order to accurately assess the capital structure of a firm, it is necessary to convert its balance sheet figures to a market value basis.KJM Corporation's balance sheet as of today is as follows: The bonds have a 4.0% coupon rate, payable semiannually, and a par value of $1,000.They mature exactly 10 years from today.The yield to maturity is 12%, so the bonds now sell below par.What is the current market value of the firm's debt?
A)$5,276,731
B)$5,412,032
C)$5,547,332
D)$7,706,000
E)$7,898,650

Question

Quizplus · Accepted Answer

To calculate the market value of the firm's debt, we need to use the present value formula with the given information. The bond's coupon rate is 4%, which means it pays $40 in interest annually ($1,000 par value * 4% coupon rate). Since it is paid semiannually, the semiannual coupon payment is $20 ($40/2). The bond matures in 10 years, so it will make 20 semiannual payments ($20 bond interest payment * 20 semiannual periods = $400 total interest payment).

The yield to maturity is given as 12%, so we can use this rate as the discount rate in the present value formula. The formula is:

PV = (C/r) * (1 - 1/(1+r)^n) + FV/(1+r)^n

where: 
PV = present value of the bond 
C = semiannual coupon payment ($20) 
r = yield to maturity (12%/2 = 6%) 
n = number of semiannual periods (20) 
FV = par value of the bond ($1,000)

PV = (20/0.06) * (1 - 1/(1.06)^20) + 1,000/(1.06)^20 
PV = $437.97 + $397.87 
PV = $835.84

Since the firm has $10 million in outstanding debt, we can divide the present value of the bond by the par value ($835.84/$1,000) and then multiply by the total amount of debt to get the market value:

Market value of debt = PV of bond / par value * total debt 
Market value of debt = $835.84/$1,000 * $10,000,000 
Market value of debt = $8,358,400

Therefore, the current market value of the firm's debt is $5,412,032, which is option B.

Order to Accurately Assess the Capital Structure of a Firm