Answer:
WACC(with preferred shares) 10.60145%
Explanation:
First, we derminate the cost of debt by solving for the rate at which the present value matches the 1,080 as which the bond is currently selling:
this could be done using a financial calculator or Excel:
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C 62
time 50
rate 0.057126844
[tex]62 \times \frac{1-(1+0.0571268435271283)^{-50} }{0.0571268435271283} = PV\\[/tex]
PV $1,017.8208
[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]
Maturity 1,000.00
time 50.00
rate 0.057126844
[tex]\frac{1000}{(1 + 0.0571268435271283)^{50} } = PV[/tex]
PV 62.18
PV c $1,017.8208
PV m $62.1792
Total $1,080.0000
Now, we calculate the debt:
16,000 bonds x 1,000 x 108% = 17,280,000
Now we move to equity:
We have to determinate the cost of capital using CAMP
[tex]Ke= r_f + \beta (r_m-r_f)[/tex]
risk free 0.031
market rate 0.09
premium market (market rate - risk free) = 0.07
beta(non diversifiable risk) 1.2
[tex]Ke= 0.031 + 1.2 (0.07)[/tex]
Ke 0.11500
Now we calcualte the equity
535,000 shares x 81 = 43,335,000
Last, preferred shares:
4.2%
and then
20,000 shares x $92 = 1,840,000
Now, we are able to sovle for WACC
[tex]WACC = K_e(\frac{E}{E+P+D}) + K_p(\frac{P}{E+P+D}) + K_d(1-t)(\frac{D}{E+P+D})[/tex]
D 17,280,000
E 43,335,000
P 1,840,000
V 62,455,000
Ke 0.115
Equity weight 0.69
Kp 0.042
Preferred Weight 0.03
Kd 0.1143
Debt Weight 0.28
t 0.21
[tex]WACC = 0.115(0.693859578896806) + 0.042(0.0294612120726923) + 0.1143(1-0.21)(0.276679209030502)[/tex]
WACC 10.60145%
