Question

Ace Industrial Machines issued 195,000 zero coupon bonds four years ago. The bonds originally had 30 years to maturity with a yield to maturity of 5.2 percent. Interest rates have recently decreased, and the bonds now have a yield to maturity of 4.9 percent. If the company has a $73 million market value of equity, what weight should it use for debt when calculating the cost of capital

Answer 1

Answer:

Coupon (R) = 0

Face value = $1,000

Years to maturity (n) = 30 years

Kd = 4.9% = 0.049

Po = R(1-(1+Kd)-n)/kd + FV/ (1+Kd)n

Po = 0(1-(1+0.049)-30/0.049 + $1,000/(1+0.049)30

Po = 0 + $238

Po = $238

                                                                        $

Market value of equity                                = 73

Market value of bond (195,000 x $238)    = 46.41

Market value of the company                       119.41

Weight of debt  = 46.41/119.41  x 100

Weight of debt = 38.87 = 39%

Explanation:

In this case, there is need to calculate the current market value of bond, which is the present value of coupon and the present value of face value of the bond. Then, we will calculate the market value of the company, which is the aggregate of market value of equity and market value of bond.

Answer 2

The price of debt is the effective rate that a business enterprise will pay on its debt, consisting of bonds and loans.  The weight of debt that can be used by the firm is 39%.

What is the cost of debt?

Debt is one a part of a business enterprise's capital structure, with the alternative being equity. it is the cost that the company pays on its debt annually or semi-annually or quarterly.

As per the given information:

Coupon(R) = 0

Face value(FV) = $1,000

Years to maturity (n) =30 years

YTM: 4.9% = 0.049

$\rm\,Po = \dfrac{R[1 - (1+Kd)^{-n}] }{Kd}+ \dfrac{FV}{(1+Kd)^{n} } \\\\Po = \dfrac{0[1 - (1+0.049)^{-30} ]}{0.049}+ \dfrac{1000}{(1+0.049)^{30} } \\\\\\Po = 0 + 238\\\\\\\ Po = \ 238$

Market value of equity = $73

Market value of debt\bond = (195,000* 238) = $46.41

Total market value = 119.41

Weight of debt = $46.41/$119.41

Weight of debt = 39%

Hence, the weight of debt that can be used by the firm is 39%.

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