# What does it mean to purchase a bond at a premium?

When you purchase a bond and you pay a price that is above the bond’s par value the bond has been purchased at a premium. Typically, the par value for bonds is set at \$100.00 for each \$100.00 of maturity value.

For an example of a bond purchased at a premium, let’s assume that an investor has purchased \$100,000 par value of a bond maturing in two years with a coupon interest rate of 4.375%. The bond has a high credit rating of “AA” and is purchased at a time when the two-year interest rates are low, let’s say 1.41%.

To purchase the bonds with a coupon of 4.375%, when the market interest rates are 1.41%, the investor will have to pay a premium above the bond’s \$100.00 par value. In the case of our example, the investor pays \$105.75 for every \$100.00 of par value. This means the investor pays \$105,750.00 for the \$100,000 of maturity value and the investor’s yield to maturity is 1.41% per year.

For each of the next two years, the investor will be paid \$4,375.00 of interest income for a total interest income of \$8,750.00.

But this bond was purchased at a premiumprice and the premium paid for this bond was \$5,750.00 (\$105,750 – \$100,000) and the bond will mature and only return \$100,000.00 of the original \$105,750.00 invested..

At the end of the two years, the investor will have been paid \$8,750.00 in interest income, but they will not receive the \$5,750.00 premium paid at the bond’s maturity. Therefore, \$8,750.00 less the \$5,750.00 premium equals \$3,000.00 net return over the two-year period to the investor.

This \$3,000.00 divided by the original \$105,750.00 invested equates to a 1.41% per year yield to maturity.

If the bond was held in a non-taxable account (for example, an RRSP, RRIF, RESP, Tax-Free Savings Account (TFSA)), then the 1.41% is the investor’s annual investment return.

However, if the bond was held in a taxable investment account, then the investor’s after-tax return will be lower and possibly negative. How can this be possible? See the example below.

Example:  Let’s assume the bond was held in a taxable account and the bondholder’s income is taxed at a 41% income tax rate. Then the \$8,750.00 of bond interest income received would require the investor to pay approximately \$3,587.50 in income tax. The investor would pay \$3,587.50 in income tax even though the net income they received was only \$3,000.00. In this example, the bond investor, by buying the bond at a premium and holding it in a taxable account,lost approximately \$587.50, over the two-year period. They made a negative investment return after paying income tax.

 Bond purchased at a premium At maturity, receive par value of \$100,000.00 Plus two years of interest income (taxable at 41%) \$8,750.00 Amount received over the two years \$108,750.00 Less the initial investment \$105,750.00 Equals the net investment income over two years \$3,000.00 Less income tax on \$8750. of interest income \$3,587.50 Estimated after-tax investment loss (\$587.50)

Purchasing a bond at a premium should only be done inside a tax preferred investment account, not inside a taxable investment account.

Related Questions