Question

The share of ABC Company is traded at the price of €22 and the estimates of dividends per share for
the next four years are the following:
D1=0.7 €, D2=0.8 € and D3 = D4 =0.9 €.
For the 5
th year earnings per share are expected to be at €1.8 for which the company's management
decides to distribute 60% as a dividend (Payout Ratio). The Company is expected to continue the same
dividend policy for the next 3 years (Year 6 to Year 8), with an annual growth rate of 2.6 % on average.
From the 9th year and after, the Company retains and invests 40% of its earnings on one-year
investments with a 12% return (Return on Equity - ROE).
The required return from investors in order to buy a share at a risk equal to that of ABC Company is
8%. You can assume that ABC Company has no external financing in its capital structure.
i. Calculate the economic value of the share (fair value).
ii. Advice an investor who intends to buy shares of the particular company. Justify your answer.

Answer 1

i.	Economic price of the share is the PV of the expected dividends discounted at
	the required rate of return of 8%.
	The dividends expected are as below:
	Year	Expected Dividend	PVIF at 8%	PV at 8%
	1	0.70	0.92593	€                   0.65
	2	0.80	0.85734	€                   0.69
	3	0.90	0.79383	€                   0.71
	4	0.90	0.73503	€                   0.66
	5	1.08	0.68058	€                   0.74
		[1.8*60%]
	6	1.11	0.63017	€                   0.70
	7	1.14	0.58349	€                   0.67
	8	1.17	0.54027	€                   0.63
				€                   5.44
	Growth rate from year 9 = ROE*retention ratio = 40%*12% =				4.80%
	PV of dividends for years 1 to 8 =			€                   5.44
	Continuing value of dividends at t8 = 1.17*1.048/(0.08-0.048) =				€          38.32
	PV of continuing value = 38.32*0.54027 =			€                20.70
	Economic value of the share [5.44+20.70]			€                26.14
ii.	The investor can buy the share if the share is not over priced, that is if the
	price of the share is €26.14 or less.