Impact of the Risky Situation on Present Value

 An investment that is more risky must offer higher returns (if only potential), than safer investments.  If it did not, why would anyone invest in it? 

One impact on the present value is that the the required interest rate will be increased by the ‘risk premium’, which is the additional rate on top of the risk-free rate.  If the risk free rate was for example 2%, and the risky investment offers a risk premium of for example, 8%, then the total interest rate of the investment would be 2% + 8% = 10%.

The simple formula for present value:

CV = PV (1 + i)^t

needs to be adjusted to include the risk premium:

CV = PV (1 + i + rp)^t

Where:

CV = cash value in the future 
PV = cash value in the present (most commonly known as present cash value) 
i = interest rate of a given time period (for example, the interest rate for 1 year) 
rp = risk premium 
t = the number of time periods to consider

Example: What is the present value of an investment that will give us $12,000 one year from now, if the risk-free interest rate was 2% and the risk premium was 8%?

CV = PV (1 + i + rp)^t  12,000 = PV (1 + 0.02 + 0.08)^1  PV = 12,000 / (1.10)  PV = $10,909

What does $10,909 mean?

1. $10,909 today, if invested for one year at the combined risk-free and risk premium rate would return $12,000 in one year.
2. $12,000 one year from now is worth $10,909 today if a comparable investment is available today.

For the sake of comparison, what is the present value of $12,000 -- to be received one year from now -- without the risk premium?

CV = PV (1 + i + rp)^t  12,000 = PV (1 + 0.2 + 0.0)^1  PV = 12,000 / (1.02)  PV = $11,534