Bonds issued by the Coleman Manufacturing Company have a par value of $1,000, wh
ID: 2717513 • Letter: B
Question
Bonds issued by the Coleman Manufacturing Company have a par value of $1,000, which of course is also the amount of principal to be paid at maturity. The bonds are currently selling for $770. They have 10 years remaining to maturity. The annual interest payment is 9 percent ($90).
Compute the yield to maturity. (Do not round intermediate calculations. Input your answer as a percent rounded to 2 decimal places.)
Bonds issued by the Coleman Manufacturing Company have a par value of $1,000, which of course is also the amount of principal to be paid at maturity. The bonds are currently selling for $770. They have 10 years remaining to maturity. The annual interest payment is 9 percent ($90).
Explanation / Answer
Calculation of Yield To Maturity (YTM):
Calculation of Yield to Maturity is similar to that of Internal Rate of Return. A Trail & Error approach is to be followed to calculate the rate of return or yield to maturity. An easy way of calculating the YTM is to use the Financial Calculator. By using financial calculator we can get the YTM is near to 13.60%. Since the cash in flows are uniform for all the 10 years at $90 per year and at the end of 10th year we can get the bond face value of $1,000. When the cash flow are uniform, we can use the Present Value Interest Factor for an Annuity (PVIFA) for interest inflows and Present Value Interest Factor (PVIF) for the bond face value which will be received at the end of 10th year.
Calculation of YTM:
Year Cash inflows Discount Factor@13.60 Present value of cash inflows
1 through 10 $90 5.298 476
10th year $1,000 0.297 297
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Present value of cash inflows $773
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The present value of cash outflows is $770. Hence the present value of cash inflow also must be equal to $770. At the interest rate of 13.60%, the cash out flows are equal to cash inflows. So the Yield to Maturity is 13.60%.
YTM= 13.60%