[Dog pounder1977]

Another CPA candidate posted this question and I replied but thought I would post it again for others who may need the same help. Keep in mind I only did the premium of a bond in my example. For the discount all you do is add the amortization amount to the carrying value at the end of each period instead of subtracting and add as well for interest payments. You will understand what I mean after reading my example.

1.) Can you explain, using your own words, the reason that bonds are sold at a discount or a premium?

Sure. First, there are two interest rates that affect the price of a bond: The stated interest rate (which does not change) and the market interest rate (aka effective interest rate). When the market interest rate is GREATER than the stated interest rate the bond will be issued at a discount. Why? Because lenders can earn more interest on bonds elsewhere. If the market interest rate is LOWER than the stated interest rate, the bond will be issued at a premium. Why? Because your stated interest rate is more attractive than the market interest rate where lenders can earn more in interest by purchasing your bond. Therefore, they will be willing to pay more for your bond creating the premium (any amount greater than the maturity value) It is this amount that is subject to amortization (depreciation).

2.) Can you explain the amortization of the discount/premium in plain English, as well as how it affects interest expense and the carrying amount?

Absolutely. Amortization of a bond is referring to how much of the premium or discount is reduced (depreciated via amortization) annually to get the bond amount to the maturity value on the maturity date. For instance, if the stated interest rate is 9% and the market interest rate is 8% the bond will be issued at a premium. Let’s say we have a bond with a par value (aka maturity value aka principal amount) is $100,000 stated interest rate of 9% for 5 years.

Interest is paid in semiannual installments or twice a year or every six months. Let’s say the market interest rate is 8%. That 1 percent difference between the market and stated interest rate will create the premium on the bond. To determine the premium amount of the bond, the first step is to determine the Present Value (PV) of the bond. You would take the par value of $100,00 x the present value of a single amount at 1/2 of the market interest rate (or present amount of $1) times the number of periods (interest payments). If the bond is for 5 years and we pay interest twice a year then the number of periods is 10. So for our example, 1/2 of the market interest rate is 4% (8 divided by 2)

The formula for determining the PV of a single amount is 1 divided by 1+(interest rate).

Step 1: Your formula would look like this: 100,000 x 0.676= $67600. Let’s stop here. I know you may be wondering “Where did you get 0.676 from?” I got that from using the PV of a single amount formula 1/1+4% or 1/1.04 getting 0.961 and keep doing that 10x (10 being the number of interest payments like I stated above). The next step is determine the PV of the stated interest. For step 2, you take the maturity value ff $100,000 (aka par value aka principal amount) and multiply that by the PV of an annuity at 4%. This is where it may get a bit tricky. Remember how I said you take 1/1.04 and keep doing that 10x? Now your going take those same amounts but ADD them to get the PV of an ANNUITY.

For example 1/1.04=0.962 (rounded). Divide 0.962 by 1.04 again and you get 0.925 (rounded). 0.925 is the PV of $1 at 2 periods. Add those two together (0.962+0.925) and you get the ANNUITY at 2 periods. The ANNUITY at 3 periods is 0.925/1.04= 0.889 +0.962+0.925= 2.776. Get it? Keep dividing and keep adding until you reach 10x. After you come up with the annuity at 10 periods amount your formula will look like this (back to STEP 2).

$100,000 x 0.045% (half of the stated interest rate 9% divided by 2). You get $4500. Step three is taking that 4500 and multiplying it by the ANNUITY amount at 10 periods (you should have this by now after dividing and adding like I explained above) So step three is $4500 x 8.111= 36499.5 rounded = 36500. Take 36500 and add that with the PV of the principal amount in Step 1 ($67600)

So now you have the PV (present value) of the bond aka the market price of the bond $104,100 (67600+36500).

Remember where I said the premium is any amount over the maturity value aka par value aka principal amount? In this example it is the extra $4100. (104,100-100,000) This amount is subject to amortization (depreciation) over the life of the bond. All you do from here (assuming it is straight line amortization) is take 4100 divided by the number of periods being 10 and you get $410. The final step for determining interest expense is subtracting 410 from every interest expense you owe. So if the stated interest expense that you promised was 9% for five years of $100,000 means you pay 9000 every year or 4500 twice a year. Subtract the premium amortization amount from that 4500 every time you pay interest and you get $4090 (4500-410). By the 5th and final year or maturity date, you will only have the $100,000 left which is the amount needed to retire the bond.

For the carrying value of the bond of the first year would be $104,100 less the amortization of the premium equals $103280 year two subtract another 820 (410 x 2 interest payments) = $102460 year three subtract another 820 giving you $101,640. Year 4 same thing $100,820 and finally year 5 $100,000 the exact amount needed to retire the bond.

One day I will face that exam.