Question

1.  The HT and USR’s stock returns are shown in the following table. Assume you invest 40% in HT and 60% in USR. Calculate your portfolio’s expected return and standard deviation.

Economy	Prob.	HT	USR
Recession	0.1	-27.00%	6.00%
Below avg	0.2	-7.00%	-14.00%
Average	0.4	15.00%	3.00%
Above avg	0.2	30.00%	41.00%
Boom	0.1	45.00%	26.00%

2.  Church Inc. is presently enjoying relatively high growth because of a surge in the demand for its new product.  Management expects earnings and dividends to grow at a rate of 25% for the next 4 years, after which competition will probably reduce the growth rate in earnings and dividends to zero, i.e., g = 0.  The company’s last dividend, D₀, was $1.25, its beta is 1.20, the market risk premium is 5.50%, and the risk-free rate is 3.00%.  What is the current price of the common stock?

Answer 1

1)

	Security if State	Returns Occurs
	Prob of State of Economy	HT	USR		portfolio
Recession	10%	-27%	6%
below average	20%	-7%	-14%
average	40%	15%	3%
above average	20%	30%	41%
boom	10%	45%	26%
	expected return	0.1240	9.80%		10.84%
	variance	0.040144	0.035416
	standard deviation	0.20	18.82%		19.31%

Expected return = sum of (probability of state * return of state)

E(X^2) =  sum of (probability of state * return of state^2)

variance = E(X^2) - (E(X))^2

Standard deviation = sqrt(variance)

2)

Expected return = risk free rate + beta * market risk premium

= 3% + 1.2 * 5.5%

= 9.6%

value of stock = Present value of dividends + Horizontal value

Horizontal value = dividend next year/(Required return - growth rate)

Horizontal value = 1.25 * 1.25^4/(0.096-0)

= 31.7891438802

value of stock = 1.25*1.25/1.096 + 1.25*1.25^2/1.096^2 + 1.25*1.25^3/1.096^3 + 1.25*1.25^4/1.096^4 +31.7891438802/1.096^4

= 29.05