Question

1.) Volbeat Co. has bonds on the market with 10.5 years to maturity, a YTM of 6.2%, a par value of $1,000, and a current price of $945. The bonds make semiannual payments. What must the coupon rate be on the bonds?

2.) If Treasury bills are currently paying 4.5% and the inflation rate is 1.6%, what is the approximate real rate of interest? The exact real rate?

Answer 1

1) Par value = $1000, Current price = $945, Years to maturity = 10.5 years , Yield to maturity = 6.2%

Since the bond pays coupon semi annually, therefore

No of half years to maturity = 2 x years to maturity = 2 x 10.5 = 21 half years

Semi annual Yield to maturity = Yield to maturity / 2 = 6.2% / 2 = 3.1%

To find coupon rate, we will first find the semi annual coupon payment,

We can find the semi annual coupon payment using PMT function in excel

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

Using PMT function in excel, we get semi annual coupon payment = 27.40

Coupon rate = (Semi annual coupon payment x 2) / par value = (27.40 x 2) / 1000 = 54.80 / 1000 = = 0.0548 = 5.48%

Hence coupon rate = 5.48%

2) Nominal interest rate = Rate of interest on treasury bills = 4.5% and inflation = 1.6%

Approximate real rate of interest = Nominal interest rate - inflation = 4.5% - 1.6% = 2.9%

Hence Approximate real rate of interest = 2.9%

Exact real rate of interest = [(1+nominal interest rate) / (1+inflation)] - 1

= [(1+4.5%) /(1+1.6%)] - 1 = [1.045/1.016] - 1 = 1.028543 - 1 = 0.028543 = 2.8543%

Exact real rate of interest = 2.8543%