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.