Six years ago the Singleton Company issued 20-year bonds with a 14%
annual coupon rate at their $1,000 par value. The bonds had a 9% 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.
To compute 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 cash flows involved.
When the bonds were issued, they had a 20-year maturity and a 14% annual coupon rate, which means the investor would receive $140 (14% of $1,000) in coupon payments each year for 20 years. At maturity, the investor would also receive the $1,000 par value.
However, since the bonds were called by Singleton, we need to adjust the cash flows accordingly. The call premium is 9% of the par value, so Singleton will need to pay an additional $90 (9% of $1,000) per bond. The call protection period is 5 years, which means Singleton cannot call the bonds until after 5 years.
To calculate the realized rate of return, we can use the following formula:
Realized Rate of Return = [(Total Cash Inflows - Total Cash Outflows) / Total Cash Outflows] * 100%
Let's compute the cash flows:
Coupon Payments = $140 per year for 5 years (before the call protection period ends)
= $140 * 5
= $700
Call Premium = $90 per bond
= $90
Total Cash Inflows = Coupon Payments + Call Premium
= $700 + $90
= $790
Total Cash Outflows = Initial Investment + Additional Interest
The initial investment is the purchase price of the bond, which is $1,000 per bond.
Additional Interest = Coupon Payments for the remaining years (15 years after the call)
= $140 per year for 15 years
= $140 * 15
= $2,100
Total Cash Outflows = $1,000 + $2,100
= $3,100
Now we can calculate the realized rate of return:
Realized Rate of Return = [($790 - $3,100) / $3,100] * 100%
= -74.19%
The negative sign indicates a negative return, which means the investor has actually lost money on this investment.
Should the investor be happy that Singleton called the bonds?
No, the investor should not be happy that Singleton called the bonds because they have incurred a negative return on their investment. The realized rate of return of -74.19% indicates that the investor has experienced a significant loss. It signifies that the investor would have been better off not holding the bonds until they were called and instead, investing their money elsewhere.