Question

Alpha Enterprises has just paid a dividend of $3 per share. The company then immediately announced that, due to expected cash flow issues from a large project, no dividends will be paid for the next three years. Dividends of $4, $5, and $6 per share will then be paid in each of the three years after that. Following these non-constant dividends, the company expects earnings and dividends to grow at 6% for the foreseeable future. The required return is 13% on the company’s stock. What should we pay for one share of Alpha’s stock today?

Answer 1

There are 2 parts of valuation

First the present value of the three dividends of $ 4, $ 5, $ 6 to be paid three years from now and then the horizon period value with a constant growth rate of 6%

Present value =Future receivable/ ( 1+ discounting rate)^n

Where n= number of years

Here discounting rate = 13%

Present value of three dividends = 4/(1.13)^4 + 5/(1.13)^5 + 6/(1.13)^6

= $ 8.04898

Horizon value of share at the end of 6th year = Dividend for 7th year / (discounting rate – growth rate)

Dividend for 7 th year = dividend for 6th year ( 1+ growth rate) = 6 * 1.06 =$ 6.36

Hence value at year end 6 = 6.36/(0.13-0.06) = $ 90.86

Horizon value at the beginning = Value at Year 6/ (1+ discounting rate)^6

= 90.86/(1.13)^6 =$ 43.64

Hence amount to be paid for Alpha’s stock= value of share=Horizon value + value of intermediate dividends = $( 8.05+43.64) =$ 51.69