Page 194 - DMGT405_FINANCIAL%20MANAGEMENT

Financial Management

Notes (b) dependent. Independent means cash flows in future years are not affected by cash flows in the
preceding or following years. On the other hand, when cash flows in one period are dependent
on cash flows in previous year, they are referred to as dependent cash flows. Let us first discuss
the application of probability theory to analyze risk in capital budgeting assumption of
independent cash flows:

n Expected cash inflow during each period
1. NPV = å – Cash outflow
+
t = 1 (1 riskless rate of interest)
t = 1 (1 + riskless rate of interest)t
t = years/period
Now expected cash inflow in each period = Diff. levels of cash inflow × Probability at each
level

2
Probability at æ different levels cash inflow expected cash inflow ö
× -
n each level ç in each period each period ÷
2. å è ø
+
t = 1 (1 riskless rate of interest) 2t
3. By making use of normal probability distribution, one can analyze further. The element
of risk in capital budgeting i.e. probability of different expected values of NPV i.e. the
probability, of NPV having the value, zero or less, greater than within the range of two
values and so on. Thus, the normal probability distribution an important statistical
technique in the hands of decision makers for evaluating the extent of risk of the project.

Notes The normal probability has a number of useful properties as follows:
1. The area under normal curve, representing the normal probability distribution
equal to 1 (0.5 on either side of the mean).
2. The curve has its maximum height at its expected value i.e., mean.

3. The probability of occurrence beyond 3 x Standard Deviation is very near zero
(0.26%).
4. Probability of an outcome falling within plus or minus 1 × standard deviation from
the mean is 0.6826 or 68.26%, Range + 2 standard deviation 95.46%. Range + 3 standard
deviation 99.74%.

Example: A company is considering an investment in a project requiring initial outlay
of 50,000 with expected cash inflow generated over 3 years as follows:
Year 1 Year 2 Year 3
Cash flow Probability Cash Flow Probability Cash Flow Probability
( ) ( ) ( )
15000 0.2 20000 0.5 25000 0.1
20000 0.4 23000 0.1 30000 0.3
25000 0.3 25000 0.2 35000 0.3
30000 0.1 28000 0.2 50000 0.3

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