Question

Home Place​ Hotels, Inc., is entering into a​ 3-year remodeling and expansion project. The construction will have a limiting effect on earnings during that​ time, but when it is​ complete, it should allow the company to enjoy much improved growth in earnings and dividends. Last​ year, the company paid a dividend of  $4.60. It expects zero growth in the next year. In years 2 and​ 3, 5​% growth is​ expected, and in year​ 4, 17​% growth. In year 5 and​ thereafter, growth should be a constant 8%per year. What is the maximum price per share that an investor who requires a return of 18​% should pay for Home Place Hotels common​ stock?

An investment banker has recommended a $65,000 portfolio containing assets B, D, and F. $10,000 will be invested in asset B, with a beta of 1.5; $35,000 will be invested in asset D, with a beta of 2.0; and $20,000 will be invested in asset F, with a beta of 0.5. What is the beta of this portfolio?

Answer 1

Price of the stock is the present value of the dividends discounted at the required rate of return

Price of the stock = Horizon value + presnt value of dividends for the first 4 years

Horizon value can be calculated using the Constant dividend growth discount model.

Horizon value = Dividend in year 5 / ( Re - g)

Re = Required rate of return

g = growth rate

Dividend for year 1 = 4.60

Dividend for year 2 = 4.60*1.05 = 4.83

Dividend for year 3 = 4.83 * 1.05 =5.0715

Dividend for year 4 = 5.0715 *1.17 = 5.933655

Dividend for year 5 = 6.4083474

Horizon value = 6.4083474 / ( 0.18 - 0.08)

= 64.08

Present value of horizon value = 64.08 / ( 1.18)^4

= 33.05

Price of the stock = 4.60 / 1.18 + 4.83 /1.18^2 + 5.0715/1.18^3 + 5.933655 / 1.18^4 + 33.05

= 3.90 + 3.47 + 3.09 + 3.06 + 33.05

= 45.76

Beta of the portfolio is the weighted average of the beta of the individual stocks where the weights are the proportion of stock in the portfolio

Portfolio beta = ( 10000 * 1.5 + 35000*2 + 20000 * 0.5) / 65000

= (15000 + 70000 + 10000) / 65000

= 95000 / 65000

= 1.46