Question

Martin Software has 11.4 percent coupon bonds on the market with 18 years to maturity. The bonds make semiannual payments and currently sell for 108.5 percent of par.

What is the current yield on the bonds? What is the YTM?

What is the effective annual yield?

Answer 1

Calculating Current Yield on bonds

Let Par value = $100, Current selling price = 108.5% of par = 108.5% x 100 = $108.5

Semi annual coupon payment = (Coupon rate x par value) / 2 = (11.4% x 100) / 2 = 11.4 / 2 = $5.70

Annual interest or coupon payment = Semi annual coupon payment x 2 = 5.70 x 2 = $11.40

Current yield = Annual interest or coupon payment / Current selling price = 11.40 / 108.5 = 0.105069 = 10.5069% = 10.51% (rounded to two decimal places)

Hence Current yield on bond = 10.51%

Calculating Yield to maturity of bond

No of half years to maturity = 2 x no of years to maturity = 2 x 18 = 36

As the coupons are paid semi annually therefore to find yield to maturity, we need to first find semi annual yield to maturity of bond

We can find the Semi annual Yield to maturity of bond using RATE function in excel

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

Using RATE function in excel, we get Semi annual yield to maturity of bond = 5.1747%

Yield to maturity= 2 x semi annual yield to maturity = 2 x 5.1747% = 10.3494% = 10.35% (founded to two decimal places)

Yield to maturity = 10.35%

Calculating Effective Annual yield

Effective Annual Yield = (1+ Semi annual yield to maturity)² - 1 = (1+5.1747%)² - 1 = (1.051747)² - 1 = 1.10617175 - 1 = 0.10617175 = 10.617175% = 10.62% (rounded to two decimal places)

Hence Effective Annual Yield = 10.62%