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Running Head: Bond Yield-to-Maturity Bond Yield-to-Maturity (Authors Name) (Institution Name) Introduction This assignment pertains to a coworkers purchase of a 10 % bond that she had purchased and the subsequent discussion she had with her broker who with insistence kept repeating that it had a 9 % yield, therefore, this assignment clarifies the confusion related to the issue as follows: Example As and example, we shall imagine our interest in buying a bond at a market price that's different from the bond's par value. We have however, to keep in mind that there are the following three commonly used methods of measuring the annual rate of return that we can earn on our investment: Coupon Rate:
Annual payout as a percentage of the bond's par value
Current Yield:
Annual payout as a percentage of the current market price you " ll actually pay
Yield-to- Maturity:
Composite rate of return off all payouts, coupon and capital gain (or loss) (The capital gain or loss is the difference between par value and the price that we actually pay. ) The best way of measuring the rate of return is through the yield-to-maturity method as it includes all the aspects of our investment. For its calculation, we have to comply with all the composite payouts: (Bond Yield-to-Maturity) Yield to Maturity (YTM) The rate of return is based on the calculating the total performance of a bond (coupon payments as well as capital gain or loss) from the time of its purchase up to the time of its maturity. (Yield to Maturity) Therefore, whatever r may be, when we calculate the present values of all the payouts and then add up these values, the will equal our initial investment amount. In an equation it will therefore be: 1.
c (1 + r) - 1 + c (1 + r) - 2 +... + c (1 + r) -n + B (1 + r) -n = P
Where
c = annual coupon payment (in dollars, not a percent)
n = number of years to maturity
B = par value
P = purchase price We should therefore try to visualize what this equation states. The left side represents n+ 1 different compound interest curves, all starting out now and each one ending at the moment that the payout it corresponds to takes place. Most of these curves will stay pretty low to the axis, because they only grow to a value of c, the coupon payment. The very last curve will be a lot taller, and end up at the par value B. And if we add up the present values of all these curves (that is on the left side of the equation), the sum will equal exactly to the purchase price of the bond (that is on the right side). As with most composite payout problems, equation 1 can not be solved with exactness in general.
The nicer part is that all yield-to-maturity calculating problems are basically the same, we can therefore manufacture programmable calculators and computer programs and even tables like the ones we did in the past gone by days to help us find r. Example: We can suppose our bond is selling for $ 1030 and has a coupon rate of 10 % and that it matures in 4 years with its par value being $ 1000. Therefore to find the YTM we would have to calculate: The coupon payment at $ 100 (which is 10 % of $ 1000) therefore its equation should be: 2.
100 (1 + r) - 1 + 100 (1 + r) - 2 + 100 (1 + r) - 3 + 100 (1 + r) - 4 + 1000 (1 + r) - 4 = 1030 However, to solve the problem, we can use the popup calculator instead, and adjust r at approximately 9 %. And if required, we can plug this number back into equation 2, to ensure that the figures check out. An important thing to note is that the YTM is greater than the current yield, which in turn is greater than the coupon rate. (Current yield is $ 100 /$ 1030 = 9. 7 %). This will always be true for a bond selling at a discounted rate and therefore we shall always have: Bond Selling At...
Satisfies This Condition
Discount
Coupon Rate < Current Yield < YTM
Premium
Coupon Rate > Current Yield > YTM
Par Value
Coupon Rate = Current Yield = YTM
(Bond Yield-to-Maturity) Our co-worker must therefore have paid some premium as an additional amount over the par value of the bond and therefore the calculations projected by her broker must be based on: Coupon Rate (10 %) > Current Yield (9. 1 %- 9. 9 %) > YTM (9 %) Conclusion Once a bond has been issued and it is trading in the market, all of its future payouts are accordingly determined and the only thing that varies in its value is its asking price. If we buy such a bond at a lower price the yield to maturity we will earn on our investment will naturally increase because of the bond prices and yields "moving" in opposite directions. This at times can be confusing as people are not most of the time consistent in the way they understand and opine about performances of bonds. When someone says " 10 year treasuries were down today", they probably mean that the asking price was down and can translate as a bad day for bond holders; but they can also mean to say that the yield to maturity was down because the asking price was up, which translates as a good day for bond holders. (Bond Yield-to-Maturity) References: Bond Yield-to-Maturity (Accessed: April 20, 2007) web Yield to Maturity (YTM) (Accessed: April 20, 2007) web
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Research essay sample on Running Head Bond Yield To Maturity
