Week 4 – Assignment Problems P3 Bond Prices And Yields

Week 4 – Assignment Problems P3 Bond prices and yields

Assume that the Financial Management Corporation’s $1,000-par-value bond has a 5.700% coupon, matured on May 15, 2017, had a current price quote of 97.708, and had a yield to maturity (YTM) of 6.034%. Given this information, answer the following questions: a. What was the dollar price of the bond? b. What is the bond’s current yield? c. Is the bond selling at par, at a discount, or at a premium? Why? d. Compare the bond’s current yield calculated in part b to its YTM and explain why they differ. Complex Systems has an outstanding issue of $1,000-par-value bonds with a 12% coupon interest rate. The issue pays interest annually and has 16 years remaining to its maturity date. a. If bonds of similar risk are currently earning a 10% rate of return, how much should Complex Systems bond sell for today? b. Describe the two possible reasons why the rate on similar-risk bonds is below the coupon interest rate on the Complex Systems bond. c. If the required return were at 12% instead of 10%, what would the current value of Complex Systems’ bonds be? Contrast this finding with your findings in part a and discuss. McCracken Roofing, Inc., common stock paid a dividend of $1.20 per share last year. The company expects earnings and dividends to grow at a rate of 5% per year for the foreseeable future. a. What required rate of return for this stock would result in a price per share of $28? b. If McCracken expects both earnings and dividends to grow at an annual rate of 10%, what required rate of return would result in a price per share of $28?

Paper For Above instruction

This comprehensive analysis addresses key concepts in bond valuation and stock valuation, integrating calculations, theoretical explanations, and market implications to offer a nuanced understanding of financial instruments’ pricing and returns.

Bond Prices and Yields

Bond valuation is fundamental to understanding the relationship between bond prices and yields. Given the parameters for the Financial Management Corporation’s bond—a $1,000 par value, 5.700% coupon rate, and a current market quote of 97.708—the actual dollar price can be calculated by multiplying the quote by the face value:

Dollar price = 97.708% of $1,000 = 0.97708 × $1,000 = $977.08.

This indicates that the bond is trading below its par value, suggesting a discount. The coupon payment is calculated as 5.700% of $1,000, which equals $57 annually. The current yield, a measure of the income component of the return relative to its market price, is calculated as:

Current yield = Annual coupon payment / Current price = $57 / $977.08 ≈ 5.83%.

This yield reflects the income relative to the bond’s current market price. Comparing the bond’s current yield (≈5.83%) with its yield to maturity (YTM) of 6.034% reveals that YTM incorporates not only the income but also the capital gain or loss upon maturity—hence, it exceeds the current yield as it accounts for the bond's discount and time remaining to maturity.

The bond is selling at a discount because its market price ($977.08) is below face value, which aligns with the fact that its YTM (6.034%) is higher than the coupon rate (5.700%). Investors require a higher yield to compensate for the discount, reflecting market interest rate conditions at the time.

Bond Valuation at Different Market Rates

For Complex Systems, with a $1,000 par value, a 12% coupon rate, and 16 years remaining, the theoretical price can be calculated based on the current market rate of return. When similar risk bonds yield 10%, the present value of the bond’s cash flows is computed as the sum of the present values of the coupon payments and the face value, discounted at 10%:

Present value of coupons = C × [1 - (1 + r)^-n] / r, where C = $120, r = 0.10, n = 16.

Present value of face value = Face value / (1 + r)^n.

Carrying out these calculations yields a market value exceeding par, indicating the bond would sell for approximately $1,183.67.

However, if the required return rises to 12%, aligning with the coupon rate, the bond’s price would fall close to par—around $1,000—because the discount rate equals the coupon rate, making the bond’s present value equal to its face value. The two reasons for the disparity between current yield and YTM are primarily market interest rate fluctuations and the bond’s relative premium or discount based on the coupon rate compared to prevailing rates.

Stock Valuation with Constant Growth

Regarding McCracken Roofing’s stock, the dividend paid last year was $1.20, and with a growth rate of 5%, the expected dividend next year is $1.20 × 1.05 = $1.26. Using the Gordon Growth Model, the required rate of return (k) associated with a stock price of $28 can be determined by:

Price = D1 / (k - g), thus, k = (D1 / Price) + g = ($1.26 / $28) + 0.05 ≈ 0.045 + 0.05 = 9.5%.

If the growth rate increases to 10%, the required rate of return to justify a $28 share price becomes:

k = ($1.26 / $28) + 0.10 ≈ 0.045 + 0.10 = 14.5%.

These calculations highlight how higher expected growth in dividends influences the required return, reflecting investor expectations and market valuation dynamics. Investments with higher growth prospects typically command higher required returns, affecting their current prices.

Overall, these financial analyses illustrate the critical interplay between coupon rates, market interest rates, dividend growth, and required returns in valuation processes, emphasizing the importance of market conditions and expectations in investment decision-making.

References

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