This document defines capital budgeting as the process of making long-term investment decisions to maximize shareholder wealth. It discusses the key steps and criteria used in capital budgeting, including estimating cash flows, cost of capital, payback period, IRR, MIRR, NPV, and profitability index. It also covers assumptions made and how to apply the decision rules to rank independent and mutually exclusive projects under conditions like varying discount rates, project size differences, unequal lives, and capital rationing constraints.

2. Definition
 process of making long-term investment decisions
that maximizes the wealth of the shareholders.
 Three Parts:
 Estimating Cash Flows (Most tedious)
 Estimating discount rate (Cost of Capital, base rate computed
once a year)
 Applying decision rules (Topic of today’s class)

3. Decision Criteria
 Payback Period
 Time value adjusted payback period
 Internal Rate of Return
 Modified Internal Rate of Return
 Net Present Value
 Profitability Index

4. Some Assumptions
 Projects belong in the same risk class.
 Project lives are identical.
 Project sizes are roughly identical.
 Project decisions are not affected by the project
financing decisions. All projects are financed
according to the company’s target capital structure.
 Cost of capital is constant over project life
We will relax the assumptions as we move along

5. Payback Period
 How long does it take to recover investment
 Steps
 Compute cumulative cash flows
 Identify the payback year (the year CCF changes to positive)
 In what fraction in the payback year the investment is fully
recovered
 (Payback year -1) + (last negative CCF/CF in PBY)

6. Payback Year-Example

 Incremental Cumulative
 Year Cash Flows Cash Flow(CCF)
 Project A Project A
 0 (Taka 10,000) (Taka 10,000)
 1 1,000 (9,000)
 2 2,000 (7,000)
 3 3,000 (4,000)
 4 5,000 1,000
 5 6,000
 6 6,000
 (Payback year -1) + (last negative CCF/CF in PBY)
 = 3+4000/5000 = 3.8 years

7. Time Value Adjusted Payback
Period
 After factoring in time value of money, how long does it take to recover initial investment.
 Incremental
Cumulative Pv of
 Year Cash Flows Pv of Cash Flows Cash
Flow (CPV)
 Project A Project A Project A
 0 (Taka 10,000) (Taka 10,000) (10,000)
 1 1,000 869.57 ( 9,130.43)
 2 2,000 1,512.29 ( 7,618.14)
 3 3,000 1,972.55 ( 5,645.59)
 4 5,000 2,858.77 ( 2,786.82)
 5 6,000 2,983.06 196.24
 6 6,000 2,593.97
 Adjusted Payback Period = (Adjusted payback year -1) + (Last negative CPV/PV in PBY)
 = 4 + (2786.82/2983.06 = 4.93

8. Internal Rate of Return (IRR)
 It is that rate that makes present value of inflows equal
to the present value of outflows, NPV = 0, it is the
geometric rate of return.
∑CFt(Outflows)/(1+i)t = ∑CFt(Inflows)/(1+i)t
 Good to have normal projects
 Solve by interpolation.
 Solve by using Financial Calculators.
 You must have both inflows and outflows.
 Some projects may not have IRR
 Some projects may have multiple IRR

9. IRR- Financial Calculator Example
 Incremental CFo = - 10,000
 Year Cash Flows CO1 = 1,000
Project A FO1 = 1
 0 (Taka 10,000) CO2 = 2,000
 1 1,000 FO2 = 1
 2 2,000 -
 3 3,000 -
 4 5,000 CO6 = 6,000
 5 6,000 FO6 = 1
 6 6,000 IRR [CPT] 22.35%

10. Net Present Value
 Residual Value after All Capital Suppliers are Satisfied.
Present Value of inflows minus present value of
outflows at a given discount rate
 NPV on Financial Calculator.
 You still have the cash flows on your calculator. Hit [NPV].
Calculator asks for I, the discount rate. You enter it, then hit
[CPT]. It will produce

11. NPV Profile
 NPV Profile.xlsx

12. NPV Profile
($2,000.00)
($1,000.00)
$0.00
$1,000.00
$2,000.00
$3,000.00
$4,000.00
$5,000.00
$6,000.00
$7,000.00
$8,000.00 7%
9%
11%
13%
15%
17%
19%
21%
23%
25%
27%
29%
31%
33%
NPV
A
B

13. Finding Crossover Rate
 Define the Difference between the Two Cash Flows.
 Compute the Differences Accordingly
 Determine the IRR of the Differences. The NPVs cross
over at this rate
 Why Does this process work?

14. The Reinvestment Rate
Assumption of IRR
 IRR assumes that interim flows are reinvested at IRR rate.
 What is the rate of return for project B if interim flows earn
only 12 percent?
-75,000 38000 38000 38000
38000(1+.12)
38000(1+.12)2
PV = -75000
FV = 128227.20
Rate of return = 19.57%

15. Modified Internal Rate of Return
(MIRR)
 Find the Future Value of (only) inflows (Value 1)
 You can find the PV and convert it FV (Value 1)(Normal
projects only)
 Find the Present Value of Outflows (Value 2). If the
Project has just the Initial Outlay as the only
outflow, Initial Outflow is Value 2
 Compute the implied interest rate using Value 2 as
PV, Value 1 as FV, n for the time frame. The implied
interest rate is MIRR

16. Profitability Index
 PI = Present Value of Inflows/Initial Outlay
If you know the NPV and that the initial outlay is the
only outflow, then
 PI = (NPV + IO)/IO

17. Decision Rules for Ranking Projects
 Accept/Reject Rules for Independent Projects
 Payback or Adjusted Payback Period
 Quicker Payback better, Rank higher
 Should be less than company’s required maximum payback
 IRR/MIRR
 Must be greater than discount rate. The higher rate, the better
rank
 NPV
 Must be Positive. The higher the NPV the better rank.
 Profitability Index
 Must be greater than 1. Higher PI ranks higher

18. Decision Rules for Mutually
Exclusive Situation. Can Choose
only One
 IRR/MIRR: Choose the Best, Reject others. (Must
exceed cost of Capital)
 NPV: Choose Project with Highest NPV, Reject Others.
(NPV must be positive)
 PI : Choose the Project with Greatest PI Value(Must
exceed 1), Reject Others.

19. Discount rate vary over life
 Use NPV
 NPV = -IO + CF1/(1+k1) + CF2 /(1+k1)(1+k2) +
CF3/(1+k1)(1+k2)(1+k3) …….
CFn/(1+k1)(1+k2)….(1+kn)

20. Project Size Difference
 Consider the following two projects. (Mutually
Exclusive)
Year 0 1 2 3
Project A -10,000 6000 6,000 6,000
Project B -75,000 38000 38000 38000
IRRA : 36.31%
IRRB : 24.26%
NPV of A (at 20%): 2,638.89
NPV of B (at 20%): 5,046.30
NPV Profile1-Scale Difference.xlsx

21. Incremental Cash Flow
Year 0 1 2 3
Project A -10,000 6000 6,000 6,000
Project B -75,000 38000 38000 38000
Project B – A -65000 32000 32000 32000
NPV of A: 2,638.89
NPV of Project B-A at 20%: 2,407.01
Conclusion: The incremental investment in B creates
Value.

22. Projects with Unequal Lives
Mutually Exclusive
 Replacement Chain
 Keep renewing the projects until both Projects end in The
Same Year
 Find the NPV on a common life basis. Project with Higher
NPV is The Better Value Creator

23. Example: Page 122
 Year CF(X) CF(Y)
 0 (6,000) (8,500)
 1 2,800 4,000
 2 3,500 4,000
 3 4,600 3,000
 4 2,000
 5 2,000
 6 1,000
 Project(X) Project(Y)
 IRR 33.44% 28.34%
 NPV@16% Taka 1,961.89 Taka 2,310.15
 PI 1.33 1.27

24. Common Life (Replacement Chain)
 Year CF(X) CF(Y)
 0 (6,000) (8,500)
 1 2,800 4,000
 2 3,500 4,000
 3 4,600 -6,000 3,000
 4 2,800 2,000
 5 3,500 2,000
 6 4,600 1,000
 Project(X) Project(Y)
 IRR 33.44% 28.34%
 NPV Taka 3,218.79 Taka 2,310.15

25. Projects with Unequal Lives
Mutually Exclusive
 Equivalent Annual Annuity (EAA)/Annual Net Present
Value (ANPV)/Uniform Annual Series (UAS)
 First find Regular one Cycle NPV
 Second, Divide Above by Appropriate PVIFA. This is
Equivalent Annual Annuity or ANPV.
 Assumption: Unlimited Renewal

26. Equivalent Annual Annuity
 EAA = NPV (Based on one cycle)/PVIFAi,n
 Project(X) Project (Y)
NPV 1,961.89 2,310.15
PVIFA 2.2459 3.6847
EAA 873.54 626.96

27. Capital Rationing
 Choose as Many Projects You Can fund Given the
Capital Budget.
 Keep in Mind That Cost of Capital, WACC, is likely to
go up as you increase the Budget for Capital
Investment.

28. Project Selection with Capital
Rationing
Total Budget: Taka 80,00,000. Discount rate 20%
Project Cost IRR NPV PI
A. 20,00,000 27% 7,00,000 1.35
B. 30,00,000 25% 8,00,000 1.27
C. 18,00,000 24% 5,50,000 1.31
D. 10,00,000 23.25% 2,80,000 1.28
E. 8,00,000 22% 2,00,000 1.25
F. 6,00,000 21.5% 1,60,000 1.27
G. 6,00,000 21% 1,50,000 1.25

29. Project Selection
On the Basis of IRR
 A+B+C+D Total Cost 78,00,000 Total NPV 23,30,000
On the Basis of NPV
 B+A+C+D Total Cost 78,00,000 Total NPV 23,30,000
On the Basis PI
 B+A+C+D Total Cost 78,00,000 Total NPV 23,30,000
Best Mix
 A+B+C+F+G Total Cost 80,00,000 Total NPV 23,60,000