Question

Halliford Corporation expects to have earnings this coming year of $3.07 per share. Halliford plans to retain all of its earnings for the next two years. For the subsequent two​ years, the firm will retain 51% of its earnings. It will then retain 20% of its earnings from that point onward. Each​ year, retained earnings will be invested in new projects with an expected return of 20.86% per year. Any earnings that are not retained will be paid out as dividends. Assume​ Halliford's share count remains constant and all earnings growth comes from the investment of retained earnings. If​ Halliford's equity cost of capital is 8.8%​, what price would you estimate for Halliford​ stock?

Answer 1

Let's revisit the following concepts before we get into solving this question:

• 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	3.0700	3.7104	4.4844	4.9615	5.4893	5.7183
Retention Ratio	RRn	100.00%	100.00%	51.00%	51.00%	20.00%	20.00%
ROE	ROE	20.86%	20.86%	20.86%	20.86%	20.86%	20.86%
Growth rate	gn+1 = ROE x RRn		20.86%	20.86%	10.64%	10.64%	4.17%
FCFE	EPSn x (1 - RRn)	-	-	2.1974	2.4311	4.3914	4.5747
Terminal growth rate	gN+1 = g6						4.17%
Cost of equity	Ke	8.80%
Terminal Value of FCFE at the end of year 5	FCFETV,5 = FCFE6 / (Ke - g6)					98.8472
PV factor	(1+Ke)-n	0.9191	0.8448	0.7764	0.7136	0.6559
PV of FCFE	FCFE x PV factor	-	-	1.7061	1.7350	2.8805
PV of Terminal Value	TV x PV factor for year 5					64.8366
Share Price	Sum of PV of FCFE and PV of TV	71.1581

Hence, estimated price for Halliford​ stock = $ 71.16 per share