Problem 713 Nonconstant Growth Stock Valuation Simpkins Corp

Problem 7-13 Nonconstant Growth Stock Valuation Simpkins Corporation does not pay any dividends because it is expanding rapidly and needs to retain all of its earnings. However, investors expect Simpkins to begin paying dividends, with the first dividend of $1.00 coming 3 years from today. The dividend should grow rapidly - at a rate of 75% per year - during Years 4 and 5. After Year 5, the company should grow at a constant rate of 9% per year. If the required return on the stock is 14%, what is the value of the stock today (assume the market is in equilibrium with the required return equal to the expected return)? Round your answer to the nearest cent. Do not round your intermediate computations.

Solution

D3=$1

D4=(1*1.75)=$1.75

D5=(1.75*1.75)=$3.0625

Value after year 5=(D5*Growth rate)/(Required return-Growth rate)

=(3.0625*1.09)/(0.14-0.09)=$66.7625

Hence current value=Future dividends*Present value of discounting factor(14%,time period)

=1/1.14^3+1.75/1.14^4+3.0625/1.14^5+66.7625/1.14^5

which is equal to

=$37.98(Approx).