SOLUTION: A Fletchbuild coupon bond matures in four years, pays an semi-annual coupon rate of 10.5 % and will be redeemed at a face value of $1,000 at maturity. If you require a semi-annual

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Question 219423: A Fletchbuild coupon bond matures in four years, pays an semi-annual coupon rate
of 10.5 % and will be redeemed at a face value of $1,000 at maturity. If you require a semi-annually compounded return of 12 % on this investment what is the most you should be willing to pay for this bond?
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
4 year bond.
semi-annual coupon rate of 10.5%
$1,000 bond.
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I'm pretty sure this is the way it's done.
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A time period is every 6 months.
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Your study is for 8 time periods.
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Your coupon is 10.5% per year paid semi-annually which means you get half of that every 6 months.
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Half of that every 6 months is .105/2 * $1,000 = $52.50 at the end of each time period.
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At the end of the 8th time period you will be getting the last of the $52.50 plus you will be getting $1,000.
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The rate of return you are looking for is an annual rate of 12% compounded semi-annually.
That means for 8 time periods you will be earning 6% compounded interest each time period.
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Present Value of $52.50 payments at the end of each of 8 time periods at 6% compounded per time period equals $326.0141751
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Present Value of a future amount of $1,000 for 8 time periods at 6% compounded per time period equals $627.4123713
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Add these up together and you get $$953.4265464.
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This is what you should pay for the bonds today.
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You will earn 12% a year compounded annually.
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To confirm this, I looked at it from a cash flow analysis point of view.
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The Future Value of $953 for 8 time period at 6% per time period is equal to $1519.617065
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If you invest $953 today, you should have $1519.617065 in your account at the end of the 8 time periods.
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This is small enough to calculate each year separately, so I'll do it.
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You invest $953 at the beginning of time period 0.
End of Time Period 1 = $52.06
End of Time Period 2 = * 1.06 + $52.5 = $108.15
End of Time Period 3 = * 1.06 + $52.5 = $167.14
End of Time Period 4 = * 1.06 + $52.5 = $229.67
End of Time Period 5 = * 1.06 + $52.5 = $295.95
End of Time Period 6 = * 1.06 + $52.5 = $366.20
End of Time Period 7 = * 1.06 + $52.5 = $440.68
End of Time Period 8 = * 1.06 + $52.5 = $519.62 + $1,000 = $1519.62 *****
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The cash flow analysis and the Future Value of a Present Amount yield the same result so it's probably accurate.
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I think I got the coupon rate right. That looks like the way they do it. the coupon rate is an annual rate based on the face value of the bond. If you get the coupon semi-annually, then you get half of it two times a year.
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Formulas I used are shown below:
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FUTURE VALUE OF A PRESENT AMOUNT

FV = Future Value
PA = present amount
i = Interest Rate per Time Period
n = Number of Time Periods
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PRESENT VALUE OF A FUTURE AMOUNT

PV = Present Value
FA = future amount
i = Interest Rate per Time Period
n = Number of Time Periods
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PRESENT VALUE OF A PAYMENT

PV = Present Value
PMT = Payment per time period
i = Interest Rate per Time Period
n = Number of Time Periods
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