Central Texas Manufacturing (CTM) plans to retain 75 percent of its earnings at

ID: 2775131 • Letter: C

Question

Central Texas Manufacturing (CTM) plans to retain 75 percent of its earnings at the end of
each of the next three years in order to finance new investments having a rate of return on
equity (ROE) of 33.33 percent. Beginning at the end of four years (date 4), CTM will cut the
earnings retention rate to 40 percent. From this point on, CTM plans to maintain a 40 percent
retention rate in perpetuity to reinvest in projects offering a constant ROE of 12.5 percent.
The consensus forecast for CTM’s date 1 earnings per share (at the end of the year) is $2.56.
Assuming that CTM’s stock has a required return of 9.0 percent, determine the current price
for CTM’s stock.

Explanation / Answer

Current Price of CTM’s stock = $ 19.92

Working

Earnings Per Share at the end of year 1 E1 = $ 2.56

Retention rate b = 75% or 0.75

Dividend Payout Ratio P= (1-b) = (1-0.75) = 0.25 or 25%

ROE ROE1= 33.33%

Period = 3 years

Retention Rate from year 4 or 0.40

Dividend Pay out ratio from Year 4 = 0.60 or 60%

ROE ROE2=12.5% or 0.125

Required Rate of Return r = 9% or 0.09

Return on Equity (ROE) = Earnings growth rate g/(1-dividend payout)

===> g = ROE * (1-pay out) = ROE * retention rate

For the first three years, earnings growth rate (and dividends growth rate) is

g = 0.3333 * 0.75 = 0.249975 or 24.9975%

Earnings and Dividends for the next three years is as follows

Year

Earnings

= Previous earning * (1+g) or

Ep *1.249975 (rounded-off)

Dividends (25% of Earnings) = EPS * 0.25

$ 2.56

$ 0.64

$ 2.56 * 1.249975 = $3.20

$ 0.80

$ 3.20 * 1.249975 = $ 4.00

$ 1.00

Constant growth rate of earnings and dividends g2 = ROE * (1-pay out) or ROE * retention rate

= 0.125 * 0.40 = 0.005 or 5%

Dividend at the end of year 4 = Dividend at the end of year 3 * (1+g2) = $ 1 * 1.005

D4 = $ 1.005 or $ 1.01 (rounded off)

Present value of Dividends from year 4 = $ 1.01 / 0.09-0.05

= $ 1.01/0.04 = $ 25.25

Current Value of Stock Price P = D1/1+r + D2/(1+r)^2 +D3/(1+r)^3 + PV of Dividends Yr 4 onwards /(1+r)^4

P = $ 0.64 /1.09 + $ 0.80 /1.09^2 +$ 1/1.09^3 + $25.25/1.09^4

P = $ 0.64 /1.09 + $ 0.80 /1.1881 +$ 1/1.295029 + $25.25/1.41158161

P = 0.5872 + 0.6733 + 0.7722 + 17.8877 = $ 19.9204 or $ 19.92 (rounded off)