Question

A company has 2 million shares outstanding that are currently priced at $4 each and have a beta of 1.3. Five years ago the company issued bonds with a total face value of $3 million. One bond has a face value of $250,000. The bonds have a coupon rate of 3% p.a. and coupons are paid every six months. The bonds mature in fifteen years from today. The bonds currently yield 4% p.a., the market return is 7% p.a., the risk-free return is 2% p.a., and the company tax rate is 30%.

What proportion of the firm's capital structure is equity?

Answer 1

Solution:

a)Calculation of market value of equity:

Market value of equity=2 millions shares*$4=$8 million

b)Calculation of market value of Bonds

Market value of bonds is the pressent value of annual coupons and maturity value,which is cacluated as follow;

Annual coupon=$250,000*3%=$7500

No.of years to maturity=15 years

Current Yield(discount rate)=4% or 0.04

Market Value of each bond is;

=Annual coupon*Present value of annuity factor@4% for 15 years+Maturity value*Present value interest factor for 15th year

=$7500*11.118388+$250,000*0.555265

=$222,204.04

Total Market value of bond=$222,204.04*(3000,000/250,000)

=$2,666,448.48

c)Calculation of Equity portion in firm's capital structure

Total value of firm's capital structure=Value of equity+value of debt

=$8000,000+$2,666,448.48

=$10,666,448.48

Propertion of equity=Value of equity/Total value of firm's capital structure

=$8000,000/$10,666,448.48

=0.75 or 75%