Question

1. C&P Trading Inc., is entering into a 3-year remodeling and expansion project. Last year, the company paid a dividend of $3.40. It expects zero growth in the next year. In years 2 and 3, and 5% growth is expected, and in year 4, and 15% growth. In year 5 and thereafter, growth should be a constant 10% per year. What is the maximum price per share that an investor who requires a return of 12% should pay for Home Place Hotels common stock?

1. Find the value of the cash dividends at the end of each year. 4'
2. Find the present value of the dividends expected during the initial growth period.3'
3. Find the value of the stock at the end of the initial growth period. 4'
4. Find the value of the stock. (Sum of PV of dividends during initial growth period and PV price of stock at end of growth period) 4'

Answer 1

Cash dividend at the end of each year

Year 1 = $ 3.40 (same as last year, since no growth in year 1)

Year 2 = Dividend in year1 * (1+g2) = $3.40*(1+0.05) = $3.40*1.05 = $ 3.57

Year 3 = Dividend in year2 * (1+g3) = $3.57*(1+0.05) = $3.57*1.05 = $ 3.7485

Year 4 = Dividend in year3 * (1+g4) = $3.7485*(1+0.15) = $3.7485*1.15 = $ 4.3108

where, g2=Growth rate of year 2 = 5% ; g3=Growth rate of year 3 = 5% ; g4=Growth rate of year 4 = 15%

Present value of the dividends expected

At the end of year 1 = Dividend/(1+required rate) = $ 3.4/(1+0.12) = $ 3.4/1.12 = $ 3.0357

At the end of year 2 = Dividend/(1+required rate) = $ 3.57/(1+0.12)2 = $ 3.57/(1.12)2 = $ 3.57/1.2544= $2.8460

At the end of year 3 = Dividend/(1+required rate) = $ 3.7485/(1+0.12)3 = $ 3.7485/(1.12)3 = $ 3.7485/1.4049= $ 2.6681

At the end of year 4 = Dividend/(1+required rate) = $ 4.3108/(1+0.12)4 = $ 4.3108/(1.12)4 = $ 4.3108/1.5735= $ 2.7396

Value of the stock at the end of initial growth period

Price of the share at the end of the year 4 = Dividend paid in year 4 * (1+constant growth rate)/(ke-constant growth rate)

= 4.3108 * (1+0.10)/(0.12-0.10)

= 4.3108 * 1.1/0.02

= 4.3108 * 55

= $ 237.0940

Maximum price per share that the investor will pay:-

Value of the stock = Present value of all dividends + Present value of the stock at the end of initial growth period

= $ 3.0357+$ 2.8460+$ 2.6681+$ 2.7396 + $ 237.0940/(1.12)4

= $ 11.2894 + $ 237.0940/1.5735

= $ 11.2894 + $ 150.6750

= $ 161.9644