Answer:
Ke = 15.35%
cost of debt: pretax 7.84%
after tax rate of 40% = 4.704%
Equity weight = 0.784313725
Debt Weight = 0.215686275
WACC 13.05380%
Explanation:
With the CAPM we solve for the cost of equity:
[tex]Ke= r_f + \beta (r_m-r_f)[/tex]
risk free = 0.05
premium market = (market rate - risk free) 0.09
beta(non diversifiable risk) = 1.15
[tex]Ke= 0.05 + 1.15 (0.09)[/tex]
Ke 0.15350
The cost of debt will be detrmiante by solve for the rate which makes the debt worth 110 of their value
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C 4.50 (100 x 9% / 2 payment per year)
time 30 ( 15 years x 2)
rate 0.039268264
[tex]4.5 \times \frac{1-(1+0.039268)^{-30}}{0.039268} = PV\\[/tex]
PV $78.5102
110.00
[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]
Maturity 100.00
time 30.00
rate 0.03927
[tex]\frac{100}{(1 + 0.039268)^{30} } = PV[/tex]
PV 31.4898
PV c $78.5102
PV m $31.4898
Total $110.0000
(the debt is quoted 110 so we need to solve for that amount)
we get 0.0392 semiannual rate using excel we multiply by 2 to get the annual costof debt:
0.0392 x 2 = 0,0784
after tax:
0.0784 x (1 - 0.4) =0.04704
the weights are calcualte with the market values
D 1,100,000,000 (1 billon x 110/100)
E 4,000,000,000 (50,000,000 x $80)
V 5,100,000,000
Now, we plug all the data and sovle for the WACC
[tex]WACC = 0.1535(0.784313725490196) + 0.0784(1-0.4)(0.215686274509804)[/tex]
WACC 13.05380%
