Question

Halliford Corporation expects to have earnings this coming year of $2.817 per share. Halliford plans to retain all of its earnings for the next two years. Then, for the subsequent two years, the firm will retain 46% of its earnings. It will retain 19% of its earnings from that point onward. Each year, retained earnings will be invested in new projects with an expected return of 24.6% per year. Any earnings that are not retained will be paid out as dividends. Assume Halliford's share count remains constant and all earning growth comes from the investment of retained earnings. If Halliford's equity cost of capital is 11.9%, what price would you estimate for Halliford Stock?

The stock price will be $____?

Answer 1

SOLUTION:

First Have an understanding of the following concepts  

• Growth rate in any period is a function of Return on equity (ROE) and retention ratio (RR) in the prior period.
• Growth, g_n+1 = ROE x RR_n where g_n+1 = growth rate in Earnings per share (EPS) in the period n+1 and RR_n = Retention ratio in the period n
• EPS_n+1 = EPS_n x (1 + g_n+1)
• Free cash flow to the equity holder, FCFE = EPS x (1 - RR)
• Terminal value of FCFE at the end of period N = FCFE_{TV, N} = FCFE_N+1 / (Ke - g_N+1) where Ke = Cost of equity capital and g_N+1 = terminal growth rate or growth rate from period N+1 onwards
• Share price today = PV of all the future FCFE = PV of future FCFE over the period t = 1 to t = N + PV of terminal value of FCFE at the end of period N.

Once these concepts are understood, we can synthesize these into the table below. Please see the column "Linkage" to understand how each row has been calculated.

Year, (n)	Linkage	1	2	3	4	N = 5	N+1 = 6
EPS	EPSn	2.817	3.510	4.373	4.869	5.420	5.673
Retention Ratio	RRn	100.00%	100.00%	46.00%	46.00%	19.00%	19.00%
ROE	ROE	24.60%	24.60%	24.60%	24.60%	24.60%	24.60%
Growth rate	gn+1 = ROE x RRn		24.60%	24.60%	11.32%	11.32%	4.67%
FCFE	EPSn x (1 - RRn)	-	-	2.361	2.629	4.390	4.595
Terminal growth rate	gN+1 = g6						4.67%
Cost of equity	Ke	11.90%
Terminal Value of FCFE at the end of year 5	FCFETV,5 = FCFE6 / (Ke - g6)					63.5546
PV factor	(1+Ke)-n	0.8937	0.7986	0.7137	0.6378	0.5700
PV of FCFE	FCFE x PV factor	-	-	1.6850	1.6768	2.5023
PV of Terminal Value	TV x PV factor for year 5					36.2261
Share Price	Sum of PV of FCFE and PV of TV	42.0902

Hence, estimated price for Halliford​ stock = $ 42.09 per share