Question

The 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 $13.00, all of which was reinvested in the company. The firm’s expected ROE for the next five years is 17% 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 12%, and the company is expected to start paying out 35% of its earnings in cash dividends, which it will continue to do forever after. DEQS’s market capitalization rate is 20% 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 , the entire return must be in . 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 15% of earnings starting in year 6?

Answer 1

(a) Current EPS = E0 = $ 13, ROE for the next 5 years = 17% (this implies that the ROE between current time i.e end of year 0 and end of year 5 is 17%), Retention Ratio = 1 as the firm retains all of its earnings for reinvesting in the business.

Growth Rate of Earnings for the next 5 years = ROE over next 5 years x Retention Ratio over next 5 years = 17 x 1 = 17%

Earnings at the end of Year 5 = E5 = E0 x (1.17)^(5) = 13 x (1.17)^(5) = $ 28.502

At the end of Year 5, the ROE falls to 12% (for the coming 6th year and thereafter) and the 35% of earnings are paid out s dividends.

Dividend Payout Ratio = 0.35, Retention Ratio = (1-0.35) = 0.65

Growth Rate at the end of Year 6 and thereafter = New Lower ROE x New Lower Retention Ratio = 12 x 0.65 = 7.8 %

Earnings at the end of Year 6 = E6 = E5 x (1+New Growth Rate) = 28.502 x (1.078) = $ 30.725

Dividend at the end of Year 6 = D6 = 35% of E6 = 0.35 x 30.725 = $ 10.754

Market Capitalization Rate = r = 20%

Intrinsic Value per Share = Total Present Value of All Perpetual Constant Growth Dividends at current time = [D6 / (r - 0.078)] x [1/(1+r)^(5)] = [10.754 / (0.2 - 0.078)] x [1/(1.2)^(5)] = $ 35.424

(b) If market price equals the intrinsic value, then the stock is fairly priced, thereby implying that the stock provides an annualized return equal to the market capitalization rate (required rate of return) of 20%.

Therefore, at the end of one year (i.e next year) the stock price should grow by 20%.

Stock Price after 1 year = 1.2 x 35.424 = $ 42.509

(c) Once again as the stock is fairly priced, the stock price should give an annualized return equal to the required rate of return of 20%. Therefore, the stock price will again grow by 20% in the second year as well.

Stock Price at the end of Year 2 = 42.509 x 1.2 = $ 51.011

(d) If the payout ratio is 15% instead of the original 35%, the growth rate for Year 6 and beyond will be higher owing to the greater retention ratio of (1-0.15) = 0.85

New Growth Rate = ROE x 0.85 = 12 x 0.85 = 10.2 %

E6 = E5 x 1.102 = 28.502 x 1.102 = $ 31.409

D6 = 31.409 x 0.15 = $ 4.711

Inrtinsic Price per Share = [4.711 / (0.2 - 0.102)] x [1/(1.2)^(5)] = $ 19.319