Question

A company currently has earnings (E₀) of $2.00 and a dividend (D₀) of $0.50. The firm’s current return on equity (ROE) is 30%. The firm will maintain the same dividend payout and ROE over the next two periods. Then it will transition in a linear reduction in years 3, 4, and 5 to a growth of 3%. The firm will then grow at 3% to perpetuity. The firm’s beta is presently 1.6, but this will transition to 1 over the same period. The risk-free rate is 4% and the market risk premium is 6%. ROE is expected to be 10% beginning in year 5 to perpetuity. What is the present value of this firm’s equity using a three-stage model with linear transition in years 3, 4, and 5?

	0	1	2	3	4	5	6
Earnings Growth Rate	0.225	0.225	0.225	0.16	0.095	0.03	0.03
EPS	2	2.45	3.00125	3.48145	3.812188	3.926553	4.04435
Div Payout (DPS/EPS)	0.25	0.25	0.25
DPS	0.5	0.6125	0.750313
Ke	0.136	0.136	0.136	0.124	0.112	0.1	0.1
PV Cashflows		0.539173	0.581414

I need to find DPS: D3, D4, D5, D6.

For D1 and D2, it was the normal formula. IE; D1: D0(1+g1) ; D2: D1(1+g2)  

Answer 1

K = E/P

where

E = Earnings per share

P= Price per share

Price per share = Earnings per share/ ke (use for year 3, 4,5,6)

	0	1	2	3	4	5	6
Earnings	2	2.45	3.00125	3.48145	3.812188	3.926553	4.04435
Return on Equity	30%	30%	30%	0.124	0.112	10%	10%
Equity	6.6666667	8.166667	10.00416667	28.07621	34.03739286	39.26553	40.4435

Using the beta and Mp and M r , we can calculate the cost of equity, using which we can calculate NPV.

therefor Beta in Year 2 =1.6

beta in Yaer 3 = 1.4

Beta in Year 4 = 1.2

beta in Year 5 = 1.0

Year	Beta	Cost of Capital
3	1.4	12.4
4	1.2	11.2
5	1	10

The EPS given in above table could be discounted at above cost of capital and added to get PV.

As is seen from table given,

g3= .16, g4=.095,g5=.03

	0	1	2	3	4	5	6
Earnings	2	2.45	3.00125	3.48145	3.812188	3.926553	4.04435
DPS	0.5	0.6125	0.750313	0.870363	0.953047573	0.981639	1.011088