Question

he Digital Electronic Quotation System (DEQS) Corporation pays no cash dividends currently and is not expected to for the next five years. Its latest EPS was $18.50, all of which was reinvested in the company. The firm’s expected ROE for the next five years is 14% per year, and during this time it is expected to continue to reinvest all of its earnings. Starting in year 6, the firm’s ROE on new investments is expected to fall to 9%, and the company is expected to start paying out 40% of its earnings in cash dividends, which it will continue to do forever after. DEQS’s market capitalization rate is 25% per year.

a. What is your estimate of DEQS’s intrinsic value per share? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

b. Assuming its current market price is equal to its intrinsic value, what do you expect to happen to its price over the next year? (Round your dollar value to 2 decimal places.)

Because there is no dividend  Correct, the entire return must be in capital gains  Correct.

c. What do you expect to happen to price in the following year? (Round your dollar value to 2 decimal places.)

d. What is your estimate of DEQS’s intrinsic value per share if you expected DEQS to pay out only 20% of earnings starting in year 6? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

(a) Current EPS = E0 = $ 18.5, The reinvestment rate between now (t=0) to end of year 5 is 100% and ROE is 14 % per year

Therefore, Growth Rate between Year 0 to Year 5 = g1 = Reinvestment Rate x ROE = 1 x 14 = 14 %

At the end of Year 5, ROE falls to 9 % and Reinvestment Rate becomes 60 % as the remaining 40 % is paid out as cash dividend.

Growth Rate beyond Year 5 = g2 = Reinvestment Rate x ROE = 0.6 x 9 = 5.4 %

Market Capitalization Rate = Discount Rate = 25 %  

Expected Earning at the end of Year 5 = E5 = 18.5 x (1.14)^(5) = $ 35.6202

Dividend at the end of Year 5 = D5 = 40 % of E5 = 0.4 x 35.6202 = $ 14.2481

Expected Earning at the end of Year 6 = E5 x 1.054 = $ 35.6202 x 1.054 = $ 37.5437

Dividend at the end of Year 6 = 40 % of E6 = 0.4 x 37.5437 = $ 15.0175

Current Intrinsic Share Price = Present Value of Dividends = E6 / (Discount Rate - g2) x [1/(1+Discount Rate)^(5)] + Present Value of D5 = [15.0175 / (0.25 - 0.054)] x [1/(1.25)^(5)] + [14.2481 / (1.25)^(5)] = $ 29.7756 ~ $ 29.78

(b) Price at the end of Year 1 (t=1) = Present Value of Dividends at the end of Year 1 = [15.0175 / (0.25 - 0.054)] x [1/(1.25)^(4)] + [14.2481 / (1.25)^(4)]= $ 37.2195 ~ $ 37.22

(c) Price at the end of Year 2 (t=2) = Present Value of Dividend at the end of Year 2 = [15.0175 / (0.25 - 0.054)] x [1/(1.25)^(3)] + [14.2481 / (1.25)^(3)]= $ 46.5243 ~ $ 46.52

(d) If the payout post end of Year 5 is 20% (intead of the original 40%), then the reinvestment rate becomes 80%

ROE = 9 %

Therefore, Growth Rate post Year 5 = 9 x 0.8 = 7.2 %

E5 = $ 35.6202 and D5 = 20 % of E5 = 0.2 x 35.6202 = $ 7.12403

E6 = 35.6202 x 1.072 = $ 38.1843 and D6 = 38.1843 x 0.2 = $ 7.63696

Current Intrinsic Share Price = 7.63696 / (0.25 - 0.072) x [1/(1.25)^(5)] + [ 7.12403 / (1.25)^(5)] = $ 16.3933 ~ $ 16.39