Assume you have a 1-year investment horizon and are trying to choose among three
ID: 2644831 • Letter: A
Question
Assume you have a 1-year investment horizon and are trying to choose among three bonds. All have the same degree of default risk and mature in 10 years. The first is a zero-coupon bond that pays $1,000 at maturity. The second has an 6.2% coupon rate and pays the $62 coupon once per year. The third has a 7.2% coupon rate and pays the $72 coupon once per year.
If all three bonds are now priced to yield 7% to maturity, what are their prices? (Round your answers to 2 decimal places. Omit the "$" sign in your response.)
If you expect their yields to maturity to be 7% at the beginning of next year, what will their prices be then? What is your before-tax holding-period return on each bond? If your tax bracket is 30% on ordinary income and 20% on capital gains income, what will your aftertax rate of return be on each? (Round your answers to 2 decimal places. Omit the "$ & %" signs in your response.)
If you expect their yields to maturity to be 6% at the beginning of next year, what will their prices be then? What is your before-tax holding-period return on each bond? If your tax bracket is 30% on ordinary income and 20% on capital gains income, what will your aftertax rate of return be on each? (Round your answers to 2 decimal places. Omit the "$ & %" signs in your response.)
Assume you have a 1-year investment horizon and are trying to choose among three bonds. All have the same degree of default risk and mature in 10 years. The first is a zero-coupon bond that pays $1,000 at maturity. The second has an 6.2% coupon rate and pays the $62 coupon once per year. The third has a 7.2% coupon rate and pays the $72 coupon once per year.
Explanation / Answer
a)
Answer
Working
Zero Coupon
Current Price = 1000/(1+7%)^10 = 508.35
6.2% Coupon Bond
Bond Value = pv(rate, nper,pmt,fv)
Nper (indicates the period) = 10
PV (indicates the price) = ?
PMT (indicate the annual payment) = 1000*6.2% = 62
FV (indicates the face value) = 1000
Rate (indicates YTM) = 7%
Bond Value = PV(7%,10,62,1000)
Bond Value = $ 943.81
7.2% Coupon Bond
Bond Value = pv(rate, nper,pmt,fv)
Nper (indicates the period) = 10
PV (indicates the price) = ?
PMT (indicate the annual payment) = 1000*7.2% = 72
FV (indicates the face value) = 1000
Rate (indicates YTM) = 7%
Bond Value = PV(7%,10,72,1000)
Bond Value = $ 1014.05
b)
Answer
Working
Zero Coupon
Price after 1 year = 1000/(1+7%)^9 = 543.93
Pre-tax rate of Return = (543.93-508.35)/508.35 = 7.00%
After-tax rate of Return = (543.93-508.35)*(1-20%)/508.35 = 5.60%
6.2% Coupon Bond
Bond Value after 1 year= pv(rate, nper,pmt,fv)
Nper (indicates the period) = 9
PV (indicates the price) = ?
PMT (indicate the annual payment) = 1000*6.2% = 62
FV (indicates the face value) = 1000
Rate (indicates YTM) = 7%
Bond Value after 1 year = PV(7%,9,62,1000)
Bond Value after 1 year = $ 947.88
Pre-tax rate of Return = ((947.88-943.81)+ 62)/943.81 = 7.00%
After-tax rate of Return = ((947.88-943.81)*(1-20%) + 62*(1-30%))/943.81 = 4.94%
7.2% Coupon Bond
Bond Value after 1 year= pv(rate, nper,pmt,fv)
Nper (indicates the period) = 9
PV (indicates the price) = ?
PMT (indicate the annual payment) = 1000*7.2% = 72
FV (indicates the face value) = 1000
Rate (indicates YTM) = 7%
Bond Value after 1 year= PV(7%,9,72,1000)
Bond Value after 1 year = $ 1013.03
Pre-tax rate of Return = ((1013.03-1014.05)+ 72)/1014.05 = 7.00%
After-tax rate of Return = ((1013.03-1014.05)*(1-20%) + 72*(1-30%))/1014.05 = 4.89%
c)
Answer
Working
Zero Coupon
Price after 1 year = 1000/(1+6%)^9 = 591.90
Pre-tax rate of Return = (591.90-508.35)/508.35 = 16.44 %
After-tax rate of Return = (591.90-508.35)*(1-20%)/508.35 = 13.15%
6.2% Coupon Bond
Bond Value after 1 year= pv(rate, nper,pmt,fv)
Nper (indicates the period) = 9
PV (indicates the price) = ?
PMT (indicate the annual payment) = 1000*6.2% = 62
FV (indicates the face value) = 1000
Rate (indicates YTM) = 6%
Bond Value after 1 year = PV(6%,9,62,1000)
Bond Value after 1 year = $ 1013.60
Pre-tax rate of Return = ((1013.60-943.81)+ 62)/943.81 = 13.96%
After-tax rate of Return = ((1013.60-943.81)*(1-20%) + 62*(1-30%))/943.81 = 10.51%
7.2% Coupon Bond
Bond Value after 1 year= pv(rate, nper,pmt,fv)
Nper (indicates the period) = 9
PV (indicates the price) = ?
PMT (indicate the annual payment) = 1000*7.2% = 72
FV (indicates the face value) = 1000
Rate (indicates YTM) = 6%
Bond Value after 1 year= PV(6%,9,72,1000)
Bond Value after 1 year = $ 1081.62
Pre-tax rate of Return = ((1081.62-1014.05)+ 72)/1014.05 = 13.76%
After-tax rate of Return = ((1081.62-1014.05)*(1-20%) + 72*(1-30%))/1014.05 = 10.30%
Zero Coupon 6.2% Coupon 7.2% Coupon Current prices 508.35 943.81 1,014.05Related Questions
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