Question

Company X needs to sell new bonds for financing purpose. Company X’s currently outstanding bonds have a $ 1000 par value, a 10 % coupon rate, and pay interest semiannually. The outstanding bonds have 25 years remaining to maturity, are callable after 5 years at a price of $ 1,090, and currently sell at a price of $ 700. The yield curve is expected to remain flat. On the basis of these data, what is the best estimate of company’s nominal interest rate on the new bonds it plans to sell?

Answer 1

On the new bonds, the nominal interest rate will equal the yield on the current outstanding bonds.

The yield on the current outstanding bonds will be the lower of yield-to-call (YTC) or yield-to-maturity (YTM). We take the lower yield, since that is the yield earned by bondholder.

YTM is calculated using RATE function in Excel with these inputs :

nper = 25*2 (25 years to maturity with 2 semiannual coupon payments each year)

pmt = 1000 * 10% / 2 (semiannual coupon payment = face value * annual coupon rate / 2. This is a positive figure as it is an inflow to the bondholder)

pv = -700 (Current bond price. This is a negative figure as it is an outflow to the buyer of the bond)

fv = 1000 (face value of the bond receivable on maturity. This is a positive figure as it is an inflow to the bondholder)

The RATE calculated is the semiannual YTM. To calculate the annual YTM, we multiply by 2.

Annual YTM is 14.48%

YTC is calculated using RATE function in Excel with these inputs :

nper = 5*2 (5 years to call date with 2 semiannual coupon payments each year)

pmt = 1000 * 10% / 2 (semiannual coupon payment = face value * annual coupon rate / 2. This is a positive figure as it is an inflow to the bondholder)

pv = -700 (Current bond price. This is a negative figure as it is an outflow to the buyer of the bond)

fv = 1090 (call price of the bond receivable on call date. This is a positive figure as it is an inflow to the bondholder)

The RATE calculated is the semiannual YTC. To calculate the annual YTC, we multiply by 2.

Annual YTC is 21.10%

The lower of YTM and YTC is the YTM, which is 14.48%

nominal interest rate on new bonds =  14.48%