How to measure risk with Standard Deviation and Coefficient of Variance?

Standard deviation: It comes under statistical technique of probability distribution method in which probability of likely occurrence of an event is multiply with cash inflows to find out the expected net cash flows which shows the certain cash inflows in future and then NPV is calculated .

With the help of expected net cash flows standard deviation is calculated to measure the risk through deviation from one project to another in cash inflows.

Formula of Standard deviation:

Standard deviation (S.D) = √ (Net Cash Flows-Expected Net cash Flows) ² *Probability

Coefficient Variance: It also helps in measuring the risk in capital budgeting by dividing standard deviation with expected cash flows. It is calculated when investors are more concern about risk then return.

Coefficient Variance = Standard deviation / Expected Net Cash Flows

Example: Find out the standard deviation with the help of expected net cash flows (ENCF) of the following 5 years cash flows @ 12% annually. The initial cost of investment is Rs.30, 000.

Year	Project A	Probability	Project B	Probability
1	33000	0.2	36000	0.3
2	47000	0.4	40000	0.2
3	52000	0.1	59000	0.1
4	68000	0.1	78000	0.3
5	76000	0.2	82000	0.1

Solution:

Calculation of Expected Net Cash Flows:

Year	Project A	Probability	Expected Net Cash Flows	Project B	Probability	Expected Net Cash Flows
1	33000	0.2	6600	36000	0.3	10800
2	47000	0.4	18800	40000	0.2	8000
3	52000	0.1	5200	59000	0.1	5900
4	68000	0.1	6800	78000	0.3	23400
5	76000	0.2	15200	82000	0.1	8200
Total			52600			56300

Calculations of Standard Deviation:

Year	Expected Net Cash Flows (ENCF)	(Cash inflows-ENCF) 2 * P	Expected Net Cash Flows	(Cash inflows-ENCF) 2 * P
1	6600	139392000	10800	190512000
2	18800	318096000	8000	204800000
3	5200	219024000	5900	281961000
4	6800	374544000	23400	894348000
5	15200	739328000	8200	544644000
Total	52600	1790384000	56300	2116265000
	S.D	√1790384000 =42312.92	S.D	√2116265000 = 46002.88

According to standard deviation higher deviation higher risk therefore project A is less risk averse than project B.

Example: Find out which project is best for investment purpose between A and B project.

Year	Project A	Probability	Project B	Probability
1	24,000	0.4	22,000	0.2
2	39,000	0.5	29,000	0.6
3	46,000	0.1	34,000	0.2

Find out the coefficient of variance.

Solution:

Calculation of Expected Net Cash Flows:

Year	Project A	Probability	Expected Net Cash Flows	Project B	Probability	Expected Net Cash Flows
1	24,000	0.4	9600	28,000	0.2	5600
2	39,000	0.5	19500	32,000	0.6	19200
3	46,000	0.1	4600	45,000	0.2	9000
			33700			33800

Calculation of Standard Deviation:

Year	Expected Net Cash Flows (ENCF) Project A	(Cash inflows-ENCF) 2 * P	Expected Net Cash Flows Project B	(Cash inflows-ENCF) 2 * P
1	9600	82944000	5600	100352000
2	19500	190125000	19200	98304000
3	4600	17139000	9000	259200000
Total	33700	444465000	33800	457856000
	S.D	√444465000 = 21082.33	S.D	√457856000 = 21397.57

Coefficient Variance = Standard deviation / Expected Net Cash Flows

Project A:

= 21082.33 / 33700

= 0.625

Project B:

= 21397.57 / 33800

= 0.633

According to coefficient of variance project A and B shows equal risk. So, anyone of them can be chosen for investment purpose.