Question

Picturetonics just reported earnings per share of $3.00 and paid out dividends of $0.60. Assume that PIcturetronics’ earnings will grow 16% a year for the next 2 years and the dividend payout ratio (dividends as a percent of earnings) will remain at 20%. After 2 years, you expect Picturetronics’ earnings will grow 6% a year forever and its dividend payout ratio will increase to 60% forever. Assume the change in the growth rate and payout policy has no impact on the firm’s risk. The risk-rate is 6%, the expected rate of return on the market is 11%, and PIcturetonics’ beta is .88. Using the dividend discount model, what should Picturetronics’ current share price be?

When solving the problem, make sure you use 4 decimal places when completing your calculations and round your final answer to 2 decimal places. Input your answer as a dollar value with 2 decimal places, without the $.

Answer 1

In the given case, we have

Earning per share (EPS at 0) = $3

Dividend per share at 0 = $0.60

Earning (EPS) will Grow for next 2 years at 16% a year

Dividend payout ratio will remain at 20% i.e (D0/EPS) i.e (0.6/3)

Rsk free return (Rf) - 6%

Rate of return on market (Rm) - 11%

Beta (B) - 0.88

Thus Rate of return (Re) can be calculated as Rf + (Rm-Rf)B i.e 6 + 5*0.88 = 10.4%

After 2 Years

Earning will grow at 6% a year forever and Dividend payout ratio will be 60% forever

Step 1 Calculation for First 2 years

Year	Earnings per share	Dividend per share	PVF @Re i.e 10.4%	Present value of Dividend using dividend discount model
1.	3.48	0.696	0.9058	0.6304
2.	4.0368	0.80736	0.8205	0.6624
			Total	1.2928

Step 2 Beyond 2 year

EPS for year 3 = 4.0368 + (4.0368*6%) = 4.2790

DPS for Year 3 (D3) = EPS * Dividend payout ratio = 4.2790*60% = 2.5674

Thus, Present value at year 2 by using dividend discount model is D3/(Re-growth rate)

Thus, Present value at year 2 will be = 2.5674/(10.4 - 6)% i.e 58.35

Thus Present value at year 0 will be 58.35 *PVF(10.4,2) i.e 58.35 * 0.8205 = 47.8762

Thus current share price by dividend discount model should be Step 1 + Step 2 i.e 1.2928 + 47.8762 = 49.169 i.e 49.17