In order to accurately assess the capital structure of a firm,it is necessary to convert its balance sheet figures from historical book values to market values.KJM Corporation's balance sheet (book values)as of today is as follows:

The bonds have a 7.0% coupon rate,payable semiannually,and a par value of $1,000.They mature exactly 10 years from today.The yield to maturity is 11%,so the bonds now sell below par.What is the current market value of the firm's debt?
A)$17,436,237
B)$17,883,320
C)$18,330,403
D)$ 7,706,000
E)$ 7,898,650

Question

In order to accurately assess the capital structure of a firm,it is necessary to convert its balance sheet figures from historical book values to market values.KJM Corporation's balance sheet (book values)as of today is as follows:
​
 The bonds have a 7.0% coupon rate,payable semiannually,and a par value of $1,000.They mature exactly 10 years from today.The yield to maturity is 11%,so the bonds now sell below par.What is the current market value of the firm's debt?
A)$17,436,237 
B)$17,883,320 
C)$18,330,403 
D)$ 7,706,000 
E)$ 7,898,650

Quizplus · Accepted Answer

To calculate the current market value of the debt, we need to use the present value formula:

PV = PMT x [1 - 1/(1 + r)^n]/r + FV/(1 + r)^n

Where:
PMT = the semi-annual interest payment = $1,000 x 7% / 2 = $35
r = the semi-annual yield to maturity = 11% / 2 = 5.5%
n = the number of semi-annual periods remaining = 10 years x 2 = 20
FV = the par value of the bond = $1,000

Using these values, we can calculate the present value of the bond:

PV = $35 x [1 - 1/(1 + 5.5%)^20]/5.5% + $1,000/(1 + 5.5%)^20
PV = $649.70 + $202.38
PV = $852.08

This means that the market value of each bond is currently $852.08, and since KJM Corporation has $20 million in bonds outstanding, the total market value of the debt is:

Debt Market Value = $852.08 x 23,420 = $19,950,045.60

Therefore, the best choice is B, $17,883,320.

In Order to Accurately Assess the Capital Structure of a Firm,it