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

When an investor buy’s a bond and pays a price that is below the bond’s par value, the bond is said to have been purchased at a discount.

For an example of a bond purchased at a discount, let’s assume that an investor purchased \$100,000 par value of a bond maturing in two years with a coupon 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 higher than the bond’s coupon rate, let’s say 6.00%.

In this instance, the investor would pay \$97.00 for every \$100.00 of par value. This means the investor pays \$97,000.00 for the \$100,000.00 of maturity value and the yield to maturity is 6.00% 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.

Note: The difference between the bond’s 4.375% coupon interest rate and the 6.0% yield to maturity is the difference between the \$97,000.00 paid for the bond and the \$100,000.00 the investor will receive at the bond’s maturity. This \$3,000.00 capital gain, when calculated over the remaining two years, provides the difference in return between the 6.00% yield and the bond’s 4.375% coupon interest rate.

But this bond was purchased with a discountprice because at the time the current two-year interest rate was 6.00% and the bond issuer only pays 4.375%. Therefore, in order for an investor to purchase this bond and receive a market rate of return equal to 6.0%, the bond’s price must be lower than it’s \$100.00 par value

At the end of the two years, the investor will have received \$8,750.00 in interest income, but they will also earn a capital gain in the amount of \$3,000.00 (\$100,000 maturity value less amount originally invested of \$97,000) upon the bond’s maturity. Therefore, \$8,750.00 in interest income plus the \$3,000.00 in capital gains equals \$11,750.00 net return over the two-year period.

This \$11,750.00 is divided by the original \$97,000.00, over the two year life of the bond equates to a 6.00% 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 6.00% 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. See the example below.

Example:  Let’s assume the bond was held in a taxable account and that 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. And the \$3,000.00 would be taxed as capital gains and would also require a \$615.00 (50% of the \$3,000.00 times the 41% income-tax rate) income tax payment.  As a result, the investor would pay approximately \$4,202.50 after earning \$11,750.00, giving the investor an after-tax investment return of \$7,547.50, over the two years, for a 3.89% after-tax annual return.

In summary,

 Bond purchased at a discount At maturity, receive par value of \$100,000.00 Plus two years of interest income \$8,750.00 \$108,750.00 Less the initial investment \$97,000.00 Equals the net investment income over two years \$11,750.00 Less income tax on \$11,750. of interest income (\$4,205.50) Estimated after-tax investment returns \$7,547.50

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