Capital Budgeting-The Basics

Definitionprocess 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)

Decision CriteriaPayback Period

Time value adjusted payback period Internal Rate of ReturnModified Internal Rate of ReturnNet Present ValueProfitability Index

Some AssumptionsProjects 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

Payback PeriodHow long does it take to recover investmentSteps

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)

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

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

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 projectsSolve by interpolation.Solve by using Financial Calculators.You must have both inflows and outflows.Some projects may not have IRRSome projects may have multiple IRR

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%

Net Present ValueResidual 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

NPV ProfileNPV Profile.xlsx

NPV Profile

7%

9%

11%

13%

15%

17%

19%

21%

23%

25%

27%

29%

31%

33%

($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

ABN

PV

Finding Crossover RateDefine the Difference between the Two Cash

Flows.Compute the Differences AccordinglyDetermine the IRR of the Differences. The

NPVs cross over at this rateWhy Does this process work?

The Reinvestment Rate Assumption of IRRIRR 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%

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

Profitability IndexPI = Present Value of Inflows/Initial OutlayIf you know the NPV and that the initial outlay

is the only outflow, thenPI = (NPV + IO)/IO

Decision Rules for Ranking ProjectsAccept/Reject Rules for Independent Projects

Payback or Adjusted Payback Period Quicker Payback better, Rank higher Should be less than company’s required maximum

paybackIRR/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

Decision Rules for Mutually Exclusive Situation. Can Choose only OneIRR/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.

Discount rate vary over lifeUse NPVNPV = -IO + CF1/(1+k1) + CF2 /(1+k1)(1+k2)

+ CF3/(1+k1)(1+k2)(1+k3) …….

CFn/(1+k1)(1+k2)….(1+kn)

Project Size DifferenceConsider the following two projects. (Mutually

Exclusive)Year 0 1 2 3Project A -10,000 6000 6,000 6,000Project B -75,000 38000 38000 38000IRRA : 36.31%

IRRB : 24.26%

NPV of A (at 20%): 2,638.89NPV of B (at 20%): 5,046.30NPV Profile1-Scale Difference.xlsx

Incremental Cash FlowYear 0 1 2 3Project A -10,000 6000 6,000 6,000Project B -75,000 38000 38000

38000Project B – A -65000 32000 32000

32000NPV of A: 2,638.89NPV of Project B-A at 20%: 2,407.01Conclusion: The incremental investment in B

creates Value.

Projects with Unequal LivesMutually ExclusiveReplacement 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

Example: Page 122Year CF(X) CF(Y)0 (6,000) (8,500)1 2,800 4,0002 3,500 4,0003 4,600 3,0004 2,0005 2,0006 1,000

Project(X) Project(Y)

IRR 33.44% 28.34%NPV@16% Taka 1,961.89 Taka 2,310.15PI 1.33 1.27

Common Life (Replacement Chain)Year CF(X) CF(Y)0 (6,000) (8,500)1 2,800 4,0002 3,500 4,0003 4,600 -6,000 3,0004 2,800 2,0005 3,500 2,0006 4,600 1,000

Project(X) Project(Y)

IRR 33.44% 28.34%NPV Taka 3,218.79 Taka 2,310.15

Projects with Unequal LivesMutually ExclusiveEquivalent Annual Annuity (EAA)/Annual Net

Present Value (ANPV)/Uniform Annual Series (UAS)First find Regular one Cycle NPVSecond, Divide Above by Appropriate PVIFA.

This is Equivalent Annual Annuity or ANPV.Assumption: Unlimited Renewal

Equivalent Annual AnnuityEAA = NPV (Based on one cycle)/PVIFAi,n

Project(X) Project (Y)

NPV 1,961.89 2,310.15PVIFA 2.2459 3.6847EAA 873.54 626.96

Capital RationingChoose 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.

Project Selection with Capital RationingTotal Budget: Taka 80,00,000. Discount rate 20%

Project Cost IRR NPV PIA. 20,00,000 27% 7,00,000 1.35B. 30,00,000 25% 8,00,000 1.27C. 18,00,000 24% 5,50,000 1.31D. 10,00,000 23.25% 2,80,000

1.28E. 8,00,000 22% 2,00,000 1.25F. 6,00,000 21.5% 1,60,000

1.27G. 6,00,000 21% 1,50,000 1.25

Project SelectionOn the Basis of IRRA+B+C+D Total Cost 78,00,000 Total NPV

23,30,000On the Basis of NPVB+A+C+D Total Cost 78,00,000 Total NPV

23,30,000On the Basis PIB+A+C+D Total Cost 78,00,000 Total NPV

23,30,000Best MixA+B+C+F+GTotal Cost 80,00,000 Total NPV

23,60,000