Question

Company X's current return on equity (ROE) is 17.06%. It pays out one-quarter of earnings as cash dividends, i.e. its payout ratio is 29.1%. Current book value per share is $38.71. The company has 5.68 million shares outstanding. Assume that the ROE and payout ratio stay constant for the next four years. After that, competition forces the ROE to 11.02% and the company changes the payout ratio to 71.52%. The company does not plan to issue or retire shares. The cost of capital is 10.77%.

(a) What is the price of stock X?

(b) How much of stock X's value is attributable to growth opportunities (PVGO)? Note that here we cannot use P=(EPS/r)+PVGO because ROE changes over time. PVGO is defined by the difference between the price of stock and the value of share if there is no growth for every period.

Answer 1

For 4 years

Cost of Capital, R = 10.77%

g = ROE * (1 - Payout Ratio )

= 0.1706 * (1- 0.291) = 0.1209 = 12.09 %

Alternatvely we will discount Net Income

BV per Share = Total equity / Total Shares

Total Equity = BV * Total Shares = 5,680,000*38.71 = 219,872,800

ROE = 17.06% = NI / TE

NI = 219,872,800 *.1706 = 37,510,299.68

Payout Ratio = 29.1% = Dividends / Net Income

Dividends = 0.291 * 37,510,299.68 = 10,915,497

D0 = Dividends / share = 10,915,497 / 5,680,000 = 1.92

D1 = 1.92 * (1+g) = 1.92 * (1+ 0.1209) = 2.152

PV of D1 = 2.152 / (1+ 0.1077) = 1.943                  (1)

D2 = 2.152 (1.1209) = 2.413

PV of D2: D2 / (1+R)² = 1.966                               (2)

D3 = 2.412 * (1.1209) = 2.704

PV of D3 = D3 / (1+R)³   = 1.990               (3)

D4 = 2.703 * (1.1209) = 3.031

PV of D4 = D4 / (1+R)⁴ = 2.014         (4)

after 4th Year:

ROE = 11.02%, Payout Ratio = 71.52 %

g1 = 0.03185 = 3.18%

Terminal Value = D4 * (1+g1) / (R - g1) = 3.029 * (1.0318) / (.1077 - .0318) = 41.211 PV of Terminal Value PV calculated above is at the end of 4th year:

PV Of Terminal Value = Terminal Value / (1+R)⁴ = 27.373             (5)

Price of Stock = PV of dividends + PV of terminal value

= 35.285

b)- Book value per share tells us value of share if operations of company ceases, i.e. 0 growth

PVGO = Price of Stock - Value without growth (BV / Sghare)

= 35.29 - 38.71 = - 3.42

Negative PVGO tells us that overall ROE is declining, and with it, its stock price.This is because for the first 4 years Cost of capital < Growth.