Part A

The dividend discount model assumes the value of a share of common stock is the present value of all future dividends. 
One year holding period 
Assume an investor wants to buy a stock, hold it for one year, and then sell it. The company earned $2.50 a share last year and paid a dividend of $1 a share. The company maintains a 40% payout ratio over time. Financial analysts suggest the firm will earn about $2.75 per share during the coming year and will raise its dividend to $1.10 per share. The risk free rate is 10% and the market risk premium is currently 4%. You project the sale price of this stock a year from now to be $22. 

· Estimate the value of this stock. 
· Would you buy this stock? 

Multiple holding period 

Assume the expected holding period is three years and you estimate the following dividend payments at the end of each year. 
Year 1 - $1.10 per share 
Year 2 - $1.20 per share 
Year 3 - $1/35 per share 
The risk free rate is 10% and the market risk premium is currently 4%. You project the sale price of this stock at the end of the period to be $34. 
· Estimate the value of this stock. 

· Would you buy this stock? 

Infinite period model with supernormal growth 

The Brown Company has a current dividend of $2 per share. The following are the expected annual growth rates for dividends. The required rate of return for the stock is 14%. 

Year 1-3: 25% 
Year 4-6: 20% 
Year 7-9: 15% 
Year 10 on: 9% 

· Estimate the value of this stock. 


Part B 
In contrast to various discounted cash-flow techniques that attempt to estimate a specific value for a stock based on its estimated growth rates and its discount rate, the relative valuation techniques implicitly contend that it is possible to determine the value of an economic entity (i.e., the market, an industry, or a company) by comparing it to similar entities on the basis of several relative ratios that compare its stock price to relevant variables that effect a stock's value, such as earnings, cash flow, book value and sales. 

Consider the following four approaches. 

1. Earnings Multiplier Model 

Assume a stock has an expected dividend payout of 50%, a required rate of return of 12% and an expected growth rate for dividends of 9%. Current earnings are $2.00 per share and the expected growth rate for earnings is 9%. 

· Calculate the earnings multiplier and stock price 

Briefly explain the following methods (for and against) 

2. Price/Cash Flow Ratio 

3. Price/Book Value Ratio 

4. Price/Sales Ratio 
 

Part C

Bent ltd has a bond issue that will mature to its $1000 par value in 12 years. It pays interest annually and has a coupon rate of 11%. 

a) Find the value of the bond if the required rate of return is 
 

· 11% 

· 15% 

· 8% 

 
b) Plot your finding on a set of required return (x-axis) and market value of bond (y-axis) 

c) Use your findings in parts a and bto discuss the relationship between the coupon interest rate on a bond and the required return and the market value of the bond relative to its par value. 

d) What possible reasons could cause the required rate to differ from the coupon interest rate 

  

Part D 

You are required to evaluate the risk and return of the following two assets - A and B individually and see how they might fit into a diversifiable portfolio. Equal halves would be shared between both assets if included in a portfolio 
 

Each asset's risk can be assessed in two ways: in isolation and as part the firm's diversified portfolio of assets. The risk-free rate is currently5%. 

  Return data for assets A and B, 2001-2010 are as follows 

  
The market index is as follows: 

Required 

a) Calculate the annual rate of return for each asset in each of the 10 preceding years, and those values to find the average annual return for each asset over the 10-year period. 

b) Use the returns to find the standard deviation and the coefficient of variation of the returns for each asset over the 10-year period 2001-2010. 

c) Use your findings in questions a and b to evaluate and discuss the return and risk associated with each asset. Which asset appears to be preferable? Explain. 

d) Use the CAPM to find the required return for each asset. Compare this value with average annual returns calculated in question a. 

e) Calculate the portfolio return and standard deviation of a portfolio consisting of both stock A and Stock B 

f) Calculate the weights of the minimum variance portfolio. 

g) Calculate the weights of the optimal risky portfolio 

h) What recommendations would you make with regard to investing in either of the two assets or in a portfolio together?