Radr and certainty equivalent techniques

RISK ADJUSTED DISCOUNT RATE

CERTAINITY EQUIVALENT METHOD

K.PREETHI

09011U0107

RISK-ADJUSTED DISCOUNT RATE

An estimation of the present value of cash for high risk investments is known as risk-adjusted discount rate.

Example:A very common example of risky investment is the real estate.

It is generally calculated as a sum of risk free rate and risk premium.

Risk-adjusted discount rate = Risk free rate + Risk premium.

The variation of risk premium is depending on the risk aversion of investor and the perception of investor about the size of property’s investment risk.

Risk free rate: it is the rate at which the future cash in-inflows should be discounted , if they had no risk.

Risk premium rate: it is the extra return expected by the investors over the normal rate on the account of project being risk.

For higher risk investment project a higher rate will be used and for a lower risk investment project, a low rate will be used.

The risk adjusted discount rate can be used with IRR and NPV methods.

If NPV is positive, then the project may be considered.

In the case of IRR method, the internal rate of return is compared with the risk adjusted rate of return and if the former exceeds the latter, the project can be accepted.

Advantages

Simple to calculate.

Easy to understand.

Risk adjusted rate has a good deal of intuitive appeal in the eyes of risk averse business person.

Disadvantages

It is completely relay on the assumption that investors are risk averse. Through it is mostly true; however, a group of seekers also exists who never demand premium for risk assumption. They willingly paying premium to take risks. Accordingly, with the level of increase, discount rate will decrease.  

Mini case study

A company X is undertaking a project for a period of 3 years. The cash out flow for this project is 1,10,000. the cash inflows for each year are 35,000;42,500; 50,000 respectively. The risk free rate is 8% and the risk premium rate is 4%.

Consider NPV method Total rate of discount is rate of

discount=8+4 =12%

year CFAT Discount factor

PV of cash flow

1 35,000 0.893 31,255

2 45,200 0.797 36,025

3 50,000 0.712 35600

Net present value=Present value of cash inflow-cash out flow

Sum of all cash inflows=1,02,880

NPV=1,02,880-1,10,000 =-7,120

If for the above case assume risk free return is 5% and risk premium rate is 2%

The total discounted rate is now 7%

year CFAT Discount factor

PV of cash flow

1 35,000 0.935 32,725

2 45,200 0.873 39460

3 50,000 0.816 40800

Sum of all cash inflows=1,12,985

NPV=1,12,985-1,10,000 =2,985. hence here we can accept the project.

CERTAINTIY EQUIVALENT METHOD procedure for dealing with risk in capital

budgeting is to reduce the forecasts of cash flows to some conservative levels.

Under the CE approach, the decision maker must first evaluate a cash flow’s risk and then specify how much money, to be received with certainty, will make him or her indifferent between the riskless and the risky cash flows.

Equivalent coefficient

Certainty equivalent =riskless cash flows risky cash flows

Riskless cash flows mean the cash flow which the management is prepared to accept in case there is no risk involved.

It assumes a value between 0 and 1

Acceptance of a project

Certainty equivalent method can be used either with NPV method or IRR method.

In NPV method, a project is accepted if NPV of certainty equivalent cash flow > 0.

In IRR method, a project is accepted if the IRR > risk free rate.

Advantages

The certainty equivalent method is simple and neat

It can easily accommodate differential risk among cash flows.

Disadvantages

There is no practical way to estimate certainty equivalents. Each individual would have his or her own estimate, and these could vary significantly.

To further complicate matters, certainty equivalents should reflect shareholders’ risk preferences rather than those of management. For these reasons, the certainty equivalent method is not used very often in corporate decision making.

Mini case study

A company is considering an investment proposal whose cost is rs.2,10,000. its economic life is 4 years. Risk free rate is 11%. Use IRR method for validating the proposal. The cash flows and certainty equivalent coefficient are as follows:

year Cash inflows Certainty coef.

1 70,000 0.8

2 90,000 0.9

3 60,000 0.85

4 1,30,000 0.75

Solution

Calculation of cash inflows with certainty

year Cash inflow

Coef. Risk less cash flow

1 70,000 0.8 56,000

2 90,000 0.9 81,000

3 60,000 0.85 51,000

4 1,30,000 0.75 97,500

Assuming return of 14% PVs of cash flows:

year Cash inflow

pvf Present value

1 56,000 0.877 49,112

2 81,000 0.769 62,289

3 51,000 0.675 34,425

4 97,500 0.592 57,720

Sum of all present values=2,03,546. Net present value=2,03,546-2,10,000 = -6,454.

Now assuming a return of 10%

year Cash in flow

pvf Present value

1 56,000 0.909 50,904

2 81,000 0.826 66,906

3 51,000 0.751 38,301

4 97,500 0.683 66592.5

Sum of resent values=2,22,704. Net present value=2,22,704-2,10,000 =12,704.

There fore IRR= 10+(12,704/12,704+6,454)x4

= 12.65%

Hence the proposal can be accepted.