the Desreumaux Company has two bond issues outstanding. Both bonds pay $100 annu
ID: 2683285 • Letter: T
Question
the Desreumaux Company has two bond issues outstanding. Both bonds pay $100 annual interest plus $1000 at maturity. Bond L has a maturity of 15 years and Bond S has a maturity of 1 year, Interest is paidannually.
a. What will be the value of each of these bonds when the going rate of interest is (1) 5% (2) 7%, and (3) 11%? Assume there is only one more interst payment to be made on Bonds.
b. Why does the longer term (15 Year) bond fluctuate more when interst rates change than does the shorter term bond (1Year)?
Explanation / Answer
To value the bonds, discount their cash flows at the appropriate rate, eg.: #1.3 (sorry, started with the last rate) ...at11%: Bond L: price = 100/1.11 + 100/1.11^2 + 100/1.11^3 +...+last payment is coupon and principal: 1,100/1.11^15 = $928.09 (Note that the further out from today time-wise, the less valuable the cash flow, for example, today's value of the 14th coupon is 100/1.11^14 = $23.20, today's value of the 15th year cash flows is: 1100/1.11^15 = $229.90) Bond S: (one year from now will receive coupon $100 + face $1,000) price = 1100/1.11 = $990.99 NOTE that the 1100 paid in year 15 for Bond L is valued at $229.90, but if you receive this same cash flow only ONE year from now, as is the case for Bond S, it's worth 1100/1.11 = 990.99. This is the time value of money, also expressed as "more, sooner, is better". This helps answer question #2 below. Back to the proper order... #1.1 at 5% Bond L = $1,518.98 Bond S = 1100/1.05 = $1,047.62 #1.2 Do the same discounting, but with a rate of 7% Bond L price = $1,273.24 ...%change in price from above = (1273.24 - 1,518.98)/1,518.98 = (16.178%) Bond S price = 1100 / 1.07 = 1,028.04...%price change = (1028.04 - 1,047.62)/1,047.62 = (1.869%) #1.3 Bond L = $928.09 Bond S = 1100/1.11 = $990.99 2. The longer bond price fluctuates more because there are more cash flows, and more cash flows much further out in time, than for Bond S. (Not to get ahead of you, but the term Duration helps explain a bond's sensitivity to interest rate changes.) In the problem here, what I wrote above about the final $1100 payment and it's worth in one year vs. in 15 years, helps explain the fluctuation in the value. The payments that are further out in time, because of the time value of money [i.e. discounting, specifically the n in the divisor in this formula...pmt/(1+r)^n] make them worth less today.
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