# Opportunity Cost of Captial and Present Value

May 23

When it comes time to inform an investment decision, it’s essential to know whether or not a present opportunity represents enough present value to justify the investment. If so, at what level and over what time period. Certainly risk factors in, and with such a broad range of opportunities today, including stock markets, bonds, start ups, etc., there’s a lot to take in to account.

The answer to the value and timing of an investment with respect to other available investments is given by the Present Value formula (ref for all equations).

$P_v=\frac{C}{(1+r)^t}$

where

• P is the present value
• C is the anticipated future cash flow
• r is the interest rate of an alternative investment of similar risk
• t is the number of investment periods. This may change depending on compounding

Another way to look at this is as a cash flow C and a Discount Factor D.

$P_v=C D_f$

where

$D_f=\frac{1}{(1+r)^t} \cdots$

The rate r above is the opportunity cost of captial, or opportunity cost.

Note that for multiple cash flows, the equation can be summed

$P_v=\frac{C_1}{(1+r)^1} + \frac{C_2}{(1+r)^2} + \cdots + \frac{C_t}{(1+r)^t}$

## Amount, Time and Risk

From an investment perspective, the focus of the above equation is cash flow. More specifically,

• Amount of cash flow
• Timing of the cash flow
• Risk associate with the cash flow

All three items factor in to the present value formula, and the present value formula informs many financial decisions, including being the basis for perpetuity and annuity analysis and calculation.

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