Answer:
Year Cashflow DF@7% PV DF@9% 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.
