Bond Investment: Realized Return Calculation | CFA Level 1 Exam Preparation

Realized Return Calculation for a Bond Investment | CFA Level 1 Exam

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Four years ago, at the advice of J.T. Lindseth, her financial planner, T.J. Ali purchased a $1,000 face, 5.70 percent, semi-annual coupon bond with four years to maturity priced to yield 8.50 percent for $906.70. Now, the bond has matured, and Lindseth calls Ali and informs her that because he had invested the coupons at an annual rate of 10.0 percent, her realized return was approximately:

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Time Saving Note:You can answer this question without doing any calculations! Because the coupon reinvestment rate was greater than the original YTM, we would expect the YTM to increase. This narrows down the choices to 8.65% and 10.00%. The rate of 10.00% is an unlikely choice because the coupon payments do not comprise 100% of the return of the bond. Thus, the realized rate will be greater than 8.50%, but less than 10.00%. The only choice that meets this criterion is 8.65%.

For those of you who want to work through the calculations: We first need to calculate the FVcoupon annuity, then calculate the Total Future Value of the Bond, and finally calculate the realized return.

Step 1: Calculate theFVcoupon annuity

jjoachim_SS15_1_B_e_FVCoupon

Here, FVcoupon annuity= [ (1 + (0.10 / 2)4*2)-1] / [0.10 / 2] * [(1000 * 0.057) / 2]

= [ ( 1.05)8"" 1] / 0.05 * 28.5 = 9.549 * 28.5 = $272.15

Alternatively, N = 8, I/Y = 5, PMT = 28.5, PV = 0, Compute FV = -272.15

Step 2: Calculate the Bond's Total Future Value (TFV)

TFV = Face Value + FVcoupon annuity= $1,000 + $272.15 = $1,272.15.

Step 3: Calculate the Realized Annual Return

jjoachim_SS15_1_B_e_RealizedR

Here, Realized ReturnAnnualized Basis= [ (1,272.15 / 906.70)1/8""1] * 2 = 0.08648, or 8.65%.

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