You are the owner of 100 bonds issued by Euler, Ltd. These bonds have 8 years re

Question

You are the owner of 100 bonds issued by Euler, Ltd. These bonds have 8 years remaining to maturity, an annual coupon payment of $80, and a par value of $1,000. Unfortunately, Euler is on the brink of bankruptcy. The creditors, including yourself, have agreed to a postponement of the next 4 interest payments (otherwise, the next interest payment would have been due in 1 year). The remaining interest payments, for Years 5 through 8, will be made as scheduled. The postponed payments will accrue interest at an annual rate of 6 percent, and they will then
be paid as a lump sum at maturity 8 years hence. The required rate of return on these bonds, considering their substantial risk, is now 28 percent. What is the present value of each bond?

Hint: Move each of the first four coupon paymens out to period 8 by 6% and replace the cash flows in periods 1 - 4 with 0. Then discount all the cash flows back to 0 at 28%.

Explanation / Answer

In this question,We heve,

Number of bonds = 100 , Number of years to Maturity = 8 years,Annual Coupon payment = $ 80, Par value of bond = $ 1,000, Coupon rate = 8% & 6%, Discount rate = 28%

We have to calculate Present value of each bond = ?

In this question has two part:

In the first part, Bondholder waved coupon payment for 4 years. In compensation of this, they pay annual interest payment @ 6% which is accre every year. Lumsum amount paid at the time of maturity of bond. So, we calculate Future value of this waved interest payment and after that calculate present value of this future cash flow. We have,

Step 1; Calculate the future value of Interest waved amount for the 4 years by Future value of Annuity method, we have,

Formula:

Future value = PMT [(1+i)n -1/ i] = 80[(1+0.06)4 -1 / 0.06]

Future vaule = 80 [(1+0.06)2 -1/ 0.06]

    Future Value = $ 349.97

Step 2: The future value of interest waved is regularty accrue for maturity period.Hence, we have to calculate Furture value at the maturity period i.e 8 years of Future value of Annuity, We have

  Future value = 349.47(1+0.06)4

  Future value of Interest waves at the maturity period ( 8 years) = $ 441.83

Step 3: Now we calculate Present value of future value of interest waves at the maturity period of amount $ 441.83 at the rate of discounting rate 28%. We Calculate by this this formula,

Present Value = Future value of Compensated interest payment / (1+i)8

Present Value =441.83/ (1.28)8

Present Value = $ 61.31

In the Second part, we calculate present value of Cash flow and price of bond at the rate of 28% for 5- 8 years. We have,

Present Value = [ 80/ (1.28)5 + 80/(1.28)6 + 80/(1.28)7 + 80/(1.28)8 + 1,000/(1.28)8]

Present Value = $ 205.56

Total Present value of bond during the period = 61.31+ 205.56 = $ 266.88

Ans: D. $ 266.88

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