Question

Assume today is the beginning of year 2011, i.e., January 1, 2011. Company ABC is a hi-tech start-up company that had total after tax earnings of $ 2 million in 2010. Of these, $500,000 were paid out as a dividend to shareholders on December 31, 2010, and the remaining dividends are invested to finance future growth. Company ABC has a total number of 1,000,000 shares outstanding so that the dividend per share is $0.5. ABC’s earnings will grow at a rate of 50% per year in year 2011, 2012 and 2013. After that, the company will enter a more mature growth phase and grow at a constant rate of 8% per year forever. The cost of equity (the discount rate for dividends) of this firm is 15%. Company ABC will keep the payout ratio (payout ratio = dividend/ total after tax earnings) unchanged in year 2011 and 2012. After that, it will only retain 40% of after tax earnings for its future growth.

a)Value Company ABC’s stock price at the beginning of year 2011.

Answer 1

All amounts are in $

a)

Stock price valuation

It is present value of future Cashflows

Value of company at the beginning of 2011

Price = (D1/1+Ke) + {D2/(1+Ke)^2} + {D3/(1+Ke)^3} + {D4/(Ke-g)}

Where

D1 = Expected dividend at end of 2011

D2 = Expected dividend at end of 2012

D3 = Expected dividend at end of 2013

D4 = Expected dividend at end of 2014

Ke = Cost of equity = 15%

Growth rate = g = 8%

^ means to the power of

Current dividend payout ratio = 500,000/2,000,000 = 25%

D1 = (Earnings of 2010 x Growth rate for 2011 x payout ratio of 25%)/no of shares

= (2,000,000 x 150% x 25%)/1,000,000

= 0.75

D2 = (2,000,000 x 150% x 150% x 25%)/1,000,000

= 1.125

D3 = (2,000,000 x 150% x 150% x 150% x 60%)/1,000,000

= 4.05

(The payout has changed to 60% from 25% in 2013)

D4 = (2,000,000 x 150% x 150% x 150% x 108% x 60%)/1,000,000

= 4.374

(For D4, growth of 8% for 2014 is also considered)

Price = (0.75/1.15)+ {1.125/(1.15)^2} + {4.05/(1.15)^3} + {4.374/(0.15-0.08)}

= 0.65217 + 0.85066 + 2.66294 + 62.48571

= 66.65148

ABC stock price at beginning of 2011 is $66.65148