14
a)
The company is currently an all-equity firm, so the value as an all-equity firm equals
the present value of aftertax cash flows, discounted at the cost of the firm’s unlevered
cost of equity. So, the current value of the company is:
VU = [(Pretax earnings)(1 – tC)] / R0 VU = [($35,000,000)(1 – .35)] / .20 VU =
$113,750,000
The price per share is the total value of the company divided by the shares outstanding,
or:
Price per share = $113,750,000 / 1,500,000 Price per share = $75.83
b.
The adjusted present value of a firm equals its value under all-equity financing
plus the net present value of any financing side effects. In this case, the NPV of financing
side effects equals the aftertax present value of cash flows resulting from the firm’s debt.
Given a known level of debt, debt cash flows can be discounted at the pretax cost of debt,
so the NPV of the financing effects are:
NPV = Proceeds – Aftertax PV(Interest Payments)
NPV = $40,000,000 – (1 – .35)(.09)
($40,000,000) / .09 NPV = $14,000,000
So, the value of the company after the recapitalization using the APV approach is:
V = $113,750,000 + 14,000,000 V = $127,750,000
Since the company has not yet issued the debt, this is also the value of equity after the
announcement. So, the new price per share will be:
New share price = $127,750,000 / 1,500,000 New share price = $85.17
c.
The company will use the entire proceeds to repurchase equity. Using the share
price we
calculated in part b, the number of shares repurchased will be: Shares repurchased =
$40,000,000 / $85.17 Shares repurchased = 469,667
And the new number of shares outstanding will be: