Capital Budgeting under Risk and Uncertainties^141
what level of sales will the project have a zero NPV?
To illustrate how the financial break-even level of sales is calculated, let us go back
to the flour mill project. The annual cash flow of the project depends on sales as
follows:- Variable costs : 66.67% of sales
- Contribution : 33.33% of sales
- Fixed costs : Rs. 1 million
- Depreciation : Rs. 2 million
- Pre-tax profit : (0.333 Sales) ñ Rs. 3 million
- Tax (at 33.3%) : 0.333 (0.333 Sales ñ Rs. 3 million)
- Profit after tax : 0.667 (0.333 Sales ñ Rs. 3 million)
- Cash flow (4 + 7) : Rs. 2 million + 0.067 (0.333 Sales ñ Rs. 3 million)
= 0.222 Sales
Since the cash flow lasts for 10 years, its present value at a discount rate of 12 per
cent is:
PV(cash flows) = 0.222 Sales x PVIFA (10 years, 12%)
= 0.222 Sales x 5.650
= 1.255 Sales
The project breaks even in NPV terms when the present value of these cash flows
equals the initial investment of Rs 20 million. Hence, the financial break-even occurs
when
PV (cash flows) = Investment
1.255 Sales = Rs. 20 million
Sales = Rs. 15.94 million
Thus, the sales for the flour mill must be Rs 15.94 million per year for the investment
to have a zero NPV. Note that this is significantly higher than Rs 9 million which
represents the accounting break-even sales.
Hillier Model
Under certain circumstances, the expected net present value and the standard deviation
of net present value may be obtained through analytical derivation. Two cases of such
analysis are discussed here: (i) no correlation among cash flows and (ii) perfect
correlation among cash flows.
Uncorrelated Cash Flows
When the cash flows of different years are uncorrelated, the cash flow for year t is