Example 12.1Suppose that the 3-year interest rate is 6% with continuous compounding. Thismeans that 1,000e 0.06x3 = $835.27 will grow to $1,000 in 3 years. The differencebetween $1,000 and $835.27 is $164.73. Suppose that a stock portfolio is worth$1,000 and provides a dividend yield of 1.5% per annum. Suppose further that a3-year at-the-money European call option on the stock portfolio can be purchasedfor less than $164.73. (From DerivaGem, it can be verified that this will be thecase if the volatility of the value of the portfolio is less than about 15%.) A bankcan offer clients a $1,000 investment opportunity consisting of:1. A 3-year zero-coupon bond with a principal of $1,0002. A 3-year at-the-money European call option on the stock portfolio.If the value of the porfolio increases the investor gets whatever $1,000 invested inthe portfolio would have grown to. (This is because the zero-coupon bond paysoff $1,000 and this equals the strike price of the option.) If the value of theportfolio goes down, the option has no value, but payoff from the zero-couponbond ensures that the investor receives the original $1,000 principal invested.

ExplanationThe solution begins by determining the present value of a zero-coupon bond needed to grow…

Answered: Example 12.1 Suppose that the 3-year…

Fundamentals Of Financial Management, Concise Edition (mindtap Course List)

10th Edition

ISBN:9781337902571

Author:Eugene F. Brigham, Joel F. Houston

Publisher:Eugene F. Brigham, Joel F. Houston

Chapter9: Stocks And Their Valuation

Section: Chapter Questions

Problem 5TCL

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A3) Finance Suppose that the risk-free interest rate is 10% per annum with continuous compounding and that the dividend yield on a stock index is 4% per annum. The index is standing at 400, and the futures price for a contract deliverable in four months is 405. What arbitrage opportunities does this create?
Suppose DO = $2.00. rs= 9%, What if g = 30% the first year, 20% the second year, and 10% the third year, and return to its long-run constant growth rate of 4%, Calculate the value of the stock today? O $62.7846 O $55.5021 O $60.3211 O $65.7223 O $72.3487
Suppose the stock price is $ 95 and the continously compounded interest rate is 7 %. a) What is the price of a 6 - month forward price, assuming dividends are zero? $ ? b) If the 6 - month forward price is $ 96.55, what is the annualized forward premium? % ? c) If the 6 - month forward price is $ 96.55, what is the annualized continous dividend yield? % ?
The S&R index spot price is 1100 and the continuously compounded interest rate is 5%. You observed a 9-month forward price of 1129.257. (a) What is the implied dividend yield? (b) Suppose you believe the dividend yield will be 3% over the next 9 months. How can you arbitrage?
Suppose that the risk-free interest rate is 6% per annum with continuous compounding and that the dividend yield on a stock index is 4% per annum. The index is standing at 400, and the futures price for a contract deliverable in four months is 405. What arbitrage opportunities does this create?
6. Suppose that the simple annual returns on an investment over a 3-year period are: 8%, 2%, and 12%. What is the closest to the annualised holding period return? (a) 22.0% (b) 7.25% (c) 7.33% (d) 23.4% 7. A stock is currently trading at 20. Assume that at the end of one month it will either be 23 or 17. The risk-free interest rate is 5% per annum. The value of an ATM put option with a maturity of 1 month is closest to (a) 0.55 (b) 0.95 (c) 1.45 (d) 3.00
11. Consider $10m invested in a stock. The annual volatility of the rate of return is 25%. Assuming that the return is IID and normally distributed with p=0. a. What is the 99% 1-day VAR? b. What is the 95% 1-day VAR? c. What is the 95% one-week VAR? d. What is the 95% 1-day ES? e. What is the 99% 10-day ES?
If d1 = 1.25, g (which is constant) = 4.7%, and Po = $26, what is the expected dividend yield for the coming year? Bond valuation related problems should be solved by using a financial calculator or MS excel spreadsheet. Accordingly, you must show the values of all relevant time valu of money variables
Assume that the dividend payout ratio will be 75 percent when the rate on long-term government bonds falls to 8 percent. Because investors are becoming more risk averse, the equity risk premium will rise to 7 percent and investors will require a 15 percent return. The return on equity will be 12 percent. To what price will the market rise if the earnings expectation is $32.00?
a) If the dividend yield is 1.40% annualized, the interest rate is -0.10% annualized, and the index is trading at 28, 144 today, what is the expected price of a 6-month forward? 28, 144e(-0.001 -0.0140)*0.50 = 27,961.66 b ) The 6-month forward is currently quoted at 28,000. Using the information above and the grid below, show how you would arbitrage this index profitably. Be sure to indicate whether each transaction is long or short ( buy or sell) and to include (+) and (-) signs on your cash flows. Use 0 decimals (whole numbers only) in your answers. Transaction Time 0 cash flows Time t cash flows Totals:
Suppose that Do = $1.00 and the stock's last closing price is $15.85. It is expected that earnings and dividends will grow at a constant rate of g = 3.50% per year and that the stock's price will grow at this same rate. Let us assume that the stock is fairly priced, that is, it is in equilibrium, and the most appropriate required rate of return is rs = 10.00%. The dividend received in period 1 is D1 = $1.00 × (1+0.0350) = $1.04 and the estimated intrinsic value in the same period is based on the D2 constant growth model: P₁: TS-8 Using the same logic, compute the dividends, prices, and the present value of each of the dividends at the end of each period. Activity Frame Dividend Price PV t 10.00% Period (Dollars) (Dollars) (Dollars) 0 $1.00 $15.85 1 1.03 16.46 $0.94 2 1.07 17.08 $0.97 3 1.11 17.69 $1.01 4 1.15 18.31 $0.97 5 1.19 18.92 $0.94 The dividend yield for period 1 is and it will The capital gain yield expected during period 1 is and it will each period. each period. If it is…
Suppose the interest rate is 12 percent and the firm is expected to grow at a rate of 7 percent for the foreseeable future. The firm's current profits are P50 million. What is the value of the firm (the present value of its current and future. earnings)?

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