Question

Chamberlain Co. wants to issue new 14-year bonds for some much-needed expansion projects. The company currently has 7.8 percent coupon bonds on the market that sell for $762.45, make semiannual payments, and mature in 14 years. What coupon rate should the company set on its new bonds if it wants them to sell at par? Assume a par value of $1,000.

Answer 1

In this question we will first find the Yield to maturity of current bonds

Par value of current bonds = $1000, Price of current bonds = $762.45, Years to maturity = 14, Coupon rate for current bonds = 7.8%

Semi annual coupon for current bonds = (coupon rate for current bonds x par value) / 2 = (7.8% x 1000) / 2 = 78/2 = 39

No of half years to maturity = 2 x years to maturity = 2 x 14 = 28 half years

First we will find semi annual YTM of current bonds using rate function in excel

Formula to be used in excel: =rate(nper,-pmt,pv,-fv)

Calculating Semi annual Yield to Maturity of current bonds 82 Current market price (pv) 83 Par value (fv) 84 No of half years to maturity (nper) 85 Semi annual Coupon (pmt) 86 Semi annual Yield to maturity (rate) 87 762.45 1000 28 39.00 RATE(H84,-H85,H82,-H83 RATE(nper, pmt, pv, [fvl, [typel, [guess])

Using rate function in excel we get semi annual yield to maturity of bonds = 5.60%

Hence Current Semi annual market rate for company's bonds = 5.60% and company will use this rate to value new bonds and set the coupon rate

Since the bonds sell at par, selling price of new bonds = par value = 1000

To find the coupon rate of new bonds, we will first first find the semi annual coupon of new bonds

To find semi annual coupon for new bonds we will use pmt function

Formula to be used in excel: =pmt(rate,nper,-pv,fv)

Calculating Semi annual coupon 71 72 Selling price (pv) 73 Par value (fv) 74 Semi annual YTM (rate) 75 No of half years to maturity (nper) 76 Semi annual coupon (pmt) 1000 1000 5.60%! 28 PMT(H74,H75,-H72,H73 PMT(rate, nper, pv, [fvl. [type])

Using pmt function, we get semi annual coupon of new bonds = 56

Coupon rate = (semi annual coupon x 2) / par value = (56 x 2) / 1000 = 112 / 1000 = 11.20%

Hence coupon rate for new bonds = 11.20%