Question

Problem 2.- Stock Valuation

Gonzales Company is a great corporation going through some good times. It has never paid a dividend in the past but plans to begin next year with a dividend of $1.50. The CFO, Dr. Gonzales, expects that the dividend growth rate will be 15% for the next 4 years, after which dividends are expected to grow at a constant rate of 2% forever. You searched yahoo finance and found that the Beta for the company is 1.5. Additionally, you know that the risk-free rate is 2% and that the return on the market is 10%. Given the results of the election, the Doctor Gonzales is interested in finding out how changing economic conditions, particularly an increase in interest rate and the return on the market. He has asked you to answer the following questions

1.   What is the current stock price for Gonzales Company?

P₀= ?

2.   Complete the table below with the changes to rm and rf:

Price of Gonzales Co under different assumptions

Price		rf
		2%	3%
rm	10%
	11%

3. Can you reach a general conclusion regarding how rf and rm affect stock prices?

Answer 1

Part (1)

D1 = 1.50; D2 = D1 x (1 + g*); ....D5 = D4 x (1 + g*)

D6 = D5 x (1 + g)

g* = 15%; g = 2%

Beta = 1.5; Cost of equity, r = Rf + beta x (Rm - Rf) = 2% + 1.5 x (10% - 2%) = 14%

Terminal value at the end of year 5 = D6 / (r - g)

Please see the table below. All financials are in $. Please see the second column to understand the mathematics. The cells colored in yellow contain your answer. Adjacent cell in blue shows the excel formula used to get the answer.

Hence, the current stock price, P0 = $ 18.28

Part (2)

We have to now change the Rf and Rm to calculate the values for each of the scenarios. I will keep changing them in my model to get the output. Summary is shown below:

	Rf = 2%	Rf = 3%
Rm = 10%	18.28	19.14
Rm = 11%	16.08	16.76

Part (3)

rf and rm affect stock prices inversely. GThey are used to calculate the cost of equity, which in turn in used to discount the cash flows to arrive at the valuation of the sotck. Hence, higher the discount rate, lower will be the valuation.

Hence, an increase in rf and rm will increase the discount rate and hence lower the stock prices and vice versa.