Question

FI Corporation disappointed investors by cutting the annual expected ROE from 12% to 6% indefinitely.At the beginning of the year, the earnings per share were $8and the firm reinvested in its projects $6 per share.If the risk free rate is 2%, the expected rate of return of the market portfolio is 8% and the beta of the stock is 1.33.

a.Calculate the current stock price using the DDM

.b. Calculate the P/E ratio

c. Two years ago the P/E ratio was 11.78 with earnings of $4.5 per share. Calculate and explain the change in the growth opportunities of the firm

Answer 1

Sustainable growth rate for a company = ROE x Retention Ratio

Retention Ratio = Reinvestment / Earnings per share

Dividend Per Share = EPS - Retained Earnings

Retention Ratio = 6/8 = 75%

Dividend Per Share = $8 - $6 = $2

Current RoE = 6%

Here, Sustained Earning 'g' = 6% x 75%

g = 4.50%

For calculating the cost of equity/ required return, we will use CAPM Model which says

Cost of Equity Re = Rf + Beta x (Rm - Rf)  

Where:

Re = Cost of Equity

Rf = Risk free rate (2%)

Rm = Market return (8%)

Beta = 1.33

Re= 2% + 1.33 x ( 8% - 2%)

= 2% + 1.33 x 6%

= 2% + 8%

Re = 10%

According to Dividend Discount Model

Price of share = D0 x (1+g) / (k -g)

where, D0 = Current year dividend (2)

g = Long period growth rate (4.5%)

k = Cost of capital (10%)  

Price of Share

= 2 X (1+4.50%) / (10% - 4.50%)

= 2.09/ 5.50%

= $38

b. The P/E ratio

= Price / EPS

= 38/ 8

= 4.75

c. The Price two years ago

= PE Ratio x EPS

= 11.78 x 4.50

= $55.95

PVGO (Present Value of Growth Opportunities) = V0 - EPS/ Ke

= 55.95 - 4.50/10%

= 55.95 - 45.00

= 10.95

PVGO Now

= 38 - 8/10%

= 38 - 80

= - 42

Infact prior to this RoE forecast, stock price would have been (2 x (1.09%) / (10%-9%) = $218

If PVGO is negative, then the company will still grow, but its overall ROE will decline, and with it, its stock price.