Question

Your company currently has $1,000 ​par, 5.25% coupon bonds with 10 years to maturity and a price of $1,087. If you want to issue new​ 10-year coupon bonds at​ par, what coupon rate do you need to​ set? Assume that for both​ bonds, the next coupon payment is due in exactly six months. You need to set a coupon rate of....%

Answer 1

Because the coupon payment is due in six months, the payment frequency is semi-annually.

To find the coupon rate to be set we first need to find the yield on the current bond.

For the current bond:

N(Number of periods) = 10*2 = 20

PV = -$1,087

FV = $1000

PMT = 1000 * 5.25%/2 = $26.25

Using the RATE function in excel:

Function Arguments RATE Nper 20 - 20 Pmt 26.25 Pv -1087 Fv 1000 个= 26.25 个 = -1087 1000 Type - number = 0.020883875 Returns the interest rate per period of a loan or an investment. For example, use 6%/4 for quarterly payments at 6% APR. Pv is the present value: the total amount that a series of future payments is worth now. Formula result = 0.020883875 OK Cancel

Yield = 0.021 * 2 = 4.2%

Because the new 10-year coupon bonds are to be issued at par, the coupon rate should be equal to the yield. Because the yield is 4.2%, the coupon rate should be 4.2%