Question

 Lang Enterprises is interested in measuring its overall cost of capital. Current investigation has gathered the following data. The firm is in the 25​% tax bracket.

Debt: The firm can raise debt by selling $1,000​-par-value,7​% coupon interest​ rate,18​-year bonds on which annual interest payments will be made. To sell the​ issue, an average discount of $50 per bond would have to be given. The firm also must pay flotation costs of $25 per bond.

Preferred stock:  The firm can sell 7% preferred stock at its $95​-per-share par value. The cost of issuing and selling the preferred stock is expected to be $5 per share. Preferred stock can be sold under these terms.

Common stock: The​ firm's common stock is currently selling for$55 per share. The firm expects to pay cash dividends of $6.5 per share next year. The​ firm's dividends have been growing at an annual rate of 7​%, and this growth is expected to continue into the future. The stock must be underpriced by $6 per​ share, and flotation costs are expected to amount to $3 per share. The firm can sell new common stock under these terms.

Retained earnings  When measuring this​ cost, the firm does not concern itself with the tax bracket or brokerage fees of owners. It expects to have available $140,000 of retained earnings in the coming​ year; once these retained earnings are​ exhausted, the firm will use new common stock as the form of common stock equity financing.

a.  Calculate the​ after-tax cost of debt.

b.  Calculate the cost of preferred stock.

c.  Calculate the cost of common stock.

d.  Calculate the​ firm's weighted average cost of capital using the capital structure weights shown in the following​ table.

Long-term debt 40%
Preferred stock 10%
Common stock equity   50%
Total 100%

Answer 1

Lang Enterprises

The firm is in the 25​% tax bracket.

Debt: The firm can raise debt by selling $1,000​-par-value,7​% coupon interest​ rate,18​-year bonds on which annual interest payments will be made. To sell the​ issue, an average discount of $50 per bond would have to be given. The firm also must pay flotation costs of $25 per bond.

Calculation of cost of debt

We assume that yield to maturity (YTM) = before tax cost of debt

Also assume that flotation cost is negligible don’t consider

The formula for YTM = (C+ ((P-M) / n)) / ((p+m) / 2)

Here,

YTM = Yield to maturity

C (coupon interest) = coupon rate * Par value =  7% * $1000 = $ 70

P (Par Value ) = $1000

M (Market Price) = $ 1000 - 50 = 950

n (years to maturity) = 18 years

By applying values into the formula we get,

YTM = ($70 + (($1000 - $ 950 ) / 18 )) / (($1000 + $950)   /   2  )

YTM = ( $70 +  2.778 ) /  975

YTM = 0.0746 or   7.46%

Before tax cost of debt is consider as YTM = 7.46%

A. After tax cost of debt = 7.46% - 25% = 5.60%

Preferred stock:  The firm can sell 7% preferred stock at its $95​-per-share par value. The cost of issuing and selling the preferred stock is expected to be $5 per share. Preferred stock can be sold under these terms

Cost Preferred stock:  = D / ( P - F )

Here,

D = dividend = 95 * 7% = 6.65

P = par value = 95 = current selling price

F= cost of issuing and selling = 5

B. Cost Preferred stock: = 6.65 / ( 95 - 5 ) = 6.65 / 90 = 0.0739 = 7.39%

Common stock: The​ firm's common stock is currently selling for$55 per share. The firm expects to pay cash dividends of $6.5 per share next year. The​ firm's dividends have been growing at an annual rate of 7​%, and this growth is expected to continue into the future. The stock must be underpriced by $6 per​ share, and flotation costs are expected to amount to $3 per share. The firm can sell new common stock under these terms.

Here we can use constant dividend growth model of calculating cost of equity

Cost of Common stock: = ( D1 / ( P - ( F + U) ) ) + G

Here,

D1 = next year dividend = $ 6.5

P = Current price = 55

F + U = flotation costs + underpriced = 6 + 3 = 9

G = growth rate = 7% = 0.07

Cost of Common stock: = ( 6.5 / ( 55 - 9) + 0.07

Cost of Common stock: = 6.5 / 46 + 0.07

C. Cost of Common stock: = 0.1413 + 0.07 = 0.2113 = 21.13%

D. Calculate the​ firm's weighted average cost of capital using the capital structure weights shown in the following​ table

Components	After tax Cost of components (K)	Weight in the structure (W)	(K) * (W)
cost of deb	5.60%	40%	2.24
Cost Preferred stock	7.39%	10%	0.739
Common stock	21.13%	50%	10.565
Weighted Average Cost of Capital (WACC)	13.54%

Weighted Average Cost of Capital (WACC)

13.54%