In order to accurately assess the capital structure of a firm, it is necessary to convert...

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) $23,500,000 Preferred stock 2,000,000 Common stock ($10 par) 10,000,000 Retained earnings 4,000,000 Total debt and equity $39,500,000 The bonds have a 8.3% 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. $21,679,615 b. $15,569,906 c. $19,708,741 d. $24,241,752 e. $22,073,790

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Expert Solution

Par value of bond = $1000

maturity, m = 10 years

no. of semi-annual periods, n = m*2 = 10*2 = 20

Coupon rate = 8.3% = 0.083

annual coupon value,C = coupon rate* par value of bond = 0.083*1000 = 83

sem-annual coupon, S = C/2 = 83/2 = 41.5

YTM = Y = 11% = 0.11

YTM (semi-annual) , R = Y/2 = 0.11/2 = 0.055

Value of bond = Present value of coupons + Present value of maturity amount

Present value of coupons = S*PVIFA

PVIFA = present value interest rate factor of annuity ( 20 years, 0.055)

= [((1+R)ⁿ-1)/((1+R)ⁿ*R)] = [((1.055)²⁰-1)/((1.055)²⁰*0.055)] = [1.917757491/0.160476662] = 11.95038248

Present value of coupons = S*PVIFA = 41.5*11.95038248 = 495.9408731

Present value of maturity amount = par value/(1+R)ⁿ = 1000/(1.055)²⁰ = 1000/2.917757491 = 342.7289633

Value of bond = 495.9408731 + 342.7289633 = $838.6698365

this is the value of one bond

No. of bonds issued = Total book value of bonds/par value of 1 bond = 23500000/1000 = 23500

current market value of firm's debt = Value of 1 bond* no. of bonds = 838.6698365*23500 = $19,708,741.16 or $19,708,741 ( rounding off to nearest dollar value)

Hence correct option is c.

jeff jeffy answered 1 year ago

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