PLEASE SHOW ALL WORK FOR FULL CREDIT ANSWERS TO QUESTIONS ARE BELOW.. 1. (calcul

Question

PLEASE SHOW ALL WORK FOR FULL CREDIT ANSWERS TO QUESTIONS ARE BELOW..

1. (calculating the present value of a bond) If a corporate bond with a face value of $1,000 has 10 years to go until it matures, has a coupon interest rate of 6% and a yield to maturity (YTM) of 8%, what should be its price in the bond market (ie, PV)?

2. (calculating the current yield of a bond) If a corporate bond with a face value of $1,000 has 10 years to go until it matures, has a coupon interest rate of 6% and a market price of $865.80, what is its current yield?

3. (calculating the YTM of a bond) If a corporate bond with a face value of $1,000 has 10 years to go until it matures, has a coupon interest rate of 6% and a market price of $865.80, what is its yield to maturity (YTM)?

4. (calculating the YTC of a bond) Assume a callable corporate bond with a face value of $1,000, a coupon interest rate of 6%, a market price of $865.80, and a call premium of 8%. Assume also that the bond has 10 years to go until it matures, but it is callable after 8 years. What is the bonds yield to call (YTC)?

5. (calculating the present value of a bond with semi-annual coupon interest payments) If a corporate bond with a face value of $1,000 has 8 years to go until it matures, has a coupon interest rate of 6%, paid semiannually, and has a yield to maturity (YTM) of 8%, what should be its price in the bond market (ie, PV)?

6. (calculating the YTM of a bond with semiannual interest payments) If a corporate bond with a face value of $1,000 has 8 years to go until it matures, has a coupon interest rate of 6%, paid semiannually, and has a market price of $883.48, what is its yield to maturity (YTM)?

7.Assume the real risk-free rate is 1%. Assume also that inflation is expected to be 1% in the coming year (year 1), 2% in the next year after that (year 2), and 3% in the year after that (year 3). Assume also that the default risk premium, the liquidity premium, and the maturity risk premium are 0%. Given these conditions, what would be the yield on three-year treasury bonds today?

Answers to numerical problems:

Question 1: $865.80

Question 2: 6.93%

Question 3: 8.00%

Question 4: 11.3%

Question 5: $883.48

Question 6: 8.0%

Question 7: 3.0%

Explanation / Answer

1.   (calculating the present value of a bond) If a corporate bond with a face value of $1,000 has 10 years to go until it matures, has a coupon interest rate of 6% and a yield to maturity (YTM) of 8%, what should be its price in the bond market (ie, PV)?

Sol- coupon rate= 6%*1000 = 60

price in the bond market = 60*(1-1/1.08^10)/8% + 1000/1.08^10= $865.80

2.   (calculating the current yield of a bond) If a corporate bond with a face value of $1,000 has 10 years to go until it matures, has a coupon interest rate of 6% and a market price of $865.80, what is its current yield?

the current yield of a bond = coupon payment/price = 6%*1000/865.80= 6.93%

3.   (calculating the YTM of a bond) If a corporate bond with a face value of $1,000 has 10 years to go until it matures, has a coupon interest rate of 6% and a market price of $865.80, what is its yield to maturity (YTM)?

Price = coupon*(1-1/(1+YTM)^t)/YTM + 1000/(YTM)^t

865.80 = 6%*1000*(1-1/(1+YTM)^10)/YTM + 1000/(YTM)^10

YTM = 8.00%

4.   (calculating the YTC of a bond) Assume a callable corporate bond with a face value of $1,000, a coupon interest rate of 6%, a market price of $865.80, and a call premium of 8%. Assume also that the bond has 10 years to go until it matures, but it is callable after 8 years. What is the bonds yield to call (YTC)?

Call premium = 8%*1000 = 80

Coupon = 6%*1000 = 60

Price = present value of all future cash flows

865.80 = 60/(1+YTC) +60/(1+YTC)^2 + 60/(1+YTC)^3

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