Question

Q1) Tawes & Co. has 100,000 semiannual coupon bonds outstanding, each with a par value of $1,000, coupon rate of 8%, and maturity of 15 years. Each bond sells at 110% of par. Tawes & Co. also has 1,000,000 shares of common stock outstanding that sell for $140 per share and have a beta of 1.7. The risk-free rate is 3%, market risk premium is 7%, and the corporate tax rate is 30%. What is Tawes & Co.'s weighted average cost of capital (WACC)?

answer by hand so I can see the steps.

A) 7.78%

B) 11.04%

C) 9.94%

D) 11.86%

E) 10.47%

Answer 1

The formula to calculate WACC is:

WACC = (E/V)*R_E + (D/V)*R_D*(1-t)

where, E = Market value of Equity, R_E = Cost of Equity

D = Market Value of Debt, R_D = Cost of Debt, t = tax rate

V = D+E

Market Value of Equity = E = No. of shares outstanding * price per share = 1000000*140 = 140000000

Price of a bond = 110%*1000 = 1100

Market value of Debt = D = Price of the bond*No. of Bonds = 1100*100000 = 110000000

V = D+E = 110000000+140000000 = 250000000

Weights of Equity and Debt

Weight of Equity = E/V = 140000000/250000000 = 14/25 = 0.56

Weight of Debt = D/V = 110000000/250000000 = 11/25 = 0.44

Cost of Equity

Cost of Equity can be calculated using the CAPM Equation

Cost of Equity = R_E = R_F + β*MRP

where, R_F = Risk-free rate = 3%, Beta of stock = β = 1.7, MRP = Market risk premium = 7%

Cost of Equity = R_E = 3%+1.7*7% = 14.9%

Cost of Debt

Cost of Debt is the YTM of the Bond

Par value of the bond = 1000

Price of the bond = 110%*1000 = 1100

The bond pays semi-annual coupons. So, we will consider semi-annual timer periods, semi-annual coupon rate

Annual coupon rate = 8%

Semi-annual coupon rate = 8%/2 = 4%

Semi-annual coupon payment = 4%*1000 = 40

Time to maturity = 15 years

No. of semi-annual periods = 15*2 = 30

Semi-annual YTM can be calculated using ba ii plus calculator as shown below:

Inser the following in ba ii plus calculator:

N = 30

PV = -1100

PMT = 40

FV = 1000

CPT -> I/Y [Press CPT and then press I/Y]

We get, I/Y = 3.45907123

Note that this is the semi-annual YTM

Annual YTM = 3.45907123%*2 = 6.91814246%

Cost of Debt = Annual YTM = R_D = 6.91814246%

WACC

WACC = (E/V)*R_E + (D/V)*R_D*(1-t)

E/V = 0.56, R_E = 14.9%, D/V = 0.44, R_D = 6.91814246%, t = 30%

WACC = 0.56*14.9% + 0.44*6.91814246%*(1-30%) = 0.08344 + 0.021307878776135 = 0.104747878776135 = 10.4747878776135%

WACC = 10.47% (Rounded to two decimals)

Answer -> 10.47% (Option E)