Investors often have confusion about the rate of return used in annuities in general and in Secondary Market Annuities in particular. Secondary Market Annuities are in reality quite simple- they are nothing more than an amortizing payment stream, with each payment containing principal and interest.  It is basic  discounted cash flow (DCF) math that uses a discount rate and an amortization schedule to arrive at price.

## Understanding the Amortization Schedule

The amortization schedule shows the principal and interest component of each payment. Amortization refers to the reduction of a debt or investment over time by paying back the debt over the period.  With amortization, each payment is comprised of both a principal repayment component and an interest component on the debt/investment.

After each payment, the remaining principal is the loan or investment balance that is still outstanding. As more principal is repaid with each passing payment, less interest is due/received on the adjusted principal balance. Over time, the interest portion of each monthly payment declines and the principal repayment portion increases.

Amortization is most commonly encountered by the general public when dealing with either mortgages or car loans but in this case, refers to the periodic principal reduction plus the interest returned to an investor over the life of an SMA.

The price paid for an SMA is calculated using the internal rate of return on the payments (IRR). This is the rate that is applied to the diminishing principal balance each month until all the principal and interest has been returned to the investor.

## Time Value of Money Example

Discounted cash flows involve the concept of Time Value of Money- a dollar tomorrow is worth less than a dollar today. How much less? That requires the ‘Discount Rate’ to calculate, and discount rate and effective rate are synonymous for these investments.

Here’s a simple example:

\$100 in 1 year at a 10% discount rate will cost \$90.91 today.

A \$90.91 investment today at a 10% Effective rate with monthly compounding will yield \$100 in 1 year.

## Calculating Effective Rate For Yourself

The Effective Interest rate is also equivalent to the Internal Rate of Return, or IRR. To calculate in MS Excel, use the formula XIRR=((payments),(dates),0). This formula calculates the discount rate, or effective rate, for a given series of payments on definite dates. XNPV may also be used to solve for the purchase price of a series of payments on definite dates at a known discount rate.

Click Here for an Excel sheet of the example above.  Now, because of slight variations in the timing of amortization credits, true Time Value of Money discounted cash flow calculations and Excel end up with slightly different values and XIRR may vary by a few thousandth’s of a point.  The SMA industry and the lending industry all use Time Value math in their calculations.