1. Risk Analysis and Real Option
Unit 3

2. Sensitivity Analysis

3. Calculation: Revenue: No of unit sold= Market share * Size of market
Annual Sales= No of unit sold * Price
Cost
Variable Cost= variable cost per unit * no of unit sold
Total Cost = Variable cost + Fixed cost

4. Example:

6. Sensitivity The change in NPV for every unit change in sales=
sensitivity = Change in NPV/ change in Sales unit
If sales were to drop by X units,
then NPV would drop by= sensitivity * X units dropped
The change in OCF for a $1 change in variable costs is:
sensitivity = Change in OCF/Change in variable cost

7. Scenario analysis

8. Financial Bep Equivalent Annual Cost = Initial investment / PVIFA
Financial BEP = EAC+FC (1-tc) – Depreciation * tc [(SP –VC)* (1-tc)]

9. Real options-expand
Expected NPV= -$12 million + $2million /.20 = - $2 million
Optimistic NPV = -$12 million + $3 milliony/.20 = $3 million
Pessimistic NPV = -$12 million + $1 milliony/.20 = -$7 million
Expected NPV = 50% * $3 million + 50% * (-$7 million) = -$2 million
Expansion of 10 location if success
NPV = 50% * 10 * $3 million + 50% * (-$7 million) = $11.5 m.

11. The option to abandon
Optimistic forecast: -$12 million + $6 million/.2 = $18 million
Pessimistic forecast: -$12 million - $2 million/.2 = -$22 million
Expected NPV =50% * $18 million + 50% * (-$22 million) = -$2 million
If project failes then abandon after year 1 Expected NPV
= 50% * $18 million + 50% * (-$12 million - $2 m/1.20) = $2.17 million

13. Timing option
Initial cost= 18 million and will decline by $130,000 per year until it reaches $1,150,000, life= 10 years and annual cash inflow of
NPV0 = –$1,800,000 + $340,000(PVIFA12%,10) = $121,075.83
NPV1 = [–$1,670,000 + $340,000(PVIFA12%,9)] / =$126,432.97
NPV2 = [–$1,540,000 + $340,000(PVIFA12%,8)] / 1.12^2 = $118,779.91
NPV3 = [–$1,410,000 + $340,000(PVIFA12%,7)] / 1.12^3 = $100,843.05
NPV4 = [–$1,280,000 + $340,000(PVIFA12%,6)] / 1.12^4 = $74,913.91
NPV5 = [–$1,150,000 + $340,000(PVIFA12%,5)] / 1.12^5 = $42,911.04
NPV6 = [–$1,150,000 + $340,000(PVIFA12%,4)] / 1.12^6 = –$59,428.45