FRA Assignment
Homework Assignment – Week 2
Chapter 3
1. Write down the formula that is used to calculate the yield to maturity on a 20-year 10% coupon bond with $1,000 face value that sells for $2,000. Assume yearly coupons.
$2000 $100/(1 i) $100/(1 i)2 $100/(1 i)20 $1000/(1 i)20
2. If there is a decline in interest rates, which would you rather be holding, long-term bonds or short-term bonds? Why? Which type of bond has the greater interest-rate risk?
You would rather be holding long-term bonds because their price would increase more than the price of the short-term bonds, giving them a higher return.
3. A financial advisor has just given you the following advice: “Long-term bonds are a great investment because their interest rate is over 20%.” Is the financial advisor necessarily correct?
No. If interest rates rise sharply in the future, long-term bonds may suffer such a sharp fall in price that their return might be quite low, possibly even negative.
4. If mortgage rates rise from 5% to 10%, but the expected rate of increase in housing prices rises from 2% to 9%, are people more or less likely to buy houses?
People are more likely to buy houses because the real interest rate when purchasing a house has fallen from 3 percent (5 percent –2 percent) to 1 percent (10 percent 9 percent). The real cost of financing the house is thus lower, even though mortgage rates have risen. (If the tax deductibility of interest payments is allowed for, then it becomes even more likely that people will buy houses.)
Chapter 3 - Quantitative Questions
1. Calculate the present value of a $1,000 zero-coupon bond with five years to maturity if the yield to maturity is 6%.
PV FV/(1 i)n where FV 1000, i 0.06, n 5 PV = 747.25
2. A lottery claims their grand price is $10 million, payable over 20 years at $500,000 per year. If the first payment is made immediately, what is this grand prize really worth? Use an interest rate of 6%.
In excel you
Chapter 3
1. Write down the formula that is used to calculate the yield to maturity on a 20-year 10% coupon bond with $1,000 face value that sells for $2,000. Assume yearly coupons.
$2000 $100/(1 i) $100/(1 i)2 $100/(1 i)20 $1000/(1 i)20
2. If there is a decline in interest rates, which would you rather be holding, long-term bonds or short-term bonds? Why? Which type of bond has the greater interest-rate risk?
You would rather be holding long-term bonds because their price would increase more than the price of the short-term bonds, giving them a higher return.
3. A financial advisor has just given you the following advice: “Long-term bonds are a great investment because their interest rate is over 20%.” Is the financial advisor necessarily correct?
No. If interest rates rise sharply in the future, long-term bonds may suffer such a sharp fall in price that their return might be quite low, possibly even negative.
4. If mortgage rates rise from 5% to 10%, but the expected rate of increase in housing prices rises from 2% to 9%, are people more or less likely to buy houses?
People are more likely to buy houses because the real interest rate when purchasing a house has fallen from 3 percent (5 percent –2 percent) to 1 percent (10 percent 9 percent). The real cost of financing the house is thus lower, even though mortgage rates have risen. (If the tax deductibility of interest payments is allowed for, then it becomes even more likely that people will buy houses.)
Chapter 3 - Quantitative Questions
1. Calculate the present value of a $1,000 zero-coupon bond with five years to maturity if the yield to maturity is 6%.
PV FV/(1 i)n where FV 1000, i 0.06, n 5 PV = 747.25
2. A lottery claims their grand price is $10 million, payable over 20 years at $500,000 per year. If the first payment is made immediately, what is this grand prize really worth? Use an interest rate of 6%.
In excel you