I have a beginner’s doubt in regards to Amortized Cost and amortized Discount concepts.
I wanted to know why Amortized discount is calculated as Interest Income minus Coupon Payment. What is the explanation behind it? And why is that, when using the amortized cost approach, we got to ADD the discount to the initial bond price?
I’m also wondering when we calculate unrealized gains of a bond, we subtract the amortized discount from the difference between fair value and initial bond cost. What’s the meaning behind this calculation? Below there is an exercise as an example.
ABC Ltd purchased a 10% annual coupon bond at the beginning of the year with a nominal value of $100,000 at a price of $94,205 to yield 12%. The fair value of the bond at the end of the year is $97,430.
Determine the impact on the company’s balance sheet and income statement if the bond is classified as:
Amortized cost.
Fair value through profit and loss.
Fair value through other comprehensive income.
Solution for Amortized Cost
Amortized discount = Interest Income - Coupon Payment = $1,305
Bond’s value at the end of the year = beginning bond investment + Amortized discount = $95,510
Solution for FVPL
The balance sheet is based on fair value of $97,430. Interest revenue of $11,305 and an unrealized gain of ($97,430−$94,205−$1,305)=$1,920($97,430−$94,205−$1,305)=$1,920.
What the amrtized cost method is trying to is 2 fold
That the income statement shows the true cost of interest on the amount borrowed. Think about a zero coupon bond. If the I/S only had coupons there would be no interest cost on the balance sheet.
The balance sheet shows the Present value of the liability. Again with a zero coupon bond think about the chnage in year. The liability will increase. Where are we showing the increase in liability on the accounts? Well it is part of the yearly cost of borrowing - the interest costs.
This is similar if you own a bond as an investment. If we own a zero coupon bond the value will increaase as we approach maturity. This is not “capital gain” just the natural move to par we would expect. We recognise this as amortiszation of the discount.
Not sure of you have looked at fixed income yet. But if we have a bond coupon (10%) < yield (12%) the bond will trade below par/maturity value. As time moves on assuming nothing else chnages we expect this bond fair value to move towards par.
So wether we own or issue a bond we reflect this movement in the blance sheet and income statement.
Whne calcating the FVPL as above we think of any gain or loss due to market value not from the purchase price but froom what we would expect the bond price to be.
With a simplier example. A 2 year zero coupon bond when yields are 10%
N = 2 i/Y = 10 FV = 100 PV = 826.
After a year of nothing happens to discount rates we expect bond to sell at
N = 1 i/Y = 10 FV = 100 PV = 909
The balance sheet reflects the PV of the liability and the difference 83 would be interest income (assuming we are talking about holding the bond as investment)
IF the amrket price of the bond was now 950 and we were using the PVPL
We would say . Well I expected bond to trade at 909.
I am going to call (909 - 826) = 83 amortization of discount iincluded in interest income
950 - 909 = 41 = market to market gain.
In this case, the coupon rate is 10%, yield rate is 12%, thus, you can purchase it at a discounted price which is $94,205. Now, imagine that there’s an another bond with a 12% coupon rate which equals to the yield rate, then you should buy it at par value which is $100,000. As time passes to the maturity date, the price of both bonds will converge to $100,000, the difference between these two coupons will gradually be compensated by the difference between the $94,205 and the $100,000 .
Back to this case, you should receive $94,20512% (the price you paid is $94,205 and the yield rate is 12%) , but you only receive your coupon which is 100,00010% , so the difference is $1,305 which is the amount compensated in the first year. Thus, the bond price at the end of year 1 should be $94,205+$1,305.
That’s amortized cost and the calculation of bond price.
Now, the price of the bond at the end of year 1 is $97,430 and it should be $95,510. Thus, the unrealized gain is $97,430- $95,510.
Thank you so much for the quick and neat explanations!
The only point that I still have doubt is why do we need to subtract the amortized discount from the unrealized gains in FVPL?
I get that we have an unrealized gain due to increase in market value of the bond (if we are the bondholder, of course)…do we subtract it because its not an actual “gain” in interest income?
On Mikey’s example, the 83 (discount) equals to interest income because there is no coupon (zero coupon), is that correct?
Assuming no changes to anything.
We would buy the bond at 826
After 1 year we would expect it to see at 909
After 2 years it will be worth 1000 = maturity value.
We think of interest income as yield on bond x opening value
10% x 826 = 82.6 (roughly 83) but that has not come in cash as there is no coupon,
The 83 is amoertisation of the discount - the movement in value over time as we are discounting by less years.
When we want to market to market becuase of chnages in price we compare to "what theoreticaly we think it should be worrth ie. 909 not what we purchases it for.
The bond priced moved from 826 to 950
but 83 of this was due the passage of time. The gain due to “interest income” we would expect on the bond.
909 to 950 = 41 is the actual gain over what I expected.
Think of a different bonn
N = 2 Y/y = 10 PMT = 100 FV = 1000 CPT Price = 1000
N =1 i/Y = 10 PMT = 100 FV = 1000 CPT Price = 1000
Here the coupons at 10% = discount rate (i/y) = 10%
Just due to time we do not expect the bond price to chnage. It reamins at par. OUr expectation due to the maths is price = 1000.
If the market price moves to 1070 at the end of year 1 we have a gain of 70. At year1 we expected 1000 but the price was 1070 = gain at 70.
Back to the first bond.
The price mobed from 826 to 950 = 124
But expected a change of 83 (amortization of the discount) so the unrealised capiital is 124 - 83 = 41.
The 83 is the chnage we epect over time and is ineffect a source of interest income not capital gain.
How does the amortized discount shows up on Balance Sheet and Income Statement?
I understood that the amortized discount sums up to the carrying value of the bond on the balance sheet (under “receivables” if we are talking on the bondholder, right?)
But how about the income statement?
We add the interest income, but what do we do with the coupon value and the amortized discount in each period? Likewise, what happens under the perspective of the issuer?