Risk-Adjusted
Discount Rate: It is a discount
rate which an investors earn for taking risk in investing in a investment
proposal. The discount rate will be higher if the project is more risky and if
project is less risky than the discount rate will be less.
Risk-Adjusted Discount Rate = risk free rate + risk
premium
Risk free rate: It
is the rate which investor earn without taking any risk in investing in
investment project.
Risk premium: It is
the rate of return which an investor earns after taking risk in investing in a
project.
Risk Premium: (Market rate of return-Risk free
rate)*Beta of investment
Advantages of Risk-Adjusted discount rate:
·
It is very simple to calculate.
·
It shows the risk associated with the
project.
Disadvantages of Risk- Adjusted discount rate:
·
It is based on assumption.
·
It does not adjust future cash flows.
·
It does not show the level of risk
involve in project.
Example: Find
out the NPV with nominal discount rate and risk-adjusted discount rate. The
information given is as follows-
·
Discount rate is 9% and risk premium
rate is 6%.
·
Cash flows for 5 years are- Rs.60, 000,
Rs.85000, Rs.52000, Rs.89000 and Rs.93000 respectively.
·
Initial investment is Rs.2, 00, 000.
Solution: Calculate NPV with Risk free rate-
Year
|
Cash flows
|
Discount rate@9%
|
Present Value
|
1
|
60000
|
1.09
|
55045.87
|
2
|
85000
|
1.18
|
72033.89
|
3
|
52000
|
1.29
|
40310.07
|
4
|
89000
|
1.41
|
63120.56
|
5
|
93000
|
1.53
|
60784.31
|
Total
|
291294.7
|
NPV = Present value of cash flows- Initial
investment
= 291294.7-2, 00,000 = Rs.91294.7
NPV is positive. So, this project is acceptable.
Calculate NPV with risk-adjusted discount rate-
Year
|
Cash flows
|
Risk-adjusted discount rate@15%
|
Present Value
|
1
|
60000
|
1.15
|
52173.91
|
2
|
85000
|
1.32
|
64393.93
|
3
|
52000
|
1.52
|
34210.52
|
4
|
89000
|
1.74
|
51149.42
|
5
|
93000
|
2.01
|
46268.65
|
Total
|
2, 48,196.43
|
NPV = Present value of cash flows-
Initial investment
= 2, 48,196.43-2, 00, 000
= Rs.48, 196.43
NPV is also positive in risk-adjusted discount
rate. So, this project is acceptable even if the NPV with risk free rate shows
negative results. But if it gives negative result then this project is not acceptable
because in that case company suffer losses which affect the goodwill of the
company.
Example:
Suppose Company A has three projects (C, D and E)
which show positive NPV. But Company does not have enough money to invest in
all three projects. So, it decides by the management to know which project
increases financial position of the company. Find out the NPV with the help of
risk-adjusted discount rate.
Particulars
|
Initial
investment
|
1st year
|
2nd
year
|
3rd
year
|
Risk free
rate
|
Risk
premium
|
Project C
|
56, 000
|
25, 000
|
10, 000
|
15, 000
|
2
|
5
|
Project D
|
50, 000
|
32, 000
|
12, 000
|
41, 000
|
1.2
|
4
|
Project E
|
85, 000
|
12, 000
|
30, 000
|
53, 000
|
3
|
7
|
Solution:
Project C
Risk-Adjusted Discount rate = 2+5 = 7%
Project D = 1.2+4 = 5.2%
Project E = 7+3 = 10%
Particulars
|
Initial
investment
|
1st year
|
2nd
year
|
3rd
year
|
Total
|
Project C
|
56, 000
|
25, 000
|
20, 000
|
15, 000
|
60, 000
|
Present
Value
|
23, 364
|
17, 544
|
12, 195
|
53, 103
|
|
Project D
|
68, 000
|
32, 000
|
12, 000
|
35, 000
|
79, 000
|
Present
Value
|
30, 418
|
10, 810
|
30, 172
|
71, 400
|
|
Project E
|
85, 000
|
12, 000
|
30, 000
|
53, 000
|
95, 000
|
Present Value
|
10, 909
|
24, 793
|
39, 850
|
75, 552
|
NPV = Present value of cash flow – Initial investment
Project C = Rs. (53, 103 – 56, 000) = -Rs.2, 897
Project D = Rs. (71, 400 – 68, 000) = Rs. 3, 400
Project E = Rs. (75, 552 – 85, 000) = -Rs. 9, 448
Project D has positive NPV. So, this project is beneficial for the Company.
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