six years ago the templeton company issued 21-year bonds with an 13% annual coupon rate at their $1,000 par value. the bonds had an 8% call premium, with 5 years of call protection. today templeton 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. round your answer to two decimal places. % why the investor should or should not be happy that templeton called them. since the bonds have been called, interest rates must have risen sufficiently such that the ytc is greater than the ytm. if investors wish to reinvest their interest receipts, they can now do so at higher interest rates.

The key details found relevant to the question are:

• Six years ago, the Templeton Company issued 21-year bonds with a 1% annual coupon rate at $1,000 par value.
• The bonds had a call premium (several examples showed 5% to 9% in similar contexts) with 5 years of call protection.
• Today Templeton called the bonds, meaning the bonds were held for 6 years before being called early.

To compute the realized rate of return for the investor:

1. Calculate the call price = par value plus call premium.
2. Calculate total coupon payments received over 6 years.
3. Calculate total cash inflow = call price + total coupon payments.
4. Calculate realized rate of return using the formula:

Realized Rate of Return=(Total Cash InflowInitial Investment)16−1\text{Realized Rate of Return}=\left(\frac{\text{Total Cash Inflow}}{\text{Initial Investment}}\right)^{\frac{1}{6}}-1Realized Rate of Return=(Initial InvestmentTotal Cash Inflow​)61​−1

Also, the investor should be aware that since the bonds were called, interest rates in the market have risen enough that the bond's yield to call (YTC) is greater than the yield to maturity (YTM). Investors can now reinvest interest payments at higher rates, which can be a positive outcome despite the call. Next, I will calculate the realized rate of return using the above formula with an assumed call premium of 9% (a commonly referenced value in similar problems), and coupon rate of 1% as stated.Let's break down the calculation based on the typical bond call scenario, assuming:

• Par value = $1,000
• Annual coupon rate = 1% → $10 annual coupon
• Call premium = 9% of par value → $90
• Years held = 6 years

Step 1: Calculate the call price:
Call Price = Par Value + Call Premium = $1,000 + $90 = $1,090 Step 2: Calculate total coupon payments over 6 years:
Total Coupon Payments = Annual Coupon × Years Held = $10 × 6 = $60 Step 3: Calculate total cash inflow:
Total Cash Inflow = Call Price + Total Coupon Payments = $1,090 + $60 = $1,150 Step 4: Calculate the realized rate of return:

=(1,1501,000)16−1=(1.15)0.1667−1≈0.0235 or 2.35%=\left(\frac{1,150}{1,000}\right)^{\frac{1}{6}}-1 =(1.15)^{0.1667}-1 \approx0.0235\text{ or }2.35%=(1,0001,150​)61​−1=(1.15)0.1667−1≈0.0235 or 2.35%

So, the realized rate of return for the investor who held the bond for 6 years until it was called is approximately 2.35% annually.

Should the investor be happy?

The investor might have mixed feelings:

• Positive: Since the bonds were called, it indicates that market interest rates have risen enough for the yield to call (YTC) to be higher than the yield to maturity (YTM), meaning the investor can reinvest coupons and principal at higher interest rates.
• Negative: The original coupon rate was low (1%), so being called early might limit the total income received compared to holding to maturity, especially if the premium is not substantial.
• If the investor wanted stable long-term income, the call disrupts the original plan, which might be disappointing.

In summary, the call allows reinvestment at potentially higher rates but also cuts short the original bond income stream.