Homework Assignment – Week 2
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: ...view middle of the document...
In excel you can use the function PV(0.06,20,500000,,1) = 6,079,058. Alternatively you can lay out 20 cashflows in excel and discount each one using an interest rate of 0.06 (remembering that the first cashflow is immediate). The last cashflow is 500000*(1.06)^19 = 165,257.
3. Consider a bond with a 7% annual coupon and a face value of $1,000. Complete the following table. What relationships do you observe between maturity and discount rate and the current price?
When the coupon rate is equal to the yield to maturity then the current bond price is equal to the bond’s face value for any maturity. When the yield to maturity is above the annual coupon then the bond’s current price is below the face value. When it is below then the bond’s current price is above the face value. If the yield to maturity is not equal to the coupon rate and is kept constant for different maturities then the shorter maturity bond will have a price closer to the current price than the longer maturity bond.
Years to Maturity | Yield to Maturity | Current Price |
3 | 5% | 1,054.46 |
3 | 7% | 1,000.00 |
3 | 9% | 949.37 |
6 | 7% | 1,000.00 |
9 | 5% | 1,142.16 |
9 | 9% | 880.10 |
4. Consider a coupon bond that has a $1,000 par value and a coupon rate of 10%. The bond is currently selling for $1,150 and has eight years to maturity? What is the bond’s yield to maturity?
To compute the yield to maturity using excel you can use the function =Rate(8,-100,1150,-1000) = 7.44%
5. You are willing to pay $15,625 now to purchase a perpetuity that will pay you and your heirs $1,250 each year, forever, starting at the end of this year. If your required rate of return does not change, how much would you be willing to pay if this were a 20-year, annual payment, ordinary annuity instead of perpetuity?
To find your “yield to maturity” on the perpetuity you take PV = CF/I 15,625 = 1,250/I I = 1,250/15,625 = 8%. From here you need to use the PV function in excel PV(8%,20,-1250) = &12,272.68.
6. What is the price of a perpetuity that has a coupon of $50 per year and a yield of 2.5%? If the yield doubles, what happens to the price?
PV = 50/2.5% = $2,000. If the yield doubles then the PV is cut in half – PV = 50/5% = $1,000.
7. Property taxes in DeKalb County are roughly 2.66% of the purchase price every year. If you just bought a $100,000 home, what is the PV of all future property tax payments? Assume that the house remains worth $100,000 forever, property tax rates never change and that a 9% interest rate is used for discounting.
The annual payment is $2,660. To value a perpetuity you have PV = 2,660/0.09 = $29,556.
8. Assume you just deposited $1,000 into a bank account. The current real interest rate is 2%, and inflation is expected to be 6% over the next year. What nominal rate would you require from the bank over the next year? How much money will you have at the end of 1 year? If you are saving to buy a stereo that...