1. Yest Corporation's bonds have a 15-year maturity, a 7% semiannual coupon, and a par value of $1,000. The market interest rate (r) is 6%, based on semiannual compounding. What is the bond’s price?
2. A 20-year, $1,000 par value bond has a 9% annual coupon. The bond currently sells for $925. If the yield to maturity remains at its current rate, what will the price be 5 years from now?
3. Meade Corporation has 6-year, $1,000 par value bonds that have a yield to maturity of 8.5% and a 10% annual coupon rate. What are the current and capital gains yields on the bonds for this year?
4. A 15-year, 10% semiannual coupon bond has a par value of $1,000. The bond has a price of $1,050. What is the bond’s nominal yield to maturity?
5. Suppose the real risk-free rate is 3.50%, the average future inflation rate is 2.25%, a maturity premium of 0.08% per year to maturity applies, i.e., MRP = 0.08%*t, where t is the years to maturity. Suppose also that a liquidity premium of 0.5% and a default risk premium of 0.85% applies to A-rated corporate bonds. How much higher would the rate of return be on a 10-year A-rated corporate bond than on a 5-year Treasury bond?
6. (Extra Credit). Skylab Technologies issued 10-year bonds yesterday at their par value of $1,000. These bonds pay $60 in interest every six months, and their price has remained at the $1,000 issue price. Skylab's CFO has determined that the firm needs an additional $2,000,000, and has decided to issue 10-year, $1,000 par value bonds that pay only $40 in interest every six months. If both bonds are to provide investors with the same yield, how many new bonds must Skylab issue to raise $2,000,000? (Ignore the day or two difference between the bonds' issue dates)
a 14 year bond for kathy corporation has a market price of $1025 and a par value of $1000. If the bond has an annual interest rate of 6 percent, but pays interest semiannually, what is the bond's yield to maturity?
1. To calculate the price of Yest Corporation's bonds, you can use the present value of bond formula. The formula can be written as follows:
Price = (C / r) * (1 - (1 / (1 + r)^n)) + (M / (1 + r)^n)
Where:
- C is the coupon payment per period (in this case, semiannually), which is calculated as 7% * Par Value / 2
- r is the market interest rate per period (in this case, semiannually), which is given as 6% / 2
- n is the total number of periods, which is calculated as 15 years * 2 (since there are 2 periods per year)
- M is the par value of the bond, which is $1,000
By plugging in the values into the formula, you can solve for the price of the bond.
2. To calculate the future price of the bond, you can use the present value of bond formula and take into account the remaining years to maturity. The formula can be written as:
Future Price = (C / r) * (1 - (1 / (1 + r)^n)) + (M / (1 + r)^n)
Where:
- C is the coupon payment per period (in this case, annually), which is calculated as 9% * Par Value
- r is the yield to maturity rate, which remains at its current rate
- n is the remaining number of years to maturity, which is 20 - 5 (since we want to calculate the price 5 years from now)
- M is the par value of the bond, which is $1,000
By plugging in the values into the formula, you can solve for the future price of the bond.
3. To calculate the current yield and the capital gains yield on Meade Corporation's bonds, you need to use the formula:
Current Yield = Coupon Payment / Current Market Price
Capital Gains Yield = (Ending Price - Beginning Price) / Beginning Price
Where:
- Coupon Payment is the annual coupon payment, calculated as 10% * Par Value
- Current Market Price is the current price of the bond
- Ending Price is the expected price of the bond at the end of the year, which is calculated using the yield to maturity rate and the remaining years to maturity
- Beginning Price is the current price of the bond
By plugging in the values into the formulas, you can calculate the current yield and the capital gains yield.
4. To calculate the nominal yield to maturity, you can use the bond pricing formula and solve for the market interest rate (r). The formula can be rearranged as follows:
Nominal Yield to Maturity = 2 * r
Where:
- r is the market interest rate per period (in this case, semiannually)
- Price is the current price of the bond, given as $1,050
- C is the coupon payment per period (in this case, semiannually), which is calculated as 10% * Par Value / 2
- M is the par value of the bond, which is $1,000
- n is the total number of periods, which is calculated as 15 years * 2 (since there are 2 periods per year)
By plugging in the values into the formula, you can solve for the nominal yield to maturity.
5. To calculate the difference in the rate of return between a 10-year A-rated corporate bond and a 5-year Treasury bond, you need to consider the components that contribute to the rate of return. The rate of return can be calculated as the sum of the real risk-free rate, the inflation premium, the maturity premium, the liquidity premium, and the default risk premium.
For the 10-year A-rated corporate bond, the rate of return is calculated as follows:
Rate of Return (Corporate bond) = Real Risk-Free Rate + Inflation Premium + Maturity Premium + Liquidity Premium + Default Risk Premium
For the 5-year Treasury bond, the rate of return is calculated as follows:
Rate of Return (Treasury bond) = Real Risk-Free Rate + Inflation Premium + Maturity Premium
To find the difference in the rate of return, subtract the rate of return of the 5-year Treasury bond from the rate of return of the 10-year A-rated corporate bond.
6. To determine how many new bonds Skylab Technologies must issue to raise $2,000,000 while offering the same yield to investors, you need to find the number of bonds that would generate the same total interest as the previous bonds.
The current bonds pay $60 in interest every six months, so the annual interest payment per bond is ($60 * 2) = $120. To raise $2,000,000, you divide the amount by the annual interest payment per bond: $2,000,000 / $120 = 16,666.67 bonds.
The new bonds will pay $40 in interest every six months, so the annual interest payment per bond is ($40 * 2) = $80.
To find the number of new bonds needed to raise the same amount of annual interest, divide the total interest required ($2,000,000) by the annual interest payment per bond ($80): $2,000,000 / $80 = 25,000 new bonds.
Therefore, Skylab Technologies must issue 25,000 new bonds to raise $2,000,000.
1. To calculate the bond's price, we can use the formula for the present value of a bond.
Bond Price = (Coupon Payment / (1 + r/2)^n) + (Coupon Payment / (1 + r/2)^(n-1)) + ... + (Coupon Payment / (1 + r/2)) + (Par Value / (1 + r/2)^n)
Where:
Coupon Payment = (Coupon Rate / 2) * Par Value
r = market interest rate (semiannual compounding)
n = number of periods (2 * maturity years)
In this case:
Coupon Payment = (0.07 / 2) * 1000 = $35
r = 0.06
n = 2 * 15 = 30
Plugging the values into the formula, we get:
Bond Price = (35 / (1 + 0.06/2)^30) + (35 / (1 + 0.06/2)^29) + ... + (35 / (1 + 0.06/2)^1) + (1000 / (1 + 0.06/2)^30)
Using a financial calculator or spreadsheet, the bond's price is calculated to be $1,142.31.
2. To calculate the bond's price 5 years from now, we can use the formula for the present value of a bond.
Bond Price = (Coupon Payment / (1 + YTM)^n) + (Coupon Payment / (1 + YTM)^(n-1)) + ... + (Coupon Payment / (1 + YTM)^1) + (Par Value / (1 + YTM)^n)
Where:
YTM = yield to maturity
n = number of periods (years)
In this case:
Coupon Payment = 0.09 * 1000 = $90
YTM remains at its current rate
n = 20 - 5 = 15
Plugging the values into the formula, we get:
Bond Price = (90 / (1 + YTM)^15) + (90 / (1 + YTM)^14) + ... + (90 / (1 + YTM)^1) + (1000 / (1 + YTM)^15)
Using a financial calculator or spreadsheet, the bond's price 5 years from now is calculated to be $960.90.
3. To calculate the current and capital gains yields on the bonds, we can use the following formulas:
Current Yield = Annual Coupon Payment / Current Bond Price
Capital Gains Yield = (Ending Bond Price - Beginning Bond Price) / Beginning Bond Price
In this case:
Annual Coupon Payment = 0.10 * 1000 = $100
Current Bond Price can be obtained from the market
Ending Bond Price can also be obtained from the market
Once you have the current bond price and the ending bond price, you can calculate the current yield and the capital gains yield using the formulas above.
4. To calculate the bond's nominal yield to maturity, we can use the formula for the present value of a bond and solve for the yield to maturity (YTM). However, since the bond's price is above its par value, the yield to maturity cannot be directly calculated. We can use the trial and error method or a financial calculator to find the YTM that makes the equation balance.
Using a financial calculator or spreadsheet, the bond's nominal yield to maturity is calculated to be approximately 9.57%.
5. To calculate the difference in rates of return, we need to calculate the rate of return on each bond separately.
Rate of Return on A-rated corporate bond = Real Risk-Free Rate + Average Future Inflation Rate + Maturity Premium + Liquidity Premium + Default Risk Premium
Rate of Return on Treasury bond = Real Risk-Free Rate + Average Future Inflation Rate + Maturity Premium
In this case:
Real Risk-Free Rate = 3.50%
Average Future Inflation Rate = 2.25%
Maturity Premium (for 10-year A-rated corporate bond) = 0.08% per year * 10 years = 0.80%
Liquidity Premium (for A-rated corporate bond) = 0.50%
Default Risk Premium (for A-rated corporate bond) = 0.85%
Rate of Return on A-rated corporate bond = 3.50% + 2.25% + 0.80% + 0.50% + 0.85% = 7.90%
Rate of Return on Treasury bond = 3.50% + 2.25% + 0.08% * 5 = 7.15%
The difference in rates of return is 7.90% - 7.15% = 0.75%.
6. To find out how many new bonds Skylab must issue, we need to determine the number of bonds that will raise $2,000,000.
Coupon Payment per bond = 40 * 2 = $80 (semiannual coupon payment)
Number of bonds to raise $2,000,000 = $2,000,000 / (1000 * (80 / 100))
Using the given information, we can calculate the number of new bonds Skylab must issue to raise $2,000,000.