High Tech Inc Issued A $1000 Par Value Bond Paying 10%
High Tech Inc Issued A 1000 Par Value Bond That Pays A 10 Percent In
High Tech Inc issued a $1,000 par value bond that pays a 10 percent interest annually. The bond matures in 15 years and is currently selling at $1,500. Your required rate of return is 8 percent.
Required: Compute the bond’s expected rate of return. Determine the value of the bond to you, given your required rate of return.
If the required rate of return is 4.00%, would the bond be attractive to you at its current selling price of $1,500? Why?
Paper For Above instruction
The bond issued by High Tech Inc provides an intriguing case study for understanding the relationship between bond pricing, expected return, and investor's required rate of return. To analyze this, we will first determine the bond’s expected rate of return based on its current price and payment structure. Subsequently, we will value the bond from the investor’s perspective given a different required rate of return and evaluate its attractiveness under varying market conditions.
Understanding Bond Basics
A bond represents a fixed-income security where the issuer agrees to pay fixed periodic interest payments, known as coupons, and return the face value at maturity. For High Tech’s bond, the face value (par) is $1,000, the annual coupon rate is 10%, leading to annual coupon payments of $100 ($1,000 * 10%). The bond matures in 15 years, providing a predictable income stream for investors.
The current market price of the bond is $1,500, which exceeds its face value, indicating that the bond is selling at a premium. This premium implies that the bond’s coupon rate (10%) is higher than the current prevailing interest rates, making it more attractive, and thus commanding a higher price.
Calculating the Expected Rate of Return (Yield to Maturity - YTM)
The expected or yield to maturity (YTM) is the internal rate of return (IRR) on the bond's cash flows, equating the present value of all future payments to the current price. It reflects the annual return an investor can expect if the bond is held until maturity.
The formula for YTM involves solving the equation:
\[
P = \sum_{t=1}^{N} \frac{C}{(1 + YTM)^t} + \frac{F}{(1 + YTM)^N}
\]
Where:
- \( P = 1500 \) (current price)
- \( C = 100 \) (annual coupon)
- \( F = 1000 \) (face value)
- \( N = 15 \) (years to maturity)
Since solving this algebraically is complex, iterative numerical methods or financial calculators are used. Using a financial calculator or Excel's RATE function, the approximate YTM is calculated.
Inputting into Excel:
```
=RATE(15, -100, -1500, 1000)
```
The calculated YTM is approximately 6.5%. This indicates that despite the bond’s coupon rate of 10%, the current price reflects a return of about 6.5% due to the premium paid.
Valuing the Bond at an 8% Required Rate of Return
Now, considering an investor’s required rate of return of 8%, we determine the bond's present value based on this rate. The valuation uses the present value formula:
\[
V = \sum_{t=1}^{N} \frac{C}{(1 + r)^t} + \frac{F}{(1 + r)^N}
\]
Where \( r = 8\% \), \( C = 100 \), \( F = 1000 \), \( N=15 \).
Using Excel or a financial calculator:
```
=PV(8%, 15, -100, -1000)
```
This calculation yields approximately $1,129.
The valuation indicates that at an 8% required rate of return, the bond's fair value is roughly $1,129, which is less than its current market price of $1,500. Therefore, from the perspective of an investor with a required return of 8%, the bond is overvalued at its current price and might not be an attractive purchase unless the price declines.
Impact of a 4% Required Return
If the investor's required rate of return drops to 4%, the bond's attractiveness increases further, as the valuation at 4% would be:
```
=PV(4%, 15, -100, -1000)
```
This yields approximately $1,326.
Again, since the current market price is $1,500, the bond remains overvalued at this lower required return, reinforcing that at its current price, it is less attractive than other opportunities that might offer better alignment with the lower required rate of return.
Conclusion
The analysis highlights how bond prices fluctuate with market interest rates and investor expectations. The bond’s YTM of about 6.5% is below the coupon rate, indicative of a premium price. When an investor’s required rate of return exceeds the bond’s YTM, the bond is overvalued relative to their required return, reducing its attractiveness. Conversely, if their required return is lower than the YTM, the bond’s current market price appears high, and the bond would not be an attractive purchase unless its price decreases.
Investors need to consider both their required rate of return and current market conditions when evaluating bond investments. Bonds priced above their intrinsic value based on an individual’s required return may lead to potential capital loss if bought at the current premium, especially if the interest rate environment shifts or the bond approaches maturity.
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