Question

Problem 6-32 Residual Income Model and Nonconstant Growth (LO3, CFA9)

When a stock is going through a period of nonconstant growth for T periods, followed by constant growth forever, the residual income model can be modified as follows:

P0	=	T	EPSt + Bt−1 − Bt	+	PT
		Σ	(1 + k)t		(1 + k)T
		t = 1

where

PT	=	BT	+	EPST (1 + g) − BT × k
				k − g

Al’s Infrared Sandwich Company had a book value of $14.95 at the beginning of the year, and the earnings per share for the past year was $5.50. Molly Miller, a research analyst at Miller, Moore & Associates, estimates that the book value and earnings per share will grow at 17.50 and 16.00 percent per year for the next four years, respectively. After four years, the growth rate is expected to be 6 percent. Molly believes the required return for the company is 10.20 percent. What is the value per share for Al’s Infrared Sandwich Company? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

VALUE PER SHARE=

Answer 1

The value per share for Al’s Infrared Sandwich Company is calculated as follows,

Value per share =Present value of (future EPS-(Book value at end-Book value at beginning))+Present value of terminal value

Year	Book Value	Earnings Per Share	EPS-(Book value at end-Book value at beginning)	Terminal value	PV factor @ 10.20%	PV of EPS-(Book value at end-Book value at beginning)	PV of Terminal value
0	14.95	5.50	-	-	-	-	-
1	17.57	6.38	3.76	-	0.91	3.42	-
2	20.64	7.40	4.33	-	0.82	3.56	-
3	24.25	8.58	4.97	-	0.75	3.72	-
4	28.50	9.96	5.71	-	0.68	3.87	-
5	30.21	10.56	-	210.62	0.68	-	142.82
Value per share	157.39

The book value and earnings per share grows at 17.50% and 16.00% for first four years and at 6% thereafter.

Terminal value =((EPS for 4 th year*(1+growth rate)) -(Book value at end of 5 th year-Book value at beginning of 5 th year))/(cost of capital- growth rate)

Terminal value =((9.96*(1+0.06)) -(30.21-28.50))/(0.102- 0.06)

Terminal value =210.62