Capital Budgeting

Risk analysis

Risk in Capital Budgeting

• Uncertainty of cash flows – variability of returns

• Events influencing forecasts:

- General Economic Conditions

- Industry factors

- Company factors

Conventional techniques to handle risk

• Payback period• Preference to shorter payback, guidelines

for 3 - 5 years• Merit – simplicity , focuses on risk ,

liquidity through capital recovery• Useful only for a special type of risk of

time nature• Ignores time value of money , even

recovery vs major recovery towards the end

Risk adjusted discount rate• Allows for time preference and risk preference

• r = rf + rr

• 0 -50000• 1 25000• 2 20000 • 3 10000• 4 10000• NPV @ 10% + 3599• NPV @ 15% - 845 • IRR Method

Certainty equivalent

• Reduce forecast of cash flows to conservative levels

• Certainty equivalent coefficient , 0 to 1

• Less risk perceived , high CE

• CE = certain NCF / Risky NCF

= 40000/ 50000 = 0.80

• Year CF CE Certain CF

• 0 - 6000 1 -6000

• 1 4000 0.90 3600

• 2 3000 0.70 2100

• 3 2000 0.50 1000

• 4 1000 0.30 300

• NPV @ 10% = - 37

• IRR method

Sensitivity analysis

• Effect on NPV or IRR by changing one variable at a time

• Decision maker asks what if questions

• Examines sensitivity of variables used to calculate NPV or IRR

• Does not try to quantify risk

• I 100,00,000

• Sales volume 1000,000

• Unit Selling price 15

• Unit variable cost 6.75

• Fixed cost 4000,000

• Depreciation( WDV) 25%

• Tax rate 35%

• Discount rate 12%

• Expected life 7 years

• NPV + 4829000

• IRR 26.8%

Contribution 8250000 8250000 8250000 8250000 8250000 8250000 8250000

FC 4000000 4000000 4000000 4000000 4000000 4000000 4000000

Depreciation 2500000 1875000 1406250 1054688 791015.6 593261.7 444946.3

PBT 1750000 2375000 2843750 3195313 3458984 3656738 3805054

PAT 1137500 1543750 1848438 2076953 2248340 2376880 2473285

CF 3637500 3418750 3254688 3131641 3039355 2970142 2918231

Disc CF 3247768 2725407 2316622 1990214 1724612 1504766 1320060

• Forecasts under different assumptions

Variable Pessimistic Expected Optimistic

Sales Vol 750 1000 1250

SP 12.75 15 16.50

VC/unit 7.425 6.75 6.075

FC 4800 4000 3200

• NPV Forecasts under different Assumptions

Variable Pessimistic Expected Optimistic

Sales Vol ( 1289) 4829 10948

SP (1845) 4829 9279

VC/unit 2827 4829 6832

FC 2456 4829 7203

Pros and cons of Sensitivity analysis

• Compels decision maker to identify variables that affect cash flows , hence helps to look at project in totality

• Indicates critical variables, weak spots

• Guides decision maker to concentrate on key variables

• Fails to focus on inter relations between variables

Scenario analysis

• Sensitivity analysis assumes variables are independent

• Scenario analysis takes a combination of variables• Variables Expected Scenario 1 • Sales vol 1000 1250• SP 15 13.5• VC / unit 6.75 7.10• FC 4000 4400NPV = (1250 ( 13.5 – 7.10) – 4400 ))* 0.65 *4.5638 +

2222 – 10000 = 2901

• Cash flow For each year

• ( R – VC – FC – Dep ) * ( 1-T) + Dep

= (R – VC – FC ) ( 1- T) + Dep – Dep ( 1- T)

= (R – VC – FC ) ( 1- T) + T * Dep

NPV =

(1250 ( 13.5 – 7.10) – 4400 ))* 0.65 *4.5638 + 2222 – 10000 = 2901

Break even analysis

(V ( 13.5 – 7.10) – 4400 ))* 0.65 *4.5638 + 2222 = 10000

(1250 ( SP – 7.10) – 4400 ))* 0.65 *4.5638 + 2222 = 10000

Statistical techniques

• Cash flow Prob Expected value

4000 0.1 400

5000 0.2 1000

6000 0.4 2400

7000 0.2 1400

8000 0.1 800

6000

Std deviation =√ ( 4000 – 6000)2 0.1 + ………

CV = sd / expected value

Uncorrelated cash flows

• Year 1 Year 2 Year 3 CF Prob CF Prob CF Prob 3000 0.3 2000 0.2 3000 0.3 5000 0.4 4000 0.6 5000 0.4 7000 0.3 6000 0.2 7000 0.3Expected CF 5000 4000 5000Variance 2400000 1600000 2400000Initial I 10000

Risk of project

• Std deviation of project

- independent ( uncorrelated) cash flows

- std dev =√ ∑ ٥ 2 / ( 1 + r)2t

- = √ (2400,000 / 1.062 + 1600,000 / 1.064 +…….

- perfectly correlated cash flows

- std dev = ∑ ٥ / ( 1 + r) t

Simulation

• Helps to understand likelihood of occurrence – not possible in Sensitivity analysis

• Steps – specify parameters which remain unchanged and stochastic vars or exogeneous vars outside the control of decision maker

Simulation • Parameters – r = 10% ,I = 13000• Annual Prob Project life Prob cash flow 1000 0.02 3 0.05 1500 0.03 4 0.10 2000 0.15 5 0.30 2500 0.15 6 0.25 3000 0.30 7 0.15 3500 0.20 8 0.10 4000 0.15 9 0.03 10 0.02

• CF Prob Cumm Random nos

1000 0.02 0.02 00-01

1500 0.03 0.05 02- 04

2000 0.15 0.20 05-19

2500 0.15 0.35 20-34

3000 0.30 0.65 35 -64

3500 0.20 0.85 65-84

4000 0.15 1.00 85-99

Random no

53 3000

66 3500

• Proj life Prob Cumm Random nos 3 0.05 0.05 00 - 04 4 0.10 0.15 05 - 14 5 0.30 0.45 15 - 44 6 0.25 0.70 45 - 69 7 0.15 0.85 70 - 84 8 0.10 0.95 85 - 94 9 0.03 0.98 95 - 97 10 0.02 1.00 98 -99 Random nos Life Annual cash flow 97 9 53 3000 99 10 66 3500

Random Nos

• Cash flow Project life 53 97 66 99 30 81 19 9 31 67 81 70 38 75 48 83 90 33 58 52

Result

• R no CF Rno Life NPV

53 3000 97 9 4277

66 3500 99 10 8506

30 2500 81 7 (829)

19 2000 09 4 ( 7660)

Decision Tree Analysis

• A firm is ready for pilot production and test marketing. This will cost Rs 20 m and takes 6 months. There is 70% chance that pilot prod and test marketing will be successful. In case of success, the firm will build a plant for 150m . The plant will generate an annual cash flow of 30 m for 20 years if demand is high and 20 m if demand is moderate. High demand has prob 0.6 and moderate demand prob 0.4. Cost of capital is 12%.