a. What is the current yield on the bond? (Enter your answer as a percent rounded to 2 decimal places.)
b. What is the yield to maturity if interest is paid once a year? (Do not round intermediate calculations. Enter your answer as a percent rounded to 4 decimal places.)
c. What is the yield to maturity if interest is paid semiannually? (Do not round intermediate calculations. Enter your answer as a percent rounded to 4 decimal places.)
Explanation
Some values below may show as rounded for display purposes, though unrounded numbers should be used for actual calculations.
a.
| Current yield | = | Annual interest / Bond price |
| = | (0.07 × $1,000) / $1,079 | |
| = | 0.0612, or 6.12% |
b.
| Bond price | = | PV of coupon payments + PV of face value |
| Bond price | = | C × ((1 / r) – {1 / [r(1 + r)t]}) + FV / (1 + r)t |
| $1,079 | = | (0.07 × $1,000) × ((1 / r) – {1 / [r × (1 + r)14]}) + $1,000 / (1 + r)14 |
To solve for r, use trial-and-error, a financial calculator, or a computer. See the calculator solution below.
c.
When interest is paid semiannually, the interest rate, payment, and number of time periods must all be expressed in semiannual terms.
Assume that both C and t are annual in the following:
| Bond price | = | PV of coupon payments + PV of face value |
| Bond price | = | C / 2 × [[1 / (r / 2)] – (1 / {(r / 2)[1 + (r / 2)](t × 2)})] + FV / [1 + (r / 2)](t × 2) |
| $1,079 | = | [(0.07 / 2) × $1,000] × [[1 / (r / 2)] – (1 / {(r / 2)[1 + (r / 2)](14 × 2)})] + FV / [1 + (r / 2)](14 × 2) |
To solve for r, use trial-and-error, a financial calculator, or a computer. See the calculator solution below.
Calculator computations:
When you have a PV, a PMT, and a FV, you must carefully assign positive and negative values. The key is to have the same sign (+ or –) on all cash flows that move in the same direction. With a bond, the PMT and FV flow in the same direction.
For example, if you purchase a bond, the PV is a cash outflow and the PMT and FV are cash inflows. It does not matter if you assign positive or negative signs to the PMT and FV as long as the signs are consistent with each other.
b.
This problem must be expressed in terms of annual periods since coupon payments are paid annually
Since N and PMT were expressed in terms of years, I/Y is the annual rate.
YTM = Annual rate = 5.7625%
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Enter
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7
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–1,079
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66
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1,000
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N
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I/Y
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PV
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PMT
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FV
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Solve for
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5.7625
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c.
This problem must be expressed in terms of semiannual periods since coupon payments are paid semiannually.
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Enter
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7 × 2
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–1,079
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66/ 2
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1,000
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N
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I/Y
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PV
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PMT
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FV
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Solve for
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2.88489
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Since N and PMT were expressed in terms of semiannual periods, I/Y is the semiannual rate.
YTM = Annual rate
= Semiannual rate × 2
= 2.88489% × 2
= 5.7698%
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