Breakeven cash inflow analyses, risk adjusted discount rate (RADR) and scenario analyses are tools that facilitate better insight into managing risk in capital budgeting.

Risk in capital budgeting especially refers to variability of the returns (variability of cash inflows), because the initial investment is more or less known with some level of confidence. Therefore, we need to ensure that present value (PV) of cash inflows will be large enough to ensure that project is acceptable.

To adjust the present value of future cash inflows for risk embodied in particular project, we can either adjust cash inflow directly or we can adjust the discount rate. Because adjusting cash inflow is highly subjective, we will rather adjust discount rate. This is when risk adjusted discount rate technique comes into play.

RADR is a discount rate that must be earned to compensate an investor for the risk undertaken. Under RADR the value of the firm must be at least maintained or must increase. Risk adjusted discount rate is the most popular risk adjustment technique that utilize NPV.

The higher is the risk of specific project, the higher RADR will be.

The deployment of RADR is best illustrated by the use of an example:

**EXAMPLE**

Amanda can invest in two shares, A and B. Both shares presently cost $50 and Amanda wants to hold shares for 4 years. Annual dividends from share A expected to be $7. Annual dividends from share B are expected to be $12. However, shares B are more risky. In 4 years time Amanda expects to be able to sale shares A for $55 each and shares B for $70 each. Amanda’s required return is 8%. However, for shares B she adjusts her return so that her risk adjusted discount rate becomes 12%. Calculate risk adjusted net present values (NPVs) of shares A and B and recommend which shares should Amanda purchase.

**Solution:**

We will use financial calculator to find risk adjusted net present values (NPVs) of shares A and B.

*Risk adjusted NPV of shares A:*

Clear calculator: second function, C ALL

CFo: -50

CF1: 7

CF2: 7

CF3: 7

CF4: 62 (7+55)

I: 8

Second function, NPV: $15.38

*Risk adjusted NPV of shares B:*

Clear calculator: second function, C ALL

CFo: -50

CF1: 12

CF2: 12

CF3: 12

CF4: 82 (12+70)

I: 12

Second function, NPV: $30.94

Since investment in shares B offers higher risk adjusted NPV, Amanda should choose to invest in shares B.

The main difficulty in using risk adjusted discount rate (RADR) technique is in determining level of risk and approximating an appropriate risk adjusted discount rate (RADR). There is currently no systematic way to adjust required return to risk adjusted discount rate (RADR). Management usually determines risk adjusted discount rate (RADR) subjectively.

Sometimes **risk index** is determined which reflects risk adjusted discount rate (RADR) for every subsequent level of risk. For example, risk can be categorized into below average, average, above average and very high. Past experience and CAPM can be used to subjectively determine the risk adjusted discount rate (RADR) appropriate for each subsequent level (category) of risk.

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