Certainty-Equivalent: It is a method in which uncertain cash flows are converted into certain cash flows by multiplying with probability of occurrence such cash flows .Certainty coefficient assumes value between 0 and 1. In this method risk free rate are used instead of risk-adjusted discount rate. We would use either IRR or NPV for evaluation of a project.
By using NPV method:
NPV > 0 project accepted
NPV < 0 project rejected
NPV = 0 project may be accepted or rejected
By using IRR method:
IRR > r project accepted
IRR < r project rejected
IRR = 0 project may be accepted or rejected
Formula of Certainty Coefficient:
Certainty Coefficient = Expected Cash Flows
(Certain cash Flows) / Risky Cash Flows
= Expected Cash Flows (Certain cash Flows)/ (1+risk
premium rate)
Example: In
below table 5 years cash inflows and certainty coefficient are given which
shows the probability of occurrence of cash flows.
Year
|
Cash inflows
|
Certainty Coefficient
|
1
|
28,000
|
0.8
|
2
|
32,000
|
0.6
|
3
|
46,000
|
0.4
|
4
|
58,000
|
0.2
|
The initial cost of investment is Rs.65, 000 and
the discount rate is 8% annually. Find out the NPV with the help of
certainty-equivalent method.
Solution:
Year
|
Cash inflows
|
Certainty Coefficient
|
Certain-Equivalent Cash flows
|
Discount Rate 8%
|
Present Value
|
1
|
28,000
|
0.8
|
22400
|
1.08
|
20,740.74
|
2
|
32,000
|
0.6
|
19200
|
1.17
|
16,410.26
|
3
|
46,000
|
0.4
|
18400
|
1.26
|
14,603.17
|
4
|
58,000
|
0.2
|
11600
|
1.36
|
8529.41
|
Total
|
60,283.58
|
NPV = Present cash inflows-Cash outflows
= Rs. (60,283.58-65, 000)
= - Rs.4,716.42
NPV is negative which means project is not
acceptable.
By using IRR method:
Let’s assume r =10%
Year
|
Certain-Equivalent Cash flows
|
Discount rate 10%
|
Present Value
|
1
|
22400
|
1.1
|
20,363.63
|
2
|
19200
|
1.21
|
15,867.76
|
3
|
18400
|
1.33
|
13,834.58
|
4
|
11600
|
1.46
|
7,945.20
|
Total
|
58011.17
|
NPV = Present Value of cash inflows – Cash Outflows
= Rs. (58011.17-65000)
=- Rs.6988.83
Let’s assume r = 4%
Year
|
Certain-Equivalent Cash flows
|
Discount rate 10%
|
Present Value
|
1
|
22400
|
1.04
|
21,538.46
|
2
|
19200
|
1.08
|
17,777.77
|
3
|
18400
|
1.12
|
16,428.57
|
4
|
11600
|
1.16
|
10,000
|
Total
|
65744.8
|
NPV = Present Value of cash inflows – Cash Outflows
= Rs. (65744.8-65000)
= Rs. 744.8
IRR = lower rate+ (NPV at lower rate/ (NPV at lower
rate-NPV at higher rate))*(higher rate-lower rate)
= 4+ (744.8/ (744.8- (6988.83)))*(10-4)
= 4.57%
So, this project is rejected due to IRR (4.57%)
< risk free rate (8%).
Example:Company
X wants to invest in project A . Find
out the certainty equivalent cash flows and NPV
of that project if the discount rate is 6% and the expected cash flows
for five year are as follows:
Cash flows
|
Certainty Coefficient
|
5,
000
|
08
|
8,
000
|
0.6
|
8,
900
|
0.7
|
12,
000
|
0.3
|
14,
400
|
0.4
|
Solution:
Year
|
Cash
flows
|
Certainty
Coefficient
|
Certain
equivalent cash flows
|
Discount
rate 6%
|
Present
Value
|
1
|
5, 000
|
0.8
|
4, 000
|
1.06
|
3,
773.58
|
2
|
8, 000
|
0.6
|
4, 800
|
1.12
|
4,
285.71
|
3
|
8, 900
|
0.7
|
6, 230
|
1.19
|
5,
235.29
|
4
|
12, 000
|
0.3
|
3, 600
|
1.26
|
2,857.14
|
5
|
14, 400
|
0.4
|
5, 760
|
1.34
|
4,
298.51
|
Total
|
|
20,
450.23
|
NPV = Present value of cash flows –
Initial investment
= 20, 450.23 – 20, 000
= Rs. 450.23
The NPV of this project is positive. So, the
project A is accepted by the company X.
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