The fair market value of a cash flow stream that includes an annuity is the amount of money you would need today to match the value of all future payments. It accounts for the time value of money, which means money now is worth more than money later because it can earn interest.

To calculate the fair market value, you find the present value of the annuity. This process discounts each payment back to the present using an interest rate, which reflects how much you could earn by investing the money.

Steps to Calculate Fair Market Value

1. Identify the cash flow stream (regular payments).
2. Determine the interest rate at which you could invest the money (the discount rate).
3. Use the formula for the present value of an annuity to calculate the fair market value.

Formula for Present Value of an Annuity

The formula is:

Where:

• $P$ = present value (fair market value)
• $R$ = regular payment amount
• $i$ = interest rate per payment period
• $n$ = total number of payments

Example

Suppose you receive $500 every year for 4 years, and the money could be invested to earn 5% annual interest. How much is this cash flow stream worth today?

Step 1: Identify the Values

• $R=500$ (payment amount),
• $i=0.05$ (annual interest rate),
• $n=4$ (4 annual payments).

Step 2: Use the Present Value Formula

Substitute the values into the formula:

Final Answer

The fair market value of the cash flow stream is $1,772.98.

This means if you had $1,773.00 today and invested it at 5% interest, it would grow to match the total value of the $500 payments over 4 years.

Key Points

• The fair market value is the present value of all future payments.
• Use the interest rate ($i$) to discount future payments back to their value today.
• Use the present value formula to calculate the total worth of the annuity.