You Are Called In As A Financial Analyst To Appraise 197913

You Are Called In As A Financial Analyst To Appraise the Bonds Of Olse

You are tasked with appraising the bonds of Olsen’s Clothing Stores, which have a par value of $1,000, an annual coupon rate of 10% paid semiannually, and a yield to maturity (YTM) of 10% annualized. The bonds have 15 years remaining to maturity. Additionally, you are asked to determine the new bond price if the YTM drops to 8% with 10 years remaining to maturity. Furthermore, you need to evaluate the value of a stock that pays a fixed dividend, and analyze changes in stock valuation based on varying dividend growth rates and required rates of return. This comprehensive appraisal involves bond valuation, stock valuation, and sensitivity analysis concerning changing market conditions.

Paper For Above instruction

The evaluation of bond prices based on cash flow analysis is fundamental in financial analysis, especially when considering the impact of interest rate movements on bond valuation. In this context, Olsen’s Clothing Stores’ bonds provide an excellent case to illustrate how fixed-income securities are valued and how their prices fluctuate with changes in market yields.

Bond Valuation at a 15-Year Maturity with 10% YTM

The bond’s price is computed as the present value (PV) of future cash flows, which comprise semiannual coupon payments and the face value at maturity. Given the bond’s par value of $1,000, a coupon rate of 10% annually, and semiannual payments, each payment amounts to $50 (since 10% of $1,000 divided by 2). The number of periods is 30 (15 years times two), and the semiannual yield (YTM per period) is 5% (half of 10%).

The present value of the coupons (PVC) is calculated as:

PVC = C × [1 - (1 + r)^-n] / r

where C = $50, r = 0.05, n = 30.

PVC = $50 × [1 - (1 + 0.05)^-30] / 0.05 ≈ $50 × 20.017 ≈ $1,000.85.

The present value of the face value (PVF) is:

PVF = FV / (1 + r)^n = $1,000 / (1 + 0.05)^30 ≈ $1,000 / 4.3219 ≈ $231.37.

The total bond price is the sum of PVC and PVF, approximately $1,000.85 + $231.37 ≈ $1,232.22.

Bond Price when YTM decreases to 8% with 10 Years Remaining

With 10 years remaining to maturity and YTM at 8% annualized, the semiannual rate is 4%. The number of periods is 20. Calculations are similar:

PVC = $50 × [1 - (1 + 0.04)^-20] / 0.04 ≈ $50 × 17.159 ≈ $857.95.

PVF = $1,000 / (1 + 0.04)^20 ≈ $1,000 / 2.1911 ≈ $456.21.

Total bond price ≈ $857.95 + $456.21 ≈ $1,314.16.

Thus, a decline in YTM from 10% to 8% results in bond price appreciation, reflecting the inverse relationship between yield and bond price.

Stock Valuation of Stagnant Iron and Steel

The valuation of a stock with a constant dividend and no growth uses the perpetuity formula:

P0 = D / Ke

Given D0 = $12.25, Ke = 18%, the stock price is:

P0 = $12.25 / 0.18 ≈ $68.06.

Since the dividend is expected to remain unchanged, this price reflects the present value of the perpetual dividends.

Impact of Changes in Required Rate of Return and Growth Rate

When the required rate of return increases to 18%, stock value decreases as the discount rate applies a larger factor to future dividends:

P0_new = D / Ke_new = $12.25 / 0.18 ≈ $68.06.

Since no growth is involved here, the initial value and new value are identical. However, if dividends change or the model incorporates growth, the valuation adjusts accordingly.

For a scenario where the dividend remains at $12.25 but the required rate (Ke) increases, the stock declines, illustrating inverse price-yield relationships in perpetuity valuation.

Stock Valuation with Increased Growth Rate

If the dividend growth rate (g) increases to 9%, the valuation model shifts to the Gordon Growth Model:

P0 = D1 / (Ke - g)

where D1 = D0 × (1 + g). Given D0 = $12.25 and g = 9%, D1 = $12.25 × 1.09 = $13.35.

P0 = $13.35 / (0.14 - 0.09) = $13.35 / 0.05 = $267.

This significant increase in stock value reflects the higher expected future dividends due to increased growth, offsetting the higher required rate of return.

Adjusting Dividend and Growth Rates for Valuation

When the dividend is increased to $7.00 with the same growth rate of 5%, the stock price becomes:

D1 = $7.00 × 1.05 = $7.35.

P0 = $7.35 / (0.14 - 0.05) = $7.35 / 0.09 ≈ $81.67.

Alternatively, if the growth rate reverts to 5%, and D1 remains at $7.35, the stock price remains approximately at $81.67, illustrating how dividend levels and growth assumptions influence valuation.

Calculating the Required Rate of Return

Given a dividend at Year 1 (D1) of $4.80, a current stock price of $80, and a growth rate of 5%, the required rate of return (Ke) is derived from the Gordon Growth Model:

Ke = (D1 / P0) + g = ($4.80 / $80) + 0.05 = 0.06 + 0.05 = 0.11 or 11%.

This indicates that investors require an 11% return given the dividend expectations and current stock valuation.

Conclusion

The analysis highlights how bond prices and stock valuations are sensitive to market interest rates, growth expectations, and dividend policies. Bond prices tend to increase when yields decline, illustrating the fixed-income market's inverse relationship between yield and price. Similarly, stock valuation models demonstrate how changes in growth rates and required returns significantly impact their current values. Financial analysts must carefully consider these variables when appraising securities, ensuring accurate investment decision-making based on market dynamics.

References

• Brigham, E. F., & Ehrhardt, M. C. (2016). Financial Management: Theory & Practice. Cengage Learning.
• Damodaran, A. (2012). Investment Valuation: Tools and Techniques for Determining the Value of Any Asset. Wiley.
• Fabozzi, F. J. (2013). Bond Markets, Analysis, and Strategies. Pearson.
• Ross, S. A., Westerfield, R. W., & Jaffe, J. (2019). Corporate Finance. McGraw-Hill Education.
• Gordon, M. J. (1959). Dividends, Earnings and Stock Prices. The Review of Economics and Statistics, 41(2), 99-105.
• DeFond, M. L., & Li, J. (2011). The Market's Reaction to the Announcement of Major Changes in Corporate Governance. Journal of Accounting and Economics, 52(2-3), 257-273.
• Fama, E. F., & French, K. R. (2004). The Capital Asset Pricing Model: Theory and Evidence. Journal of Economic Perspectives, 18(3), 25-46.
• Lintner, J. (1965). The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets. The Review of Economics and Statistics, 47(1), 13-37.
• Higgins, R. C. (2012). Analysis for Financial Management. McGraw-Hill Education.
• Myers, S. C. (2001). Modigliani-Miller Theorem. The New Palgrave Dictionary of Economics, 3, 466-468.