Question

 

The Kenny Company has 10,000 bonds outstanding. The bonds are selling at 98% of face value, have a 10% coupon rate, pay interest semi-annually, and mature in 9 years. There are 1.87 million shares of common stock outstanding with a market price of $15 a share and a beta of 0.89. The common stock just paid a dividend of $0.7474 and expects to increase those dividends by 1.35% annually. The flotation cost for equity is 6.5% and the flotation cost for debt is 4.5%. The firm's marginal tax rate is 34%. The market risk premium is 5.5% and the Treasury bill rate is 1.5%. The company's initial investment for a new project is $1,915,070

i- What is the cost of equity based on the dividend growth model? (6.4%)

ii- What is the after-tax cost of debt financing? (6.82%)

iii- What is the company's weighted average cost of capital? (6.51%)

iv- What is the company's initial investment after taking the flotation costs into account. ($2,036,875.13)

Answer 1

Answer 1.

Last Dividend, D0 = $0.7474
Growth Rate, g = 1.35%
Current Price, P0 = $15

D1 = D0 * (1 + g)
D1 = $0.7474 * 1.0135
D1 = $0.7575

Cost of Equity = D1 / P0 + g
Cost of Equity = $0.7575 / $15.00 + 0.0135
Cost of Equity = 0.064 or 6.40%

Answer 2.

Number of bonds outstanding = 10,000
Face Value = $1,000
Current Price = 98%*$1,000 = $980

Annual Coupon Rate = 10%
Semiannual Coupon Rate = 5%
Semiannual Coupon = 5%*$1,000 = $50

Time to Maturity = 9 years
Semiannual Period to Maturity = 18

Let semiannual YTM be i%

$980 = $50 * PVIFA(i%, 18) + $1,000 * PVIF(i%, 18)

Using financial calculator:
N = 18
PV = -980
PMT = 50
FV = 1000

I = 5.173%

Semiannual YTM = 5.173%
Annual YTM = 2 * 5.173%
Annual YTM = 10.346%

Before-tax Cost of Debt = 10.346%
After-tax Cost of Debt = 10.346% * (1 - 0.34)
After-tax Cost of Debt = 6.83%

Answer 3.

Equity:

Number of shares outstanding = 1,870,000
Current Price = $15

Value of Common Stock = 1,870,000 * $15
Value of Common Stock = $28,050,000

Debt:

Number of bonds outstanding = 10,000
Current Price = $980

Value of Debt = 10,000 * $980
Value of Debt = $9,800,000

Value of Firm = Value of Debt + Value of Equity
Value of Firm = $9,800,000 + $28,050,000
Value of Firm = $37,850,000

Weight of Debt = $9,800,000/$37,850,000
Weight of Debt = 0.2589

Weight of Common Stock = $28,050,000/$37,850,000
Weight of Common Stock = 0.7411

WACC = Weight of Debt * After-tax Cost of Debt + Weight of Equity * Cost of Equity
WACC = 0.2589 * 6.83% + 0.7411 * 6.40%
WACC = 6.51%

Answer 4.

Weighted-average Flotation Cost = Weight of Debt * Flotation Cost for Debt + Weight of Equity * Flotation Cost for Equity
Weighted-average Flotation Cost = 0.2589 * 4.50% + 0.7411 * 6.50%
Weighted-average Flotation Cost = 5.98%

Initial Investment * (1 - Weighted-average Flotation Cost) = Net Investment
Initial Investment * (1 - 0.0598) = $1,915,070
Initial Investment * 0.9402 = $1,915,070
Initial Investment = $2,036,875.13