Question

Duplan Street Mills is an all-equity firm with 28,000 shares of stock outstanding. The firm expects sales of $600,000 one year from today (next year). Sales are expected to grow by 8 percent per year for the following three years and then level off to a constant 3 percent growth rate per year in perpetuity. Net cash flow varies in direct proportion to sales and is currently equal to 15 percent of sales. The required return for this firm is 14 percent.

1. What is the estimated current value of one share of stock?

Answer 1

the value of the stock (the discount value of the free cash flow) will be $ 32.87

Step-by-step explanation:

sales are 600,000

the free cash flow is 15% of this amount

600,000 x 15% = $90,000

This will grow at 8% during three years

and then indefinitely at 3%

We will use the gordon model to solve for the value a single share:

First we calculate the cashflow:

90,000 x 1.08 = 97,200

97,200 x 1.08 = 104,976

104,976 x 1.08 = 113,374.08

113,374.08 x 1.03 = 116,775.30

Then, we discount as the present value of a lump sum.

`(Cashflow)/((1 + rate)^(time) ) = PV`

The 5th year will used to calculate the present value of all the future cash flow:

113,775.30/ (0.14-0.03)

and then discounted.

`\left[\begin{array}{ccc}Year&cashflow&PV\\1&90,000&78,947.3684\\2&97,200&74,792.2438\\3&104,976&70,855.8099\\4&113,374.08&67,126.5567\\4&116,775.3024&628,548.6676\\&TOTAL&920,270.6464\\\end{array}\right]`

Then, we divide by the number of shares to get the value of a share:

920,270.65 / 28,000 shares outstanding = 32,8668 = $ 32.87