Answer:
a.- 85 millions
b.- 71.8 millions
c.- 3.92%
Explanation:
bonds book value of debt: 55,000,000
zero cuopon book value: 30,000,000
total book value of the debt 85,000,000
market value of the bonds:
55,000,000 x 94% = 51,700,000
market value of the zero coupon:
30,000,000 x 67% = 20,100,000
Total market vale of the debt 71,800,000
Cost of debt:
We will calculate each debt coponent rate;
zero coupon:
[tex]20.1 \times (1+r)^{8} =30[/tex]
[tex]r= \sqrt[8]{\frac{30}{20.1}}-1[/tex]
r =
bond rate (approximation of the YTM)
[tex]YTM = \frac{C + \frac{F-P}{n }}{\frac{F+P}{2}}[/tex]
C= 50 (1,000 bond x 5% / 2 payment per year)
F= 1000
P= 940 (94% of the face value)
n= 40 ( 20 years and 2 payment per year)
YTM= 5.3092784%
To calculate an estimated cost of debt for the whole firm, we will weight each debt rate by their influence in the compay's total debt:
0.051333842 x 20.1/71.8 + 0.053092784 x 51.7/78 =
0.014370616 + 0.035190986 = 0.049561602
Finally, we apply the tax shield:
0.049561602 x ( 1 - 0.21) = 0,03915366558 = 3.92%
