Otto enterprises has a bond issue outstanding with a coupon of 8 percent that matures in 15 years. the bond is currently priced at $923.60 and has a par value of $1,000. interest is paid semiannually. what is the yield to maturity? a. 8.67%b. 9.93%c. 9.16%d. 8.93%e. 8.45%

Year   Cashflow    [email protected]%      PV           [email protected]%     PV

               $                                 $                                  $

  0        (923.60)           1           (923.60)          1         (923.60)

1-15         80             9.1079       728.63      8.0607     644.86

15          1,000          0.3624     362.40      0.2745     274.50

                                  NPV         167.43             NPV  (4.24)                    

Kd = LR     + NPV1/NPV1+NPV2    x (HR – LR)

Kd = 7       + 167.43/167.43 + 4.24 x (9 – 7)

Kd = 7       + 167.43/171.67 x 2

Kd = 8.95%    

The yield to maturity is approximately 8.95%

The correct answer  is  D

Explanation:

The yield to maturity of the bond is calculated by applying internal rate of return formula. The current market price of the bond is the cashflow for year 0. The coupon on the bond (R = 8% x $1,000) is the cashflow for year 1 to 15 and the cashflow for year 15 is the face value.

All cashflows are discounted at 7% and 9% discount rates. The net present values were obtained by deducting the present value in year 0 from the present value of year 1 to 15.

Finally, the yield to maturity is calculated by applying the interpolation formula stated above, where LR denotes the lower discount rate,                             HR represents the higher discount rate, NPV1 refers to the positive NPV and NPV2 refers to the negative NPV.                                                                                                                                                                                                                                      

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