You Are Called In As A Financial Analyst To Appraise The Bon
You Are Called In As A Financial Analyst To Appraise The Bonds Of Olse
You are asked to evaluate the bonds issued by Olsen’s Clothing Stores. The bonds have a par value of $1,000, accrue interest at a quoted annual rate of 10%, paid semiannually. The bonds have 15 years remaining until maturity. Your task is to compute the current price of these bonds based on a semiannual analysis. Additionally, assess the impact on the bond price if the yield to maturity decreases to 8% when there are 10 years left to maturity. Use a PV factor rounded to three decimal places and round your final answers to two decimal places, omitting the dollar sign.
Furthermore, imagine Stagnant Iron and Steel currently pays a $12.25 annual dividend, which remains constant. If the required rate of return for the stockholders is 18%, determine the stock's current price. Similarly, analyze Ecology Labs, Inc., which will pay a dividend of $6.40 in the next year, with a required return (Ke) of 14%, and a constant growth rate of 5%. For each subsequent question, keep all variables the same except the one specifically altered; each scenario is independent.
Calculate the stock price in each situation: first with the base data, then with the increased Ke to 18%, then with the growth rate raised to 9%, and finally with D1 increased to $7.00. Also, determine the required rate of return given the dividend of $4.80 at year-end, a stock price of $80, and a growth rate of 5%. Ensure all calculations adhere to proper financial formulas and the assumptions as described.
Paper For Above instruction
In the realm of fixed-income securities, bonds serve as essential financial instruments that provide a fixed stream of income to investors. Accurately appraising the value of bonds requires understanding of various factors including the bond's coupon rate, maturity, yield to maturity (YTM), and payment structure. This paper will analyze the valuation of Olsen’s Clothing Stores bonds, examining the impact of interest rate changes on bond prices, and explore key valuation principles for stocks and dividends in different scenarios.
Valuation of Olsen’s Clothing Stores Bonds
The bonds in question possess a face value of $1,000 with a 10% annual coupon rate paid semiannually. That means each period, investors earn $50 in interest (10% of $1,000 divided by 2). With 15 years until maturity, there are a total of 30 semiannual periods. The bond's price can be calculated through the present value of its future coupon payments plus the present value of the face value at maturity, discounted at the bond's yield to maturity (YTM). Since the YTM is 10% annually, with semiannual payments, the period rate is 5% (10% divided by 2).
Using the bond valuation formula:
Price = (C × PV Annuity factor) + (FV × PV Lump Sum factor)
Where:
- C = semiannual coupon payment = $50
- FV = face value = $1,000
- YTM per period = 5%
- Number of periods = 30
The present value of the coupon payments is:
PV Coupons = C × [1 - (1 + r)^-n] / r = 50 × [1 - (1 + 0.05)^-30] / 0.05 = 50 × PV Annuity factor
Calculating PV Annuity factor with PV factor rounded to three decimal places:
PV Annuity factor = (1 - (1 + 0.05)^-30) / 0.05 ≈ 18.256
Thus, PV Coupons ≈ 50 × 18.256 ≈ 912.80
The present value of the face value:
PV Face = FV / (1 + r)^n = 1,000 / (1.05)^30 ≈ 1,000 / 4.321 ≈ 231.45
Therefore, the current bond price is approximately:
Bond Price ≈ 912.80 + 231.45 = 1144.25
When the YTM drops to 8% (annual), semiannual rate becomes 4%. The number of periods remains 30, with similar calculations:
PV Annuity factor at 4% = (1 - (1 + 0.04)^-30) / 0.04 ≈ 20.024
PV Coupons ≈ 50 × 20.024 ≈ 1001.20
PV Face ≈ 1,000 / (1.04)^30 ≈ 1,000 / 3.243 ≈ 308.49
New bond price ≈ 1001.20 + 308.49 ≈ 1309.69
Stock Valuation of Stagnant Iron and Steel
When a company's dividends are expected to remain constant, the stock's value can be computed using the perpetuity formula:
P0 = D / Ke
Substituting D = $12.25 and Ke = 18% (or 0.18):
P0 = 12.25 / 0.18 ≈ 68.06
This represents the current fair value of the stock assuming no growth and a required rate of 18%.
Valuation of Ecology Labs, Inc. Stocks
Ecology Labs pays a dividend D1 of $6.40, with a required return Ke of 14% and a growth rate g of 5%. The Gordon Growth Model gives:
P0 = D1 / (Ke - g) = 6.40 / (0.14 - 0.05) = 6.40 / 0.09 ≈ 71.11
This is the intrinsic value under current assumptions.
Adjustments to the model include:
- Increasing Ke to 18%: P0 = 6.40 / (0.18 - 0.05) = 6.40 / 0.13 ≈ 49.23
- Increasing g to 9%: P0 = 6.40 / (0.14 - 0.09) = 6.40 / 0.05 = 128.00
- Increasing D1 to $7.00: P0 = 7.00 / (0.14 - 0.05) = 7.00 / 0.09 ≈ 77.78
Lastly, given a current dividend D1 of $4.80, a stock price of $80, and g of 5%, the required rate of return Ke can be calculated using the Gordon model rearranged to solve for Ke:
Ke = (D1 / P0) + g = (4.80 / 80) + 0.05 = 0.06 + 0.05 = 0.11 or 11%
Conclusion
Valuation of bonds and stocks demands meticulous analysis of cash flows, discount rates, and growth expectations. Changes in market interest rates significantly influence bond prices, with prices rising when rates decline and falling when rates rise. For stocks with fixed dividends, the perpetuity model provides a straightforward valuation method under steady conditions. When dividends grow, the Gordon Growth Model effectively estimates intrinsic values, contingent on accurate input parameters. Overall, understanding these valuation techniques enables investors and analysts to make informed decisions aligned with market conditions and expected returns.
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