Question

Company A is considering going public and is trying to determine its value based on its future dividend payments. Their current EPS is $5.00, and over the next 5 years they anticipate a payout ratio of 20% and ROE of 15%. During this high-growth period, their beta is estimated at 1.20, with a risk-free rate of 1.0% and a market risk premium of 5%. At the end of the 5-year high growth period, they estimate their stable beta will be 1.05, with ROE of 12% and growth of 2.0%. (Risk-free rate and market risk premium will remain the same.) Using this information, determine the per-share value for the company and show the calculation in details.

Answer 1

Payout ratio = 20%

Retention ratio, R = 1 - Payout ratio = 1 - 20% = 80%

ROE = 15%

Hence, growth rate in high growth period, g1 = R x ROE = 80% x 15% = 12%

Also cost of equity in this period = Rf + Beta x market risk premium = 1% + 1.20 x 5% = 7%

Please see the table below. Please be guided by the second column titled “Linkage” to understand the mathematics. All financials are in $.

Year, n	Linkage	0	1	2	3	4	5
EPS	A	5.00	5.60	6.27	7.02	7.87	8.81
Payout ratio	B		20%	20%	20%	20%	20%
DPS	C = A x B		1.12	1.25	1.40	1.57	1.76
Retention ratio	D = 1 - B		80%	80%	80%	80%	80%
ROE	E		15%	15%	15%	15%	15%
Growth rate	F = D x E		12.00%	12.00%	12.00%	12.00%	12.00%
Beta	G		1.20	1.20	1.20	1.20	1.20
Cost of equity	H = 1% + G x 5%		7.00%	7.00%	7.00%	7.00%	7.00%

In the stable phase,

ROE = 12%, growth g = 2%

hence, retention ratio = g / ROE = 2% / 12% = 16.67%

Hence, payout ratio = 1 - retention ratio = 1 - 16.67% = 83.33%.

Beta = 1.05

Cost of equity, Ke = Rf + beta x market risk premium = 1% + 1.05 x 5% = 6.25%

Hence, DPS for year 6 = D6 = EPS6 x Payout ratio for yer 6 = EPS5 x (1 + g) x 83.33% = 8.81 x (1 + 2%) x 83.33% = $ 7.49

Hence terminal value of dividends at the end of yer 5 = D6 / (Ke - g) = 7.49 / (6.25% - 2%) = 176.23

Please see the table below now. Please be guided by the second column titled “Linkage” to understand the mathematics. All financials are in $.

Year, n	Linkage	0	1	2	3	4	5
EPS	A	5.00	5.60	6.27	7.02	7.87	8.81
Payout ratio	B		20%	20%	20%	20%	20%
DPS	C = A x B		1.12	1.25	1.40	1.57	1.76
Retention ratio	D = 1 - B		80%	80%	80%	80%	80%
ROE	E		15%	15%	15%	15%	15%
Growth rate	F = D x E		12.00%	12.00%	12.00%	12.00%	12.00%
Beta	G		1.20	1.20	1.20	1.20	1.20
Cost of equity	H = 1% + G x 5%		7.00%	7.00%	7.00%	7.00%	7.00%
Terminal value	I						176.23
Net cash flows	J = C + I		1.12	1.25	1.40	1.57	178.00
PV factor	K = (1 + H)^(-n)		0.9346	0.8734	0.8163	0.7629	0.7130
PV of Cash flows	L = J x K		1.05	1.10	1.15	1.20	126.91
Per share value	Cumulative L	131.40

Hence, per share value = $ 131.40