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Session 4

Capital Budgeting

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Capital Budgeting - Methods

1. Average Return on Investment

2. Payback

3. Net Present Value

4. Internal Rate of Return

5. Modified IRR

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Average Return on Investment

AROI = Avg. Net Income Per Year

Avg. Investment

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Average Return on Investment

Example:

Year Net Income Cost

1 6,000 100,000 Initial

2 8,000 0 Salvage Value

3 11,000

4 13,000

5 16,000

6 18,000

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Avg. Net Income 72,000

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Avg. Investment 100,000

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AROI 12,000

50,000

Average Return on Investment

= 12,000

= 24%

= 50,000

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Advantages

Disadvantages

Average Return on Investment

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Payback Method

# Years required to recover the original investment

Example:

Year Net Income Cash Flow Cumulative CF

1 6,000 26,000 26,000

2 8,000 28,000 54,000

3 11,000 31,000 85,000

4 13,000 33,000 118,000

5 16,000 36,000 154,000

6 18,000 18,000 172,000

Payback = 3 + 100,000 - 85,000

118,000 - 85,000 = 3.45 Years

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Payback Method

Advantages

Disadvantages

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Time Value of Money

FV = PV (1 + r)n

Compounding: Finding FV

Discounting: Finding PV: PV = FV/(1 + r) n

Internal Rate of Return: Finding r

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Net Present Value

NPV = Present Value of All Future Cash Flows less Inital Cost

= CF1 + CF2 + CF3 +.......CFn - Io

1+r (1+r)2 (1+r)3 (1+r)n

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Net Present Value - Example

Year CF Disc. Factor PV

0 -100000 1 -100000

1 26000 1/1.1 = .9091 23637

2 28000 1/(1.1)2 = .8264 23139

3 31000 1/(1.1)3 = .7573 23290

4 33000 1/(1.1)4 = .6830 22539

5 36000 1/(1.1)5 = .6209 22352

6 18000 1/(1.1)6 = .5645 10161

NPV = 25121

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Net Present Value

Advantages

Disadvantages

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Internal Rate of Return

Discount rate that makes NPV Zero (i.e., that equates PV of benefits with the cost).

IRR: Io = CF1 + CF2 + ..... + CFn

1+r (1+r)2 (1+r)n

Solve for r.

Example:

100,000 = 26000 + 28000 + 31000 + .......... + 18000

1+r (1+r)2 (1+r)3 (1+r)6

r = 18.2%

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Internal Rate of Return

Advantages

Disadvantages

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Profitability Index

PI = PV of all Benefits

PV of all Cost

Example:

PV (Benefits) = 26000 + 28000 +.......... + 18000

1.1 (1.1)2 (1.1)6

= 125121

PV (Cost) = 100000

PI = 125121 = 1.25

100000

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Profitability Index

Advantages:

Disadvantages:

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NPV Profile

Year CF Disc. Factor PV

0 -100,000 1 -100,000

1 26,000 0.91 23,636

2 28,000 0.83 23,140

3 31,000 1/(1.1)3 = .7573 23,291

4 33,000 1/(1.1)4 = .6830 22,539

5 36,000 1/(1.1)5 = .6209 22,352

6 18,000 1/(1.1)6 = .5645 10,161

NPV = 25,121

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NPV Profile

Dis. Rate NPV

0% 7200

5% 45725.7

10% 25120.76

15% 8711.838

20% -4538.97

25% -15376.1

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NPV Profile

80000

60000

40000

20000

0

-20000

0 0.05 0.1 0.15 0.2 0.25

Disc. Rate

NP

V

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Choosing Between Projects

Year CF(A) CF(B)

0 -25000 -25000

1 2000 21000

2 2000 10000

3 35000 2000

NPV 6351 4606

IRR 17% 22%

NPV Profile

-10,000

-5,000

0

5,000

10,000

15,000

20,000

0% 5% 10% 15% 20% 25% 30%

Discount rate

NP

V

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Modified IRR

Reinvestment Rate Assumption (Project A)

   

Project  Outlay  25,000

Cash Flows: YR1  2,000                     YR2  2,000                     YR3  35,000  

    NPV @ 8%: 6,351  IRR: 17%

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NPV: Project A

    YR1:   2,000     YR2:   2,000 + 2,000 + 160 = 4,160    YR3:   35,000 + 4,160 + 333 = 39,493

[Note: PV of 39,493, three years from now @ 8% =  31,351                                                          Less: outlay  25,000

                                                                  NPV  6,351]

Modified IRR

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IRR @ 17%     YR1:   2,000   = 2,000     YR2:   2,000 + 2,000 + 340 = 4,340     YR3:   35,000 + 4,340 + 738 = 40,078

[25,000 invested for three years @ 17% = 25,000(1.17)3 = 40,040]

Modified IRR

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Modified Internal Rate of Return

   

Find k such that   (1+k)nI0  = Final value

    i.e.     (1+k)3 25000  = 39,439                                  k  = 16.5%

Modified IRR

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Reinvestment Rate Assumption (Project B)

  

Project  Outlay  25,000

Cash Flows: YR1  21,000                     YR2  10,000                     YR3  2,000  

    NPV @ 8%: 4,606  IRR: 22.12%

Modified IRR

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NPV: Project B        

YR1: 21,000 = 21,000        YR2: 10,000 + 21,000 + 1,680 = 32,680         YR3:  2,000 + 32,680 + 2,614   = 37,294

[Note: PV of 37,294, three years from now @ 8% =  29,606                                                        Less: outlay  25,000                                                        NPV  4,606 ]

Modified IRR

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   IRR of 22.12%       

  YR1:   21,000    = 21,000         YR2:   10,000 + 21,000 + 4,645 = 35,645         YR3:   2,000 + 35,645 + 7,885 = 45,530

[25,000 invested for three years @ 22.12% = 25,000(1.2212)3 = 45,530]

Modified IRR

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Modified Internal Rate of Return

Find k such that   (1+k)nI0  = Final value

            i.e.     (1+k)3 25000  = 37,294                                           k  = 14.26%

Modified IRR

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Estimating Cash Flows

NPV = CF1 + CF2 +.............. + CFn - Io

l+r (l+r)2 (l+r)n

Cash Flows Incremental

After Tax

Net Working Capital

Sunk Costs

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Procedure

1. Initial Costs: New CAPEX

Additional W. Cap

Sale of Old Assets

2. Annual Costs: Revenue Less Costs

After Tax

3. Terminal Cash Flows: Salvage Value

Recoupment of NWC

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Cash Flow Estimates

Sale of Existing Plant

CF= Selling Price + T (B.V. - S.P.)

Annual Cash Flows

OCF= (Sales-Cost)(1-T) + T, DEPREC

or

OCF= Net Inc + Depreciation

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New Product Proposal

Annual Sales $20m

Annual Costs $16m

Net Working Capital $2m

Plant Site $0.5m

Plant and Equipment $10m

Depreciation Straight Line over 20 years

Salvage Value nil

Tax Rate 40%

Required Return 8%

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New Product Proposal

INITIAL CASH FLOWS

ANNUAL CASH FLOWS

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New Product Proposal

TERMINAL CASH FLOWS

CALCULATION

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Evaluating Capital Projects

1) Focus on Cash Flow, Not Profits.

– Cash Flow = Economic Reality.

– Profits Can Be Managed.

2) Carefully Estimate Expected Future Cash Flows.

3) Select a Discount Rate Consistent with the Risk of Those Future Cash Flows.

4) Account for the Time Value of Money.

5) Compute a “Base-Case” NPV.

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6) Net Present Value = Value Created or Destroyed by the Project.– NPV is the Amount by which the Value of the Firm Will

Change if you Undertake the Project.

7)Identify Risks and Uncertainties. Run a Sensitivity Analysis.– Identify “Key Value Drivers.”– Identify Breakeven Assumptions.– Estimate Scenario Values.– Bound the Range of Value

Evaluating Capital Projects

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8) Identify Qualitative Issues.

– Flexibility

– Quality

– Know-How

– Learning

9) Decide

Evaluating Capital Projects