Building on your experience in the world of education, you are considering buying a for-profit educational institution, University of Tucumcari (UOT). UOT had earnings of $4.00 per share (at time 0) with a retention ratio of 40%. It has been facing more competition in recent years and anticipates that its growth rate for earnings in future years is as follows:
First two years 10% per year
Following two years 8% per year
Following ten years 6% per year
Following two years 4% per year
After these 16 years, it anticipates that it will grow at annual rate of 3% for the foreseeable future. The company is expected to maintain its retention ratio (40%) for the foreseeable future. There is some risk associated with this venture, so you decide that you need to consider this risk in determining the appropriate required rate of return. Using historical information, you calculate that the beta of UOT has been 1.2. The expected return on the market is 12%. A recently issued, now having thirty years to maturity, 5% coupon, semiannual Treasury bond is selling for 95% of par ($950 for a $1000 bond).
(a)How much should one pay for a share of UOT? That is, what is a fair price for UOT?
(b) What is the price anticipated at year 20? (c)What rate of return should you anticipate that you should earn on UOT for the first year (i.e. between time 0 and year 1)? (d)What is the capital gains yield and dividend yield for first year? (e)What is the capital gains yield and dividend yield that you would anticipate for the 34th year?
Solution completed in excel for you.