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Ch08 P08 Build a Model
| Spring 1, 2013 | ||||||||||||||||||||||||||||||||||||||||||
| 7/22/12 | ||||||||||||||||||||||||||||||||||||||||||
| Chapter 8. Ch 08 P08 Build a Model | ||||||||||||||||||||||||||||||||||||||||||
| Except for charts and answers that must be written, only Excel formulas that use cell references or functions will be accepted for credit. | ||||||||||||||||||||||||||||||||||||||||||
| Numeric answers in cells will not be accepted. | ||||||||||||||||||||||||||||||||||||||||||
| You have been given the following information on a call option on the stock of Puckett Industries: | ||||||||||||||||||||||||||||||||||||||||||
| P | = | $65 | X = | $70 | ||||||||||||||||||||||||||||||||||||||
| t = | 0.5 | rRF = | 4% | |||||||||||||||||||||||||||||||||||||||
| s = | 50.00% | |||||||||||||||||||||||||||||||||||||||||
| a. Using the Black-Scholes Option Pricing Model, what is the value of the call option? | ||||||||||||||||||||||||||||||||||||||||||
| First, we will use formulas from the text to solve for d1 and d2. | ||||||||||||||||||||||||||||||||||||||||||
| Hint: use the NORMSDIST function. | ||||||||||||||||||||||||||||||||||||||||||
| (d1) | N(d1) = | |||||||||||||||||||||||||||||||||||||||||
| (d2) | N(d2) = | |||||||||||||||||||||||||||||||||||||||||
| Using the formula for option value and the values of N(d) from above, we can find the call option value. | ||||||||||||||||||||||||||||||||||||||||||
| VC | ||||||||||||||||||||||||||||||||||||||||||
| b. Suppose there is a put option on Puckett’s stock with exactly the same inputs as the call option. What is the value of the put? | ||||||||||||||||||||||||||||||||||||||||||
| Put option using Black-Scholes modified formula | ||||||||||||||||||||||||||||||||||||||||||
| Put option using put-call parity |
Sheet2
Brushy Mountain Mining Company’s ore reserves are being depleted, so its sales are falling. Also, its pit is getting deeper each year, so its costs are rising. As a result, the company’s earnings and dividends are declining at the constant rate of 5% per year. If D0 = $3 and rs = 17%, what is the value of Brushy Mountain Mining’s stock? Round your answer to the nearest cent.
$
Boehm Incorporated is expected to pay a $1.70 per share dividend at the end of this year (i.e., D1 = $1.70). The dividend is expected to grow at a constant rate of 10% a year. The required rate of return on the stock, rs, is 18%. What is the value per share of the company’s stock? Round your answer to the nearest cent.
$
Investors require a 17% rate of return on Brooks Sisters’ stock (rs = 17%).
a. What would the value of Brooks’s stock be if the previous dividend was D0 = $3.75 and if investors expect dividends to grow at a constant compound annual rate of (1) – 2%, (2) 0%, (3) 5%, or (4) 13%? Round your answers to the nearest cent.
1. $
2.
$
3. $
4. $
b. Using data from part a, what is the Gordon (constant growth) model’s value for Brooks Sisters’s stock if the required rate of return is 17% and the expected growth rate is (1) 17% or (2) 18%? Are these reasonable results? Explain.
1.
2.
Problem
A company currently pays a dividend of $3.5 per share, D0 = 3.5. It is estimated that the company’s dividend will grow at a rate of 19% percent per year for the next 2 years, then the dividend will grow at a constant rate of 7% thereafter. The company’s stock has a beta equal to 1.95, the risk-free rate is 6.5 percent, and the market risk premium is 5 percent. What is your estimate is the stock’s current price? Round your answer to the nearest cent.
$
Nick’s Enchiladas Incorporated has preferred stock outstanding that pays a dividend of $5 at the end of each year. The preferred stock sells for $30 a share. What is the stock’s required rate of return? Round the answer to two decimal places.
The risk-free rate of return, rRF , is 12%; the required rate of return on the market, rM, 16%; and Schuler Company’s stock has a beta coefficient of 1.6.
a. If the dividend expected during the coming year, D1, is $2.75, and if g is a constant 2.25%, then at what price should Schuler’s stock sell? Round your answer to the nearest cent.
$
b. Now, suppose the Federal Reserve Board increases the money supply, causing a fall in the risk-free rate to 6% and rM to 13%. How would this affect the price of the stock? Round your answer to the nearest cent.
$
c. In addition to the change in part b, suppose investors’ risk aversion declines; this fact, combined with the decline in rRF, causes rM to fall to 10%. At what price would Schuler’s stock sell? Round your answer to the nearest cent.
$
d. Suppose Schuler has a change in management. The new group institutes policies that increase the expected constant growth rate to 7%. Also, the new management stabilizes sales and profits, and thus causes the beta coefficient to decline from 1.6 to 1.0. Assume that rRF and rM are equal to the values in part c. After all these changes, what is Schuler’s new equilibrium price? (Note: D1 goes to $2.88.) Round your answer to the nearest cent.
$
The beta coefficient for Stock C is bC = 0.3, and that for Stock D is bD = – 0.5. (Stock D’s beta is negative, indicating that its rate of return rises whenever returns on most other stocks fall. There are very few negative-beta stocks, although collection agency and gold mining stocks are sometimes cited as examples.)
a. If the risk-free rate is 6%and the expected rate of return on an average stock is 14%, what are the required rates of return on Stocks C and D? Round the answers to two decimal places.
1. rC =
2. rD =
b. For Stock C, suppose the current price, P0, is $25; the next expected dividend, D1, is $1.50; and the stock’s expected constant growth rate is 4%. Is the stock in equilibrium? Explain, and describe what would happen if the stock is not in equilibrium.
I. In this situation, the expected rate of return = 8.40%. However, the required rate of return is 10%. Investors will seek to buy the stock, raising its price to $34.09. At this price, the stock will be in equilibrium.
II. In this situation, the expected rate of return = 10%. However, the required rate of return is 8.40%. Investors will seek to buy the stock, raising its price to $34.09. At this price, the stock will be in equilibrium.
III. In this situation, the expected rate of return = 10%. However, the required rate of return is 8.40%. Investors will seek to sell the stock, raising its price to $34.09. At this price, the stock will be in equilibrium.
IV. In this situation, the expected rate of return = 8.40%. However, the required rate of return is 10%. Investors will seek to sell the stock, raising its price to $34.09. At this price, the stock will be in equilibrium.
V. In this situation, both the expected rate of return and the required rate of return are equal. Therefore, the stock is in equilibrium at its current price.
