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Yield to Maturity and Required Returns The Brownstone Corporation's bonds have 5 years remaining to maturity....

Yield to Maturity and Required Returns

The Brownstone Corporation's bonds have 5 years remaining to maturity. Interest is paid annually, the bonds have a $1,000 par value, and the coupon interest rate is 9%.

  1. What is the yield to maturity at a current market price of $832? Round your answer to two decimal places.
    %
  2. What is the yield to maturity at a current market price of $1,093? Round your answer to two decimal places.
    %

Solutions

Expert Solution

13.00% 14.00%
Year Cash Flow PV fatctor = 1/ (1+r)^t PV PV fatctor = 1/ (1+r)^t PV
0                                   (832) 1.000        (832.00) 1.000      (832.00)
1                                       90 0.885            79.65 0.877         78.95
2                                       90 0.783            70.48 0.769         69.25
3                                       90 0.693            62.37 0.675         60.75
4                                       90 0.613            55.20 0.592         53.29
5                                       90 0.543            48.85 0.519         46.74
5                                 1,000 0.543         542.76 0.519       519.37
           27.31          (3.65)
NPV @ 0.13                                 27.31
NPV @ 0.14                                  (3.65)
Difference in both                                 30.96
YTM =Lower rate + Difference in rates*(NPV at lower rate)/(Lower rate NPV-Higher rate NPV)
'=0.13+ (0.14-0.13)*(27.310/(27.310+3.6540)
YTM 0.1388
YTM 13.88%
6.00% 7.00%
Year Cash Flow PV fatctor = 1/ (1+r)^t PV PV fatctor = 1/ (1+r)^t PV
0                                (1,093) 1.000     (1,093.00) 1.000 (1,093.00)
1                                       90 0.943            84.91 0.935         84.11
2                                       90 0.890            80.10 0.873         78.61
3                                       90 0.840            75.57 0.816         73.47
4                                       90 0.792            71.29 0.763         68.66
5                                       90 0.747            67.25 0.713         64.17
5                                 1,000 0.747         747.26 0.713       712.99
           33.37        (11.00)
NPV @ 0.06                                 33.37
NPV @ 0.07                                (11.00)
Difference in both                                 44.37
YTM =Lower rate + Difference in rates*(NPV at lower rate)/(Lower rate NPV-Higher rate NPV)
'=0.06+ (0.07-0.06)*(33.370/(33.370+10.996)
YTM 0.0675
YTM 6.75%

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