Yield to call
Six years ago, the Singleton Company issued 20-year bonds with a 14 percent annual coupon rate at their $1,000 par value. The bonds had a 9 percent call premium, with 5 years of call protection. Today, Singleton called the bonds. Compute the realized rate of return for an investor who purchased the bonds when they were issued and held them until they were called. Explain why the investor should or should not be happy that Singleton called them.
Current yield, capital gains yield, and yield to maturity
Hooper Printing Inc. has bonds outstanding with 9 years left to maturity. The bonds have an 8 percent annual coupon rate and were issued 1 year ago at their par value of $1,000, but due to changes in interest rates, the bond’s market price has fallen to $901.40. The capital gains yield last year was _9.86 percent.
a. What is the yield to maturity?
b. For the coming year, what is the expected current yield and the expected capital gains yield?
c. Will the actual realized yields be equal to the expected yields if interest rates
change? If not, how will they differ?
Q1. FV= (1000*.09)+1000= 1090, PV= -1000, n=6, pmt= 140. Cpt I/y= 15.027%. They should be happy because they were making a less (14%) than the 15.027%.
Q3. The current yeild is $80 (the coupon) divided by $901.40 (The current market value). Sorry my calculator is in the other room. It should be a little less than 9%.
Expected Capital gains will be a little less than $10. (1000-901.40)/9 is a quick approximation. Actually, it's 901.40 times the ninth root of (1000/901.40 - 1) [if I remember the formula that I learned about 25 years ago].
Now "C". Current yield will be the same regardless of the change in interest rates. Unrealized Capital Gains will be higher if interest rates go lower and lower if interest rates rise.
Now A. The current yield to maturity is the sum of the rates mentioned in B above.
I'm calling this up out of a 25 year old memory, so check with your text book to see if I got it. Hope it helps.
Why did the cow go to the comedy club? Because it wanted to see some moo-sic!
Now let's get serious and answer your questions:
For the first question, to calculate the realized rate of return, we need to consider the price at which the investor purchased the bonds and the price at which they were called. Since the bonds were called at a 9 percent premium, the price at which they were called would be $1,000 + ($1,000 * 0.09) = $1,090. The investor, who purchased the bonds at their par value of $1,000, would have received a call price of $1,090.
To calculate the realized rate of return, we can use the formula: (call price - purchase price) / purchase price. In this case, the realized rate of return would be: ($1,090 - $1,000) / $1,000 = 9%.
Now, should the investor be happy that Singleton called the bonds? Well, it depends on the perspective. The investor would have received a higher call price, resulting in a positive return of 9%. However, if the investor was expecting to continue earning the coupon payments for the remaining 15 years, they might be disappointed that the bonds were called early. It's a mixed bag of happiness and disappointment!
For the second question:
a. To calculate the yield to maturity, we need to find the discount rate that makes the present value of the bond's cash flows equal to its current market price. In this case, the market price is $901.40, and the bond has a par value of $1,000 and an 8% coupon rate. By using a financial calculator or other methods, we can determine that the yield to maturity is approximately 10%.
b. The current yield is calculated by dividing the annual coupon payment by the market price. The annual coupon payment is 8% of the par value, which is $1,000 * 0.08 = $80. The current yield would be $80 / $901.40, approximately 8.87%.
As for the expected capital gains yield, we can calculate it by subtracting the current yield from the yield to maturity. In this case, the expected capital gains yield would be approximately 10% - 8.87% = 1.13%.
c. Will the actual realized yields be equal to the expected yields if interest rates change? No, they will differ. The yields mentioned above are based on the current market conditions and assumptions. If interest rates change, the bond's market price will fluctuate, and the actual realized yields will be affected. The yield to maturity will change accordingly, and the current yield and capital gains yield will also be different from the initial expectations. So, keep an eye on those changing interest rates!
I hope this has been helpful and brought a smile to your face. If you have any more questions, feel free to ask!
1. To calculate the realized rate of return for an investor who purchased the bonds when they were issued and held them until they were called, we need to consider the coupon payments and any capital gains or losses. Here are the steps to compute it:
Step 1: Calculate the annual coupon payment:
Annual coupon payment = Coupon rate * Par value
Annual coupon payment = 14% * $1,000 = $140
Step 2: Calculate the number of years the bonds were held:
Years held = 6 years
Step 3: Calculate the call premium:
Call premium = Call premium rate * Par value
Call premium = 9% * $1,000 = $90
Step 4: Calculate the total coupon payments received:
Total coupon payments = Annual coupon payment * Years held
Total coupon payments = $140 * 6 = $840
Step 5: Calculate the call value received at the time of the call:
Call value = Par value + Call premium
Call value = $1,000 + $90 = $1,090
Step 6: Calculate the realized rate of return:
Realized rate of return = (Total coupon payments + Call value - Cost of bonds) / Cost of bonds * 100%
Cost of bonds = Par value = $1,000
Realized rate of return = ($840 + $1,090 - $1,000) / $1,000 * 100%
Realized rate of return = $930 / $1,000 * 100%
Realized rate of return ≈ 93%
Explanation: The investor should be happy that Singleton called the bonds because the realized rate of return of approximately 93% is higher than the initial coupon rate of 14%. The call option allowed the investor to realize a higher return than they would have received if they had held the bonds until maturity.
2. Now let's calculate the yield to maturity (YTM) for Hooper Printing Inc. bonds:
a. To calculate the YTM, we need to use the current market price, coupon payments, and time to maturity. Here are the steps:
Step 1: Calculate the annual coupon payment:
Annual coupon payment = Coupon rate * Par value
Annual coupon payment = 8% * $1,000 = $80
Step 2: Calculate the number of years to maturity:
Years to maturity = 9 years
Step 3: Calculate the YTM using a financial calculator, Excel, or an online YTM calculator.
b. To calculate the expected current yield and expected capital gains yield for the coming year, we can use the current market price and coupon payments. Here are the steps:
Step 1: Calculate the current yield:
Current yield = Annual coupon payment / Current market price * 100%
Current yield = $80 / $901.40 * 100%
Current yield ≈ 8.87%
Step 2: Calculate the expected capital gains yield:
Expected capital gains yield = (Current market price - Previous market price) / Previous market price * 100%
Previous market price = Par value = $1,000
Expected capital gains yield = ($901.40 - $1,000) / $1,000 * 100%
Expected capital gains yield ≈ -9.86%
c. The actual realized yields may not be equal to the expected yields if interest rates change. If interest rates increase, the bond's market price may decrease further, resulting in a lower actual current yield and a larger negative capital gains yield. Conversely, if interest rates decrease, the bond's market price may increase, resulting in a higher actual current yield and a smaller negative or positive capital gains yield. Therefore, the realized yields will differ from the expected yields if interest rates change.
To calculate the realized rate of return for an investor who purchased the bonds when they were issued and held them until they were called, you need to consider the cash flows from the bonds and the call premium.
Step 1: Calculate the cash flow from the annual coupon payments. Each year, the investor receives a coupon payment of 14% of the par value, which is $1,000. Therefore, the annual coupon payment is 0.14 * $1,000 = $140.
Step 2: Calculate the cash flow from the call premium. The call premium is 9% of the par value, which is $1,000. Therefore, the call premium is 0.09 * $1,000 = $90.
Step 3: Calculate the total cash flow from the bonds. For the first 5 years, there are no call payments because of the call protection. So the total cash flow from the bonds for these 5 years is $140 * 5 = $700. However, because the bonds were called, the investor will receive the call premium of $90 in addition to the last coupon payment of $140.
Step 4: Calculate the realized rate of return. To calculate the realized rate of return, we need to know the investor's initial investment. Let's assume the investor bought the bonds at par value, which is $1,000.
The total cash flow received by the investor is $700 + $90 + $140 = $930. The realized rate of return is the Total Cash Flow / Initial Investment. Therefore, the realized rate of return is $930 / $1,000 = 0.93 or 93%.
Now, as for whether the investor should be happy or not that Singleton called the bonds, it depends on the current market interest rates. If interest rates have fallen since the bonds were issued, Singleton may be calling the bonds to refinance them at a lower interest rate, which would save them money. In that case, the investor would not be happy because they would lose out on higher coupon payments. However, if interest rates have risen, Singleton may be calling the bonds to issue new bonds at a lower coupon rate, which would be beneficial for the investor as they would be able to reinvest in higher yielding securities.
Moving on to the second question:
a. To calculate the yield to maturity, we need to use the bond's market price, coupon payments, and time to maturity. The bond's market price is $901.40, the coupon rate is 8% of the par value ($1,000), and it has 9 years left to maturity.
You can use a financial calculator, spreadsheet software, or an online bond yield calculator to find the yield to maturity. Alternatively, you can use the following formula:
Yield to Maturity = [(Annual Coupon Payment + (Par Value - Market Price) / Time to Maturity) / (Par Value + Market Price) / 2] x 100
In this case, the annual coupon payment is 0.08 * $1,000 = $80, the par value is $1,000, the market price is $901.40, and the time to maturity is 9 years. Plugging in these values into the formula will give you the yield to maturity.
b. The expected current yield is calculated by dividing the annual coupon payment by the bond's market price. In this case, the annual coupon payment is $80 and the market price is $901.40. Therefore, the expected current yield is $80 / $901.40.
The expected capital gains yield is the difference between the market price now and the market price last year, divided by the market price last year. In this case, the market price last year was $1,000, and the market price now is $901.40. Therefore, the expected capital gains yield is ($901.40 - $1,000) / $1,000.
c. The actual realized yields may not be equal to the expected yields if interest rates change. This is because bond prices are inversely related to interest rates. As interest rates rise, bond prices fall, and vice versa. If interest rates have changed since the bond was issued, the actual realized yields will differ from the expected yields. The actual current yield will depend on the prevailing market price of the bond, and the actual capital gains yield will depend on the change in market price from the original purchase price.