Microtech Corporation is expanding rapidly and currently needs to retain all of
ID: 2643454 • Letter: M
Question
Microtech Corporation is expanding rapidly and currently needs to retain all of its earnings; hence, it does not pay dividends. However, investors expect Microtech to begin paying dividends, beginning with a dividend of $1.50 coming 3 years from today. The dividend should grow rapidly - at a rate of 41% per year - during Years 4 and 5; but after Year 5, growth should be a constant 7% per year. If the required return on Microtech is 13%, what is the value of the stock today? Round your answer to the nearest cent.
Explanation / Answer
Value of the stock is given by the formula
D1/(1+k)1 + D2/(1+k)2 + D3/(1+k)3 + _ _ _ _ + Dn/ (1+k)n + [Dn+1/ (k-g)] / (1+k)n
where, [Dn+1/ (k-g)] is the terminal value
When growth becomes constant, the terminal value at time n becomes Dn+1/(k-g)
So, in this case, dividend starts from year 3, grows at 32% for 2 years and then growth becomes constant after year 5. The reuired return is 16%.
Thus, the value of the stock today = D1/(1+k)1 + D2/(1+k)2 + D3/(1+k)3 + D4/(1+k)4+ D5/(1+k)5 + [D6/(k-g)]/(1+k)5
D1 = D2 = 0
D3 = $1.5
D4= 1.5 * (1 + 32%) = $1.98
D5= 1.98 * (1 + 32%) = $2.6136
D6= 2.6136 * (1 + 8%) = $2.822688
Terminal Value at the end of year 5 = D6/(k-g) = 2.822688 / (16% - 8%) = 2.822688/0.08 = $35.2836
Value of the stock today = 0/(1+ 0.16)1 + 0/(1+ 0.16)2 + 1.50/(1+ 0.16)3 + 1.98/(1+ 0.16)4 + 2.6136/(1+ 0.16)5 +
35.2836/(1+ 0.16)5 = $20.10