Question

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?

Answer 1

To calculate the current market value of the firm's debt, we need to discount the bond's future cash flows at the yield to maturity rate.

Step-by-step explanation:

The current market value of the firm's debt can be determined by calculating the present value of the bond's future cash flows. In this case, the bond has a 4.0% coupon rate and pays interest semiannually. It matures in 10 years. The yield to maturity is 12%.

To calculate the market value, we need to discount the bond's future cash flows at the yield to maturity rate. The bond pays $40 in interest semiannually, so the annual cash flow is $80. Using a financial calculator or spreadsheet, we discount all the cash flows (including the face value of $1,000) at a 12% yield to maturity rate.

The market value of the debt is the sum of the present values of all the cash flows from the bond. This value represents the current market price at which the bond is selling below par.

Answer 2

Value of Firm's Debt is $541.20

Step-by-step explanation:

Coupon payment = 1000 x 4% = $40 / 2 = $20

Number of periods = n = 10 years x 2 = 20

Face value = $1,000

YTM = 12% / 2 = 6% = 0.06

Price of bond is the present value of future cash flows, to calculate Price of the bond use following formula:

Price of the Bond = C x [ ( 1 - ( 1 + r )^-n ) / r ] + [ F / ( 1 + r )^n ]

Price of the Bond =$20 x [ ( 1 - ( 1 + 6% )^-20 ) / 6% ] + [ $1,000 / ( 1 + 6% )^20 ]

Price of the Bond = $20 x [ ( 1 - ( 1.06 )^-20 ) / 0.06 ] + [ $1,000 / ( 1.06 )^20 ]

Price of the Bond = $229.4 + $311.80

Price of the Bond = $541.20