 600/1000 of
the second years CFs
1. 6 years payback period. If this is less than the
cut-off period, the project is acceptable.

16. Discounted Payback Rule Illustrated
1 year and /826.45
of the second years CFs
1. 78 years discounted payback period. If this is less
than the cut-off period, the project is acceptable.

17. Excel Calculations (double click on Excel Sheet)

18. Net Present Value (NPV) and Internal Rate of Return (IRR)
Advantages of NPV
Correctly accounts for time value of money
Incorporates the risk-adjusted discount rate
Always gives the correct accept/reject decision
Disadvantages of NPV
None - (Unless if a preference by individuals toward another method is considered a disadvantage)
Advantages of IRR
Easy to understand and compare with other projects.
Gives the same accept/reject decisions as NPV for projects that are (1) independent and (2) have conventional cash flows.
Disadvantages of IRR
Assumes reinvestment of cash flows at IRR
Sometimes no IRR exists
Does not differentiate between borrowing and lending
Can have more than one IRR.
Can give the wrong decision when comparing mutually exclusive problems. Can incorrectly rank projects
Cannot consider changing interest rate expectations

19. Sometimes no IRR exists.

20. IRR does not differentiate between borrowing and lending (Example 1).

21. IRR does not differentiate between borrowing and lending (Example 2)

22. Can have more than one IRR

23. Problems in Ranking Mutually Exclusive Projects
Problems in Ranking Mutually Exclusive Projects. Mutually exclusive means that either A or B may be taken, but not both.