Question

APEX Company paid a €1.50 dividend per share this year. Over the next two years, dividends and earnings are expected to grow at a rate of 12%. After two years, the company is expected to grow at a constant rate of 5%. Additional information: Risk-free rate of return 4.5% Equity risk premium 5.0% Beta coefficient 0.9

1) Estimate the required rate of return on equity using the CAPM.

2) Estimate the expected future dividend at the end of year 1.

3) Estimate the expected future dividend at the end of year 2.

3) Estimate the expected future dividend at the end of year 3.

4) Assume that a dividend discount model (DDM) is an appropriate choice for valuing the APEX Company. Using a two-stage dividend discount model, estimate the company's value per share.

Answer 1

1) Required rate of return using capm = Rf + Beta * Equity Risk premium

Rf = Risk free rate of return

= 4.5% + 0.9 * 5% = 4.5% + 4.5%

Required arte of return = 9%

2) Calculation of the expected future dividend at end of year 1 :-

D1 = D0 (1+g)

Here D1 = future dividend at end of year 1

D0 = dividend paid this year

g = growth rate

D1 = 1.50 * ( 1+ 0.12) = 1.5 * 1.12 = $ 1.68 per share

D1 = $ 1.68

3) Calculation of the expected future dividend at end of year 2 :-

D2 = D1 (1+g)

Here D2 = future dividend at end of year 2

D1 = dividend paid this year = $ 1.68

g = growth rate = 12%

D2 = 1.68 * ( 1+ 0.12) = 1.68 * 1.12 = $ 1.8816 per share

D2 =$ 1.8816

Calculation of the expected future dividend at end of year 3 :-

D3 = D2 (1+g)

Here D3 = future dividend at end of year 3

D2 = dividend paid this year = 1.8816

g = growth rate = 5%

D3 = 1.8816 * ( 1+ 0.05) = 1.8816 * 1.05 = $ 1.97568 per share

4) Calculation Value per share :-

Here we calculate Horizen value of dividends from year 3 at end of year 2.

Horizen value at end of year 2 = D3 / (r - g)

Here D3 = 1.97568

r = required rate of return = 9%

g = growth rate from year 3 = 5%

Horizen value at end of year 2 = $ 1.97568 / ( 0.09 - 0.05) = $ 49.392

After calculating Horizen value of dividends next calculate the present value of dividends of year 1 & 2 and horizen value.

years	CF	PVF@9%	PV of CF
1	1.68	0.91743119	1.5412844
2	1.8816	0.84167999	1.58370508
Horizen value at year 2	49.392	0.84167999	41.5722582
Value of stock	$ 44.6972477