Your company currently has $ 1 comma 000 par, 6 % coupon bonds with 10 years to maturity and a price of $ 1 comma 078. 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.

The next  coupon rate that is needed to set is 5.00%

Explanation:

Solution

Recall that:

Your company presently has =$1,000 par

Coupon bonds = 6%

Maturity = 10 years

The next step is to find the coupon rate that is needed or required to set.

Now,

The number of semi annuals to maturity, NPER =  (10 YEARS * 2)= 20

Semiannual coupon payments, PMT = ($1000 * 6%/2) = $30

The current selling price per bond  (FV) = $1078

The maturity value at the end is = $1000

The semiannual compound type, = 0 (It is 0 if compounded at the end of each semiannual and is 1 if compounded at the start of each semiannual)

Semi annual interest rate is = 2.5%

Thus,

The number of semi annuals in a year is = 2

The annual coupon rate of bonds (new) = 2/50 % * 2

= 5.00%

It is important to note that the semi annual coupon rate is computed suing the excel function rate (nper, pmt, pv,  fv, type),

Whereby

PV =1078

NPR = 20

PMT =30

FV = 1000

TYPE = 0.

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explanation: