Question

1.) 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:

Long-term debt (bonds, at par)                                       $30,000,000
Preferred stock                                                                    2,000,000
Common stock ($10 par)                                                  10,000,000
Retained earnings                                                                4,000,000
Total debt and equity                                                      $46,000,000

The bonds have a 6.50% coupon rate, payable semiannually, and a par value of $1,000. They mature exactly 10 years from today. The yield to maturity is 10%, so the bonds now sell below par. What is the current market value of the firm's debt?

a. $11,410,229

b. $15,638,226

c. $16,343,202

d. $18,638,226

e. $23,457,300

Answer 1

A	B	C	D	E	F	G	H	I	J	K
2
3		Par Value of Debt	$30,000,000
4		Par Value of Bond	$1,000
5
6		Number of Bond	=Par Value of Debt / Par Value of Bond
7			=$30,000,000 / $1,000
8			30000
9
10		Market value of bond can be calculated as follows:
11		Par value (F)	$1,000
12		Coupon rate	6.50%
13		Yield to maturity	10.00%
14		Time to maturity	10	Years
15
16		Interest is paid twice a year i.e. semiannual.
17		Semiannual coupon (C)	$32.50
18		Semiannual Period (n)	20
19		Semiannual YTM (i)	5.00%
20		Current Value of the bond can be calculated by finding the present value of cash flows of bonds.
21		Cash Flow of Bonds can be written as follows:
22		Semiannual Period	0	1	2	3	4	…	20
23		Cash Flow of Bonds		$32.50	$32.50	$32.50	$32.50	$32.50	$1,032.50
24
25		Current Value of Bond	=C*(P/A,i,n)+F*(P/F,i,n)
26		Where, C is Semiannual coupon, F is par value of bond, i is semiannual market rate and n is total semiannual periods.
27
28		Current Value of Bond	=C*(P/A,i,n)+F*(P/F,i,n)
29			=$32.50*(P/A,5%,20)+$1,000*(P/F,5%,20)
30			$781.91	=D17*PV(D19,D18,-1,0)+D11*(1/((1+D19)^D18))
31		Hence current market value of bond is	$781.91
32
33		Current market value of debt	=Number of Bonds*Market value of bond
34			=30,000*$781.91
35			$23,457,340	=D8*D31
36
37		Hence Current market value of debt	$23,457,340
38		Thus the option (e) is correct.
39

Formula sheet