# Illustration of Bonds Purchased at a Premium

When bonds are purchased at a premium, the investor pays more than the face value up front. However, the bond's maturity value is unchanged; thus, the amount due at maturity is less than the initial issue price! This may seem unfair, but consider that the investor is likely generating higher annual interest receipts than on other available bonds - that is why the premium was paid to begin with. So, it all sort of comes out even in the end. Assume the same facts as for the above bond illustration, but this time imagine that the market rate of interest was something less than 5%. Now, the 5% bonds would be very attractive, and entice investors to pay a premium:

 1-1-X3 Investment in Bonds 5,300 Cash 5,300 To record the purchase of five \$1,000,5%, 3-year bonds at 106 interest payable semiannually

The above entry assumes the investor paid 106% of par (\$5,000 X 106% = \$5,300). However, remember that only \$5,000 will be repaid at maturity. Thus, the investor will be "out" \$300 over the life of the bond. Thus, accrual accounting dictates that this \$300 "cost" be amortized ("recognized over the life of the bond") as a reduction of the interest income:.

 6-30-X3 Cash 125 Interest Income 75 Investment in Bonds 50 To record the receipt of an interest payment (\$5,000 par X .05 interest X 6/12 months = \$125; \$300 premium X6 months/36 months = \$50 amortization)

The preceding entry is undoubtedly one of the more confusing entries in accounting, and bears additional explanation. Even though \$125 was received, only \$75 is being recorded as interest income. The other \$50 is treated as a return of the initial investment; it corresponds to the premium amortization (\$300 premium allocated evenly over the life of the bond - \$300 X (6 months/36 months)) and is credited against the Investment in Bonds account. This process of premium amortization (and the above entry) would be repeated with each interest payment date. Therefore, after three years, the Investment in Bonds account would be reduced to \$5,000 (\$5,300 - (\$50 amortization X 6 semiannual interest recordings)). This method of tracking amortized cost is called the straight-line method. There is another conceptually superior approach to amortization, called the effective-interest method, that will be revealed in later chapters. However, it is a bit more complex and the straight-line method presented here is acceptable so long as its results are not materially different than would result under the effective-interest method.

In addition, at maturity, when the bond principal is repaid, the investor would make this final accounting entry:

 12-31-X5 Cash 5,000 Investment in Bonds 5,000 To record the redemption of bond investment at maturity

In an attempt to make sense of the above, perhaps it is helpful to reflect on just the "cash out" and the "cash in." How much cash did the investor pay out? It was \$5,300; the amount of the initial investment. How much cash did the investor get back? It was \$5,750; \$125 every 6 months for 3 years and \$5,000 at maturity. What is the difference? It is \$450 (\$5,750 - \$5,300) - which is equal to the income recognized above (\$75 every 6 months, for 3 years). At its very essence, accounting measures the change in money as income. Bond accounting is no exception, although it is sometimes illusive to see. The following "amortization" table reveals certain facts about the bond investment accounting, and is worth studying to be sure you understand each amount in the table. Be sure to "tie" the amounts in the table to the entries above:

Sometimes, complex topics like this are easier to understand when you think about the balance sheet impact of a transaction. For example, on 12-31-X4, Cash is increased \$125, but the Investment in Bond account is decreased by \$50 (dropping from \$5,150 to \$5,100). Thus, total assets increased by a net of \$75. The balance sheet remains in balance because the corresponding \$75 of interest income causes a corresponding increase in retained earnings.

# Illustration of Bonds Purchased at a Discount

The discount scenario is very similar to the premium scenario, but "in reverse." When bonds are purchased at a discount, the investor pays less than the face value up front. However, the bond's maturity value is unchanged; thus, the amount due at maturity is more than the initial issue price! This may seem like a bargain, but consider that the investor is likely getting lower annual interest receipts than is available on other bonds - that is why the discount existed in the first place. Assume the same facts as for the previous bond illustration, except imagine that the market rate of interest was something more than 5%. Now, the 5% bonds would not be very attractive, and investors would only be willing to buy them at a discount:

 1-1-X3 Investment in Bonds 4,850 Cash 4,850 To record the purchase of five \$1,000,5%, 3-year bonds at 97 - interest payable semiannually

The above entry assumes the investor paid 97% of par (\$5,000 X 97% = \$4,850). However, remember that a full \$5,000 will be repaid at maturity. Thus, the investor will get an additional \$150 over the life of the bond. Accrual accounting dictates that this \$150 "benefit" be recognized over the life of the bond as an increase in interest income:

 6-30-X3 Cash 125 Investment in Bonds 25 Interest Income 150 To record the receipt of an Interest payment (\$5,000 par X .05 Interest X 6/12 months = \$125; \$150 discount X6 months/36 months = \$25 amortization)

The preceding entry would be repeated at each interest payment date. Again, further explanation may prove helpful. In addition to the \$125 received, another \$25 of interest income is recorded. The other \$25 is added to the Investment in Bonds account; as it corresponds to the discount amortization (\$150 discount allocated evenly over the life of the bond - \$150 X (6 months/36 months)). This process of discount amortization would be repeated with each interest payment. Therefore, after three years, the Investment in Bonds account would be increased to \$5,000 (\$4,850 + (\$25 amortization X 6 semiannual interest recordings)). This is another example of the straight-line method of amortization since the amount of interest is the same each period.

When the bond principal is repaid at maturity, the investor would also make this final accounting entry:

 12-31-X5 Cash 5,000 Investment in Bonds 5,000 To record the redemption of bond investment at maturity

Let's consider the "cash out" and the "cash in." How much cash did the investor pay out? It was \$4,850; the amount of the initial investment. How much cash did the investor get back? It is the same as it was in the preceding illustration ~ \$5,750; \$125 every 6 months for 3 years and \$5,000 at maturity. What is the difference? It is \$900 (\$5,750 - \$4,850) - which is equal to the income recognized above (\$150 every 6 months, for 3 years). Be sure to "tie" the amounts in the following amortization table to the related entries.

Can you picture the balance sheet impact on 6-30-X5? Cash increased by \$125, and the Investment in Bond account increased \$25. Thus, total assets increased by \$150. The balance sheet remains in balance because the corresponding \$150 of interest income causes a corresponding increase in retained earnings.