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Capital Budgeting under Risk and Uncertainties^159

that is acceptable to management. This is quite understandable. If the profitability index

is high, one profitability that the net present value is negative (profitability index is less

than 1) is negligible even if the dispersion is wide.

Risk Adjusted Discount Rate Method

The risk adjusted discount rate method calls for adjusting the discount rate to reflect

project risk. If the risk of the project is equal to the risk of the existing investments of

the firm, the discount rate used is the average cost of capital of the firm, if the risk of

the project is greater than the risk of the existing investments of the firm, the discount

rate used is higher than the average cost of capital of the firm; if the risk of the project

is less than the risk of the existing investment of the firm the discount rate used is less

than the average cost of capital of the firm. The risk adjusted discount rate is :

rk = i + n + dk

where rk = risk-adjusted discount rate for project k

i = risk-free rate of interest

n = adjustment for the firmís normal risk

dk = adjustment for the differential risk of project k

It may be noted that (1 + n) measures the firmís cost of capital dk may be positive or

negative depending on how the risk of the project under consideration compares with

the existing risk of the firm.

The adjustment for the differential risk of project, k quite understandably, depends on

managementís perception of the project risk and managementís attitude towards towards

risk (risk return preference). A large pharmaceutical concern, for example, uses the

following riskadjusted discount for various types of investments.

Investment category Risk-adjusted discount rate

Replacement investments Cost of capital

Expansion investments Cost of capital + 3%

Investment in related lines Cost of capital + 6%

Investment in new lines Cost of capital + 10%

Once the projectís risk-adjusted discount rate (rk) is specified, the project is accepted

if its net present value, calculated as follows, is positive.

NPV =

A

rk

t

t

t

n

( 1 )

1

1 +

• =

I ...(8.7)

where NPV = net present value of project k