Question

In 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, January 1, 2004, is as follows:

Long-term debt (bonds, at par) $10,000,000
Preferred stock 2,000,000
Common stock ($10 par) 10,000,000
Retained earnings 4,000,000
Total debt and equity $26,000,000

The bonds have a 4 percent coupon rate, payable semiannually, and a par value of $1,000. They mature on January 1, 2014. The yield to maturity is 12 percent, so the bonds now sell below par. What is the current market value of the firm's debt?

Answer 1

The correct answer is $5,412,000.

Step-by-step explanation:

According to the scenario, the given data are as follows:

Coupon rate = 4%

Coupon rate (semiannual) (C) = 2% of $1000 = $20

Time period = 10 years

Time period (semi annual ) (t) = 20

Face value (F) = $1,000

Yield rate = 12%

Yield rate (semiannual) (r) = 6%

Number of bonds =10,000,000 ÷ 1,000 = 10,000 bonds

So, we can calculate the market value by using following formula:

Market value = C ×
`(1 - (1)/((1+r)^(t) ) )/(r) + (F)/((1+r)^(t) )`

By putting the value, we get

= $20 ×
`(1 - (1)/((1+0.06)^(20) ) )/(0.06) + (1000)/((1+0.06)^(20) )`

So, Market value = $541.20

Now, The total debt value = Market value × Number of bonds

= $541.20 × 10,000

= $5,412,000