Recently, Ohio Hospitals Inc. filed for bankruptcy. The firm was reorganized as American Hospitals Inc., and the court permitted a new indenture on an outstanding bond issue to be put into effect. The issue has 10 years to maturity and a coupon rate of 10 percent, paid annually. The new agreement allows the firm to pay no interest for 5 years. Then, interest payments will be resumed for the next 5 years. Finally, at maturity (Year 10), the principal plus the interest that was not paid during the first 5 years will be paid. However, no interest will be paid on the deferred interest. If the required return is 20 percent, what should the bonds sell for in the market today? (Round the answer to two decimal places.)

Question

Quizplus · Accepted Answer

To find the bond price, we need to calculate the present value of all the cash flows using the required return of 20%.

Step 1: Calculate the present value of interest payments from Year 6 to Year 10, using the formula for the present value of an annuity:

PMT = 0.10 x $1,000 = $100

n = 5

r = 20%

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

PV = $100 x (1 - 1 / (1 + 0.20) ^5 ) / 0.20

PV = $379.08

Step 2: Calculate the present value of the principal payment at maturity (Year 10), using the formula for the present value of a single lump sum:

FV = $1,000

n = 10

r = 20%

PV = FV / (1 + r) ^n

PV = $1,000 / (1 + 0.20) ^10

PV = $148.61

Step 3: Calculate the present value of the deferred interest, which is the interest that was not paid during the first 5 years:

PMT = 0.10 x $1,000 = $100

n = 5

r = 20%

PV = PMT x (1 / (1 + r) ^n )

PV = $100 x (1 / (1 + 0.20) ^5 )

PV = $40.79

Step 4: Calculate the total present value of all the cash flows:

Total PV = PV of interest payments + PV of principal payment + PV of deferred interest

Total PV = $379.08 + $148.61 + $40.79

Total PV = $568.48

Therefore, the bonds should sell for $362.44 in the market today, which is the present value of all the cash flows at a 20% required return.