Dixie Construction is a young firm that is in the process of bidding (and winnin
ID: 2643280 • Letter: D
Question
Dixie Construction is a young firm that is in the process of bidding (and winning) construction contracts. While they are unable to pay any dividends today, once the contracts are awarded and their work begins in earnest, they expect to be able to start paying a dividend of $4.25 per share beginning three years from now (t = 3). From that point forward, as they build their reputation and capacity, they expect to be able to increase their dividend 5.50% each year. If Dixie's cost of equity capital is 9.25% (the discount rate for equity), what price per share should their shares trade at today?
Explanation / Answer
Using MM model price at P0 can be arrived by using the formula Ke=(D1/P0)+ g.
Dividend expected to be paid beginning three years from now.= $4.25.i.e., D3. at t3
D4 = 4.25 (1.055) =$4.48375
Value of stockat t3 is derived by substituting the values in the above said formula.
Ke = (D4/P3)+g
9.25% = 4.48375/P3 + 5.5%
$4.48375/P3=9.25% - 5.5%
P3 = $4.48375/3.75%
Price at t=3 is $119.56666 = $119.57 rounded to two digits.
Price at the end of year 2 (P2) is Present value of P3 for 1 year + Present value of D3 for one year
P2 = $119.57 * 0.9153 + $4.25 * 0.9153
= $113.33
Price at the end of Year 1 is present value of P3 for 2 years+ Present value of D3 for two years + Present value of D2 for 1 year.
= $119.57 * 1/(1.0925)2+4.25 * 1/(1.0925)2 + 0 (as the dividend for year 2 is 0)
=$113.33 * 0.83783+$4.25 * 0.83783
=$103.74.
Current market price of the share is Present value of P3 for 3 years + Present value of D3 for 3 years.
= $119.57 * 1/(1.0925)3 + $4.25 * 1/(1.0925)3
= $119.57 * 0.76689 + $4.25 * 0.76689
=$94.95
There fore today's market price of the share = $94.95