Question

Protected Steel Corporation (PSC) has a book value of $6 per share. PSC is expected to earn $0.60 per share forever and pays out all its earnings as dividends. The required rate of return on PSC’s equity is 12 percent. Calculate the value of the stock based on a) dividend discount model and b) residual income model

Answer 1

a) Expected earnings = Next year earnings = $0.60

Since PSC pays out all its earnings as dividends, Dividend next year = D₁ = Next year earnings = 0.60

As a results of constant earnings per share and 100% payout ratio, growth rate of earnings and dividends = g = 0%

Hence Dividend for any year = 0.60

Required rate of return on equity = r = 12%

According dividend discount model

Value of stock = Present value of expected future dividends discounted at Required rate of return on equity

As dividends are constant, they form a perpetuity

Present value of perpetuity = Cash flow / discount rate

Hence value of stock = Dividend for a year / Required rate of return on equity = 0.60 / 12% = 0.60 / 0.12 = 5

Hence value of stock based on dividend discount model = $5

b) Current book value = Book value at beginning of year 1 = $6

As company pays out all its earnings as dividends and it also maintains a constant EPS forever, therefore EPS for a year will be equal to dividend for a year, We know that

Book value for a year = book value for previous year + Earnings per share for a year - Dividends for a year

Book value for a year = book value for previous year + Earnings per share for a year - Earnings per share for a year

Book value for a year = Book value for Previous year

Hence Book value of all years will equal, So Book value of any year = $6

Residual income for a year = EPS for a year - Required rate return of equity x Beginning book value for previous year

As EPS and beginning Book value are constant, so residual income will also remain constant forever

Residual income for a year = 0.60 - 12% x 6 = 0.60 - 0.72 = - 0.12

Hence residual income will also remain constant and form a perpetuity

Present value of expected future residual income = Constant Residual income / Required rate of return on equity = -0.12 / 12% = -0.12 / 0.12 = 1

Now according to residual income model

Value of stock = Book value at Beginning of year 1 + present value of expected future residual income

Value of stock = 6 - 1 = 5

Hence value of stock on basis of residual income model = $5