Question

4.) Company ABC has 7 percent, semiannual, coupon bonds outstanding with a current market price of $1,023.46, a par value of $1,000, and a yield to maturity of 6.72 percent. How many years is it until these bonds mature? Round to the second decimal.

5.) A bond pays a coupon of 7.0% and matures in 5 years. The coupon is paid semi-annually on 1st January, and 1st July. The bond is quoted for 966 value on April 30, 2018. What is the dirty price if the par value is $1000? DO NOT USE DOLLAR SIGNS OR COMMAS IN YOUR ANSWER. ROUND ANSWER TO THE NEAREST CENT (2 Decimals). LIST THE NUMBER AS A POSITIVE NUMBER.

Answer 1

4) Coupon rate = 7%, Current market price = 1023.46, Par value = 1000, Yield to maturity = 6.72%

Semi annual coupon = (Coupon rate x par value ) / 2 = (7% x 1000)/2 = 70/2 = 35

Semi annual Yield to maturity = Yield to maturity / 2 = 6.72%/2 = 3.36%

We will use nper function in excel to calculate no. of half years to maturity

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

                              =nper(3.36%,-35,1023.46,-1000)

Calculating No of Half years to maturity
Current price (pv)	1023.46
Par value (fv)	1000
Semi annual Coupon (pmt)	35
Semi annual Yield to maturity (rate)	3.36%
No of half years to maturity (nper)	25.05

Using nper function in excel, we get no of half years to maturity = 25.05 half years

No of years to maturity = no of half years to maturity/2 = 25.05/2= 12.525 = 12.53 years

5) Coupon rate= 7% , Years to maturity = 5, par value = 1000 Quoted price = Clean price = 966

Semi annual coupon = (Coupon rate x par value)/2 = (7% x 1000)/2 = 35

Quoted date = April 30, 2018, last coupon date = 1st January 2018, Coupon per period = semi annual coupon = 35

Using most commonly used 30/360 convention for bond,

30/360 convention considers no of days in a month = 30 , no of days in a half year = 180

no of days from last coupon payment to quoted date = days in January + days in February + Days in march + days in April = 30 +30+30+30 = 120, no of days in coupon period = days in half year = 180

Dirty price = Clean price + Accrued Interest

where

Accrued Interest = (no of days from last coupon payment to quoted date / no of days in coupon period) x Coupon per period

Accrued interest = (120/180) x 35 = 23.33

Therefore Dirty price = 966 + 23.33 = 989.33