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DebtBook's Premium/Discount Amortization Methodology Explained

DebtBook’s new Premium/Discount Amortization feature gives clients the ability to track their amortization of original issuance premium/discount (“OIP” or “OID”) within their DebtBook profile. Utilizing data shown in our “Maturity Detail” tab in your Issue Detail view, DebtBook programmatically calculates the original issue premium/discount on a maturity-by-maturity basis, allowing us to seamlessly generate your premium/discount amortization schedules once you select your amortization method.

Via DebtBook’s Accounting settings, users have the ability to select one of two methodologies for amortizing their premium and discount: (1) “Effective Interest Rate” or (2) “Straight-Line”. Below we walk through how we calculate each methodology and why we support these two methodologies specifically.

Effective Interest Rate

GASB No. 62 states that any original issue discount or premium on a bond be amortized over the life of the bond utilizing the “interest method” as stated below:

“The objective of the interest method is to arrive at a periodic interest cost (including amortization) that will represent a level effective rate on the sum of the face amount of the debt and (plus or minus) the unamortized premium or discount and expense at the beginning of each period. The difference between the periodic interest cost so calculated and the nominal interest on the outstanding amount of the debt is the amount of periodic amortization.”

DebtBook’s Effective Interest Rate methodology reflects this “interest method” as referenced in GASB 62. While we know a majority of governmental issuers utilize the “Straight-Line” method due to its simplicity, DebtBook’s Premium/Discount feature will allow you to comply with the GASB standard by simply selecting the “Effective Interest Rate” method in your Accounting Settings.

The Effective Interest Rate method calculates a premium/discount amortization for each maturity on a stand-alone basis, then combines these values to generate a total amortization schedule for the issue in whole.

Callable Bonds. Unlike the straight-line method, the Effective Interest Rate method takes into account if a maturity is “Priced to Call” or “Priced to Maturity”. Municipal bonds are required to be reported at their “yield to worst”, or lowest yield. In the event a premium bond (coupon > yield) is callable, in the overwhelming majority of cases that bond will be priced assuming it is redeemed at its call date, and not its actual maturity date. This results in a yield that is “worst”, or lower, on the bond's call date, as opposed to the yield if the bond was redeemed at maturity. Let’s take a look at the pricing of our Series 2022 Water and Sewer Revenue Bond Series which was issued on 7/16/2022:

PD Blog-Fig 1-Series 2022 Bond Pricing

The 8/1/2035 maturity of our bond series has a 5.00% coupon and a 2.53% yield, and is callable on 8/1/2032. The 2.53% yield represents the yield assuming the bond is called on 8/1/2032, as compared to the Yield to Maturity which assumes the bond is outstanding until maturity. As the yield to call represents the lower yield or “yield to worst”, this is the yield on which the price is calculated, and thereby the premium is generated.

PD Blog Replace 1

The opposite is true for bonds that are callable but structured as discount (coupon<yield) bonds. See the example below. As the “yield to worst” on a discount bond is the yield to maturity and not the yield to call, the price of a callable discount bond is calculated off of the yield to maturity, and thereby the discount is generated.

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Given the price for each maturity is calculated off of the “yield to worst”, when amortizing premium/discount over the life of the bond, you would amortize the premium or discount to whichever date the bond is priced. So using our example above, on our callable premium bond maturing on 08/01/2035, we would amortize our premium to 08/01/2032, the call date of the issue and the date to which the bond is priced. In the case of our discount bond, we would amortize the discount amount to 08/01/2041, the maturity date of the bond. Note non-callable bonds will always be amortized to their maturity date as there is no alternative redemption date available.

How it’s Calculated. Now that we’ve established to which date we’ll be amortizing our premium or discount, we can walk through the calculation. The Effective Interest Rate method compares a bond’s Face Value Stated Interest to the bond’s Book Value Effective Interest, let’s walk through what each of these terms mean and how they are calculated.

Face Value Interest. Face value interest simply means the actual interest paid through the life of the maturity. Using our examples above, the stated interest is outlined in the below chart for each of our example maturities. For purposes of our effective interest rate calculation, the stated interest on the 8/1/2035 maturity is shown to the 8/1/2032 call date and not the 8/1/2035 maturity date, as we’re showing our face value interest to the date that coincides with which the price is calculated.

PD Blog - Fig 4-Face Value

Book Value Effective Interest. Book Value Effective interest is calculated similar to traditional Face Value Interest, but uses different inputs. “Book Value” represents the Par Amount of a maturity plus/(minus) the outstanding premium/discount amount on the maturity. Using our previous examples, see below for the initial book value of our bonds maturing on 8/1/2035 and 8/1/2041.

PD Blog-Figure 5

As we amortize the premium/discount over the life of the bond, the book value is reduced back to its original par amount at either the maturity date or the call date, again depending on how the bond is priced.

To calculate the Book Value Effective Interest, the Outstanding Book Value on a maturity is multiplied by that maturity’s yield.

Outstanding Book Value * Yield on Maturity = Effective Interest

To calculate the effective interest amount on our First Interest Payment date for our 8/1/2035 maturity, we would do the following calculation:

$14,406,692 * 2.530% = $197,432

Putting it all together. Now that we know the component parts of the Effective Interest Rate Method, we can put them together to generate our premium/discount amortization schedule. To calculate the amount of premium amortized on each payment date, the following calculation is applied:

Face Value Interest - Effective Interest = Premium/(Discount) Amortization

See the example below for the calculation of Premium Amortization on the first Interest Payment date for the 2035 maturity of the Series 2022 Bonds:

PD Blog-Figure 6

Our Face Value Interest of $320,396 less our Effective Interest of $197,432 results in a premium amortization of $122,964 on our first interest payment date on 2/1/2023. We can then reduce our premium balance and book balance by the $122,964 premium amount, to give us our remaining outstanding Book Balance of $14,283,728 on 2/1/2023.

This calculation is then continued through either the maturity date of the bonds or the call date, as is the case for our 8/1/2035 maturity and is shown below. As a callable premium bond, our premium is amortized in full on the call date of 8/1/2032.

PD Blog-Figure 7

Provided below is the same calculation for our 8/1/2041 maturity, which is amortized to maturity as a discount bond.

PD Blog-Fig 8

These calculations are applied individually to each maturity within a series when using the Effective Interest Rate method. See below for our total premium/discount amortization schedule for our Series 2022 issue. Note the dynamic of the premium amortization rolling off on the call date, and the discount amortization continuing thereafter, reflective of the dynamic we discussed above.

PD Blog - Fig 9

 

Straight-Line Method

While the Effective Interest Rate method provided in DebtBook is the “correct” approach per the standard, we know in practice many issuers utilize the “Straight-Line” method when calculating their premium/discount amortization.

As is to be expected, the calculation for Straight-Line is more straightforward than the Effective Rate Method outlined above. In the case of Straight-Line, the total net premium/discount is simply divided by the number of days from the dated date, to the final maturity date, thereby generating a level or “Straight-Line” amortization across the life of the bonds. We can use the example of the Series 2022 Bonds we used for our effective interest rate calculations.

Our Series 2022 Bonds have a total net premium amount of $32,340,205 with a dated date of 7/16/2022, and a final maturity date of 8/1/2041. Assuming a 30/360 day count, there’s a total of 6,855 days from our dated date to our final maturity date. When we divide our total premium of $32,340,205 by 6,855 days (assuming a 30/360 day count), we will be amortizing $4,717.75 per day of our net premium. By amortizing daily, we can see our straight-line amortization at any date alignment and frequency we prefer. The graphic below shows the amortization on our payment dates (actual frequency) and on an annual frequency.

PD Blog-Fig 10

Amortization Start Date. When utilizing straight-line methodology, we also give clients the flexibility to set when they want to begin the net premium/discount amortization. The default setting in the application will start amortizing your net premium/discount on the bond’s Dated Date. Again, keeping in mind the application amortizes premium/discount daily, if our bond is dated on 7/16/2022 like in our example, the application would amortize 15 days of premium/discount (assuming a 30/360 day count) in July, then a level 30 days in each month thereafter. As an alternative, DebtBook offers the option of “First of the Month after Dated Date”, which in our scenario above would begin amortizing the bonds on 8/1/2022, and show no amortization in July. As we’re shifting 15 days of amortization, this results in slightly different amortization schedules on a monthly basis depending on which approach you choose.

PD Blog-Fig 11

Day Count Methodology. As we amortize our premium/discount daily, DebtBook gives you the option of utilizing a 30/360 day count or an Actual/Actual day count when generating your premium/discount amortization schedules when using either Effective Interest or Straight-Line methodologies. The graphic below demonstrates the difference between both methods when viewing the Straight-Line amortization on a monthly basis for the first 4 months the issue is outstanding. As you would expect, utilizing “Actual/Actual” day count amortizes premium based on the actual days of the month (31 days of amortization in October), vs. 30/360 which assumes a level 30 days in every month (30 days of amortization in October).

PD Blog-Fig 12

 

 

 

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