Investors often have confusion about the rate of return used in annuities in general and in Secondary Market Annuities in particular. All our SMA cases are shown with an effective rate, which is equivalent to an Internal Rate of Return or Annual Percentage Yield (APY).
Effective rate, Internal Rate of Return, and Annual Percentage Yield (APY) are three terms to describe the same thing for these cases. The effective rate is the yield of the series of cash flows, including the investment (negative) and payments (Positive).
You can calculate this using the XIRR function in MS excel or HP handheld calculators, and we use a program called T-Value.
Effective rate also takes into consideration the return of principal with each payment. For example, with an SMA, if you have 100 equal monthly payments, a portion of each payment is principal and a portion is interest. When you receive principal back with payment #1, the next compounding period has less of a base of principal to work with, therefore payment #2 has slightly less interest and slightly more principal. This is how an amortizing mortgage works also.
Nominal interest rate is also defined as a stated interest rate, Annual Percentage Rate, and APR. This rate does not reflect the true yield on the investment or loan because it does not take into account the compounding periods.
For example, your mortgage might have a 4% nominal Annual Percentage Rate. However as you pay down the principal, more money is returned to the lender, thus their Annual Percentage Yield or Effective Rate, is higher than the 4% Nominal Rate.
Nominal Rate Vs Effective Rate
Most likely you have seen APR and APY disclosures on mortgage loans and credit card offers. Often times, the APR, or nominal interest rate is less than the effective rate. However, the Effective Rate depicts the true picture of financial payments because it includes the compounding period and any return of principal.
Effective Rate is the true measure of the yield of an investment.
Interest Rate and Time
As shown in the example below, interest rate is only meaningful in the context of time and the compounding period. Most often, when people say an interest rate it’s with the assumed context of “per year.”
But there are other compounding periods available – common options are month, week, or day.
It’s important to note that the Effective Yield to you as an SMA investor or as a lender with compounding other than annual will be different than the nominal rate.
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 annual compounding will yield $100 in 1 year. The annual compounding is critical- the nominal and effective rate are both 10% in this example.
But if monthly compounding is used, the same investment of $90.91 results in $100 in 1 year, and the same Effective Rate (APY) of 10%, but a Nominal Rate (APR) of 9.56%. The payments are the same, but the rates are different because of the compounding period.
Now lets look at a slightly different example:
You borrow $98,770.17 with a 10 year amortizing mortgage with a 4% nominal interest rate and monthly compounding. You make 120 monthly payments of exactly $1000/ month. Your total payments are $120,000.
The nominal rate on the mortgage is 4%, but the lender’s Effective Rate or APY 4.074%.
This type of payment stream is just like an SMA, but you are the one receiving the payments. Your Effective Rate is 4.074%, your investment is $98,770.17, and you have 120 monthly payments of $1000.
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, TVal 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 TVal in their calculations.