Question

1. Salt Lake City Services, Inc., provides maintenance services for commercial buildings. Currently, the beta on its common stock is 1.08. The risk-free rate is now 10 percent, and the expected return on the market portfolio is 15 percent. It is January 1, and the company is expected to pay a $2 per share dividend at the end of the year, and the dividend is expected to grow at a compound annual rate of 11 percent for many years to come. Based on the CAPM and other assumptions you might make, what dollar value would you place on one share of this common stock?

2. Schmendiman, Inc., is the sole manufacturer of schmedimite (an inflexible, brittle building material made of radium and asbestos). Assume that the company’s common stock can be valued using the constant dividend growth model (also sometimes known as the “Gordon Dividend Growth Model”). You expect that the return on the market will be 14 percent and the risk-free rate is 6 percent. You have estimated that the dividend one year from now will be $3.40, the dividend will grow at a constant 6 percent, and the stock’s beta is 1.50. The common stock is currently selling for $30.00 per share in the marketplace.

1. What value would you place on one share of this company’s common stock?

2. Is the company’s common stock overpriced, underpriced, or fairly priced? Why

Answer 1

Answer:

Salt Lake City Services Inc

1. Valuation of shares using Gordon Dividend Growth model:

Value of stock =

= $ 2 / (0.154 - 0.11)

= $ 2 / ( 0.044 )

= $ 45.4545454545

Where, D1 = Expected dividend per share

k = Cost of capital equity

g = Dividend growth rate

Note:

Cost of capital using CAPM :

= 10 % + 1.08 (15 % - 10 %)

= 10 % + 1.08 (5 %)

= 10 % + 5.4 %

= 15.4 %

Where, Rf = Risk free rate

= Beta of the investment

   = Expected return on morket portfolio

Schmendiman, Inc.

2.Valuation of share using Gordon Dividend growth model:

Value of stock =

= $ 3.40 / ( 0.18 - 0.06 )

= $ 3.40 / ( 0.12 )

= $ 28.33333333

Where, D1 = Expected dividend per share

k = Cost of capital equity

g = Dividend growth rate

Note:

Cost of capital using CAPM :

= 6 % + 1.50 ( 14 % - 6 % )

= 6 % + 1.50 ( 8 % )

= 6 % + 12 %

= 18 %

Where, Rf = Risk free rate

= Beta of the investment

   = Expected return on morket portfolio

The common stock is currently selling for $ 30 per share

The value of common stock as per Gordon dividend growth model is $ 28.3333 per share

Hence, the company's common stock is overpriced, because the current selling price is higher than the value of stock.