You Are Considering the Purchase of Two $1,000 Bonds, Both

question 47

Essay

You are considering the purchase of two $1,000 bonds, both issued by Tranig Corp. Your expectation is that interest rates will drop, and you want to buy the bond which provides the maximum capital gains potential. The first Tranig bond has a coupon rate of 6% with five years to maturity, while the second has a coupon rate of 9% and comes due six years from now. If market rates of interest are 8% for both bonds, which bond has the best price potential? (Use duration to answer the question.)
Coupon rate 6%
$\begin{array}{|c|c|c|r|r|r|}\hline\text { (1) } & \text { (2) }&\text {(3) } & \text { (4) }&\text { (5) }&\text { (6) }\\ \hline&& \text { PV Factor } & \text { PV of } &\text { Weights }&\\ \hline\underline{ \text { Year } }& \underline{ \text{ Cash Flow}} &\underline{ \text { @ } 10{\%} }&\underline{ \text { Cash Flow } }&\underline{ (4) \text { Value }} &\underline{ (1) \times(5)} \\\hline1& \$ 60 & .926 & \$ 55.56 & .06035 & .06035 \\\hline 2 & 60 & .857 & 51.42 & .05585 & .11170 \\\hline 3 & 60 & .794 & 47.64 & .05175 & .15525 \\\hline 4 & 60 & .735 & 44.10 & .04790 & .19160 \\\hline 5 & 60 & .681 & 40.86 & .04438 & .22190 \\\hline 5 & 1,000 & .681 & \underline{681.00} & .73975 & \underline{3.69875} \\\hline\end{array}$

$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { PV of Bond }=\$ 920.58 \quad \text { Duration }=4.43955$ Coupon rate 9% $\begin{array}{|l|l|l|l|l|l|}\hline\text { (1) } & \text { (2) }&\text {(3) } & \text { (4) }&\text { (5) }&\text { (6) }\\ \hline&& \text { PV Factor } & \text { PV of } &\text { Weights }&\\ \hline\underline{ \text { Year } }& \underline{ \text{ Cash Flow}} &\underline{ \text { @ } 8{\%} }&\underline{ \text { Cash Flow } }&\underline{ (4) \text { Value }} &\underline{ (1) \times(5)} \\\hline 1 & \$ 90 & .926 & \$ 83.34 & .07967 & .07967 \\\hline 2 & 90 & .857 & 77.13 & .07373 & .14746 \\\hline 3 & 90 & .794 & 71.46 & .06831 & .20493 \\\hline 4 & 90 & .735 & 66.15 & .06325 & .25292 \\\hline 5 & 90 & .681 & 61.29 & .05859 & .29295 \\\hline 6 & 90 & .630 & 56.70 & .05421 & .32526 \\\hline 6 & 1,000 & .630 & 630.00 & .60225 & .3 .61350 \\\hline\end{array}$
$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { PV of Bond } = \$ 1046.07 \quad \text { Duration } = 4.91669$

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