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Homework answers / question archive / 1)Suppose a ten-year, $1,000 bond with an 8
1)Suppose a ten-year, $1,000 bond with an 8.9% coupon rate and semiannual coupons is trading for $1,035.05. a. What is the bond's yield to maturity (expressed as an APR with semiannual compounding)? b. If the bond's yield to maturity changes to 9.9% APR, what will be the bond's price?
2) If $42.9 million dollars' worth of haircuts were sold through barbershops and hair salons in a given 12 month period, and the First Choice Haircutters chain sold $5.6 million dollars' worth, while the Tangles chain sold $3.5 million dollars' worth, what were the First Choice and Tangles' shares of the haircut market during that 12-month period?
1.Face value = $ 1,000, Bonds price = $ 1,035.05
Coupon = 8.9% coupons are paid semi-annually.
Coupon = 8.9% × 1,000 = $ 89
Semi annually coupon paid = $ 44.50
The current scenario can be expressed mathematically as
We can determine the rate using trial and error method. Assume rate = 4%
Now, assume rate = 5%
Now applying linear interpolation to determine the YTM.
Rate = 4.20% semi annual
Nominal rate = 8.40% per year
APR = 8.4% compounded semi-annually.
b. When the YTM = 9.9%
The value of bond can be determined as follows\
please see the attached file.
2.
Total annual hair cut business = $ 42.9 Million
First Choice Haircutters share % = (First Choice Annual Business divided by Total annual hair cut business) multiplied by 100
Therefore, First Choice Haircutters market share = ( $ 5.6 Million / $ 42.9 Million) X 100 = 13.05 %
Tangles Chain market share % = (Tangles Annual Business divided by Total annual hair cut business) multiplied by 100
Therefore, Tangles Chain market share = ( $ 3.5 Million / $ 42.9 Million) X 100 = 8.16 %
=> Market Share of others = 100- (First Choice + Tangles market share)
=100 - ( 13.05 + 8.16) = 78.79%
