The carrying value of a bond refers to its face value, plus any unamortized premiums or minus any unamortized discounts.

We can quickly calculate a bond's carrying value with only a few pieces of information about the bond. Here's how.

Calculating the carrying value of a bond
The effective interest method is the most common way to amortize premiums and discounts, and perhaps one of the easiest methods for calculating carrying values. (See the article on straight-line amortization if you're interested in calculating the value of a bond via another method.)

Let's assume that a company issues three-year bonds with a face value of \$100,000 that have an annual coupon of 9%. Investors view the company as being relatively risky; thus, they are willing to willing to buy this bond only if it offers a higher yield of 10%.

Because the yield to maturity (10%) is higher than the coupon rate (9%), this bond will be sold at a discount. Therefore, its carrying value will be less than its face value (\$100,000).

You can calculate the carrying value of the bond by typing in the relevant pieces of information into a finance calculator or spreadsheet (use the PV function).

FV = \$100,000 (par value)
N = 3 (number of periods)
PMT = \$9,000 (9% coupon rate X \$100,000 par value)
INT = 10% (Investors required yield to maturity)

Solve for PV to get -\$97,513.15, or the amount the investors will pay for these bonds to get a 10% yield to maturity. This is the carrying value at the time it is issued, \$97,513.15.

What if you need to calculate the carrying value after two years of interest payments for the same bond? Simple. Run the same calculation, changing only the number of periods from three to one.

FV = \$100,000 (par value)
N = 1 (number of remaining periods)
PMT = \$9,000 (9% coupon rate X \$100,000 par value)
INT = 10% (Investors' required yield to maturity.)

Solving for present value, we arrive at -\$99,090.91, or the amount investors would pay for this bond. Thus, its carrying value is \$99,090.91, a smaller discount to its face value.

Calculating the carrying value of a bond using the effective interest method is as simple as calculating what the bond would be worth at a given yield to maturity. As yield to maturity goes up, the value of the bond will go down. Similarly, as yield to maturity goes down, the value of the bond will go up, resulting from the bond's "inverse relationship" with interest rates.

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