Final 307 Summer 2017 Name

Fina 307summer 2017name

Fina 307 Summer 2017 Name: ID#: Assignment 2 (due at the beginning of class on Monday, June 19th): Remember: you will be expected to show your all work, including timeline, formulas, inputs and outputs from your calculator. 1. Calculate the price of a 9 % bond with $1,000 par and 6 years to maturity that pays semi- annual coupons. The yield to maturity on similar bonds is 8.5 %. 2. A 15-year bond with 6 percent annual coupon rate. The bond pays semi-annual coupon. The bond’s market price is $963.20. Calculate the Yield to Maturity. 3. A bond has a face value of $1,000, a coupon of 4% paid annually, a maturity of 36 years, and a yield to maturity of 7%. What rate of return will be earned by an investor who purchases the bond for $608.94 and holds it for 1 year if the bond’s yield to maturity at the end of the year is 9%? 4. General Matter’s outstanding bond issue has annual coupon rate of 10.6%, and it sells at a yield to maturity of 8.70%. The firm wishes to issue additional bonds to the public at face value. What coupon rate must the new bonds offer in order to sell at face value? 5. Fincorp will pay a year-end dividend of $2.40 per share, which is expected to grow at a 4% rate for the indefinite future. The discount rate is 12%. What is the stock selling for? 6. How much should you pay for a share of stock that offers a constant growth rate of 10%, requires a 16% rate of return, and is expected to sell for $50 one year from now? 7. JetHair’s earnings are $1.5 per share. The firm’s ROE is 15% and its payout ratio is 30%. a. What is JetHair’s dividend for next year if its required rate of return is 20%? b. What is the stock price?

Paper For Above instruction

This assignment encompasses several fundamental concepts of bond valuation, stock valuation, and return calculations, central to understanding financial decision-making. The problems primarily focus on calculating bond prices, yields to maturity, rates of return, and stock prices under different growth and market conditions. These calculations utilize the core principles of present value, future value, dividend discount models, and yield calculations based on given cash flows and market data. Analyzing these financial metrics equips investors and financial managers with insights necessary for making informed investment and financing decisions.

Bond Valuation and Yield Calculations

The first two problems involve bond valuation and the calculation of yield to maturity (YTM). Bond valuation hinges on estimating the present value of future cash flows—comprising semi-annual coupon payments and the face value at maturity—discounted at the market yield. In problem 1, calculating the bond's price requires us to determine the present value of semi-annual coupons and the face value, discounted at 8.5% annual YTM, considering the semi-annual periods. The formula involves:

\[ P = \sum_{t=1}^{n} \frac{C}{(1 + r/2)^{2t}} + \frac{F}{(1 + r/2)^{2n}} \]

Where \( C \) is the semi-annual coupon payment, \( F \) is face value, \( r \) is annual YTM, and \( n \) is total periods.

Similarly, in problem 2, the market price of a bond is given, and the task is to reverse-engineer the YTM by solving the present value equation or via financial calculator or software, considering semi-annual coupons.

Return and Yield to Maturity at Different End-Period Yields

Problem 3 examines the rate of return earned by an investor who purchases a bond at a given price and holds it for a year, considering changes in YTM from 7% to 9%. This involves calculating the bond's price at purchase, its accrued income, and the new price after one year, then calculating total return incorporating capital gains/losses and coupons received. The yield-to-maturity reflects the internal rate of return (IRR) of the bond's cash flows discounted at market yields.

Coupon Rate Adjustment for Bonds Selling at Par

In problem 4, to determine the coupon rate that would result in issuance at face value when the YTM is known, we use the relationship between coupon rate, YTM, and bond price. When bonds are issued at face value, coupon rate equals the YTM at issuance. The problem asks for adjusting the coupon rate to align with the market YTM of 8.70%, implying the coupon rate must be set equal to this yield to ensure the bond sells at face value.

Stock Valuation via Dividend Discount Model

Problem 5 employs the Gordon Growth Model (Dividend Discount Model) to value stock based on perpetual dividend growth, where the stock price equals the next year's dividend divided by the difference between required rate of return and growth rate:

\[ P = \frac{D_1}{r - g} \]

Here, \( D_1 \) is the dividend expected next year, \( r \) is the required rate of return, and \( g \) is the growth rate. Plugging in the data provides a present valuation reflecting market expectations.

Stock Price Calculation with Constant Growth

Problem 6 involves determining the price of a stock based on expected future price and growth rate, using the growth model:

\[ P_0 = \frac{P_1}{1 + r} \]

where \( P_1 \) is the expected sale price after one year, \( r \) is the required return.

Dividend and Stock Price Estimation for a Company

Problems 7a and 7b focus on dividend estimation and stock valuation. Given earnings, ROE, payout ratio, and required return, dividend next year can be calculated as earnings multiplied by payout ratio, and stock price using dividend discount models, which consider the dividend growth and required rate.

Conclusion

Overall, these problems illustrate key financial valuation techniques vital for investors and corporate financial managers. They underscore the importance of understanding cash flow timing, discount rates, growth assumptions, and market yields to accurately assess prices and returns of bonds and stocks. Mastery of these concepts enables effective investment decisions, risk management, and strategic financial planning.

References

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