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What is Risk-Adjusted Discount Rate? How it measure risk?

 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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