Wednesday, October 17, 2007

Calculating Bond Price When Market Rate Is Lower Than Stated Rate

Calculating the price of bonds always seems to be the hardest thing remember if you don't use it on a daily basis. Some key ideas to keep in mind are:

Price of bonds = Present value of principal + Present value of interest payments

Interest to be paid each period is determined by coupon rate (stated interest rate) for that period.

Present value calculation is based on market interest rate.


On January 1, 2006, Company A issues long-terms bonds which are due on January 1, 2011. Interest is paid semiannually on January 1 and July 1 each year. Face amount of bonds is $500,000 with stated interest rate (coupon rate) of 10%. At the time of issuance, market interest rate is 8%. What will be the price of bonds issued by Company A?

Market interest rate = 8%

Market interest rate for a semiannual period = 8% / 2 = 4%

r = 0.04 (per semiannual period),

n = 10 (semiannual periods)


Present value of principal

= $500,000 x Present value factor for a single payment (4%, 10 periods)

= $500,000 x 0.6756

= $337,800


Interest payment each semiannual period

= $500,000 x 5%

= $25,000

(Coupon rate for a semiannual period = 10% / 2 = 5%.)


Present value of interest payments

= Interest payment each semiannual period

x Present value factor for an ordinary annuity (4%, 10 periods)

= ($500,000 x 5%) x 8.1109

= $202,773


Price of bonds

= Present value of principal + Present value of interest payments

= $337,800 + $202,773

= $540,573


The bonds will be sold at a $40,573 premium over the face amount.

($540,573 - $500,000 = $40,573)


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