Question

11. Suppose a 10-year, $1000 bond with an 8% coupon rate and semi-annual coupons is trading for a price of $1034.74. a. What is the bond's yield to maturity (expressed as an APR with semi-annual compounding)? b. If the bond's yield to maturity changes to 9% APR, what will be the bond's price? Plan: The bond consists of an annuity of 20 payments of $40, paid every six months, and one lump-sum payment of $1000 in 10 years (20 six-month periods). We can use Eq. (6.3) to solve for the yield to maturity. However, we must use six-month intervals consistently throughout the equation. We can also use an annuity spreadsheet in Excel (also shown below) to find the bond's yield to maturity. Also, given the yield, we can compute the price using Eq. (6.3). Note that a 9% APR is equivalent to a semi-annual rate of 4.5%. Again, we can use a spreadsheet in Excel to find the new price of the bond. Execute: Using Eq. (6.3) to find the bond's yield to maturity: 40 40 8. 1034.74 - sa room 1040 a. 1034.74 = 7 = + = +...+ 6 YTM = 7.5% 20 YTM IM ** VTM NTM

With the given answer for (a) How was the answer (7.5%) calculated? Please provide steps, and how to execute using only a scientific calculator.

Answer 1

Par Value = $1,000

As Bond is Semi Annual so half coupon will be paid each time, twice in a year.

Coupon = 8%, Semi Annual = 8/2 = 4% = Coupon = $40

Duration = 10, total number = 10*2 = 20

Current Price = 1034.74

(ParValue - Market Price/Numberof Years) YTM = Annual Interest+- (ParValue + Market Price)/2

YTM = 40 + (1000 – 1034.70/20) (1000 + 1034.70)/2

YTM = 7.52% = 7.5%

If YTM changes to 9% what would be price

Bond Price =

Price = PV of Coupons + PV of Redemption Price

PV of Coupon = (Coupon Rate/Annual Frequency*Par Value) * (1-(1+YTM/Annual Frequency)^(-No of Times)) / (YTM/Annual Frequency)

PV of Redemption =  (Face Value)/((1+YTM/Annual Frequency)^No of Times)

PV of Coupon = (40*(1-(1+0.045)^-20)/ 0.045

PV of Redemption = (1000)/((1+0.045)^20)

Current Price = 934.96

Hope this helps and this equation can be solved in scientific calculator using simple calculations.