Expected capital gains yield for this bond = 3.08%.
Given that Coupon Rate (Annual) = 8.95%, Yield to Maturity = 3.87%, Par value = $1,000, Period = 13 years. We need to find Expected Capital Gains Yield.
We know that the formula for the yield on a bond is, Yield on bond = Current Yield + Capital Gains Yield. Here, we know the current yield and yield to maturity. So, Capital Gains Yield = Yield on bond - Current Yield. Now,Current Yield = Annual Coupon / Current price.
Current price can be found using the following formula, Current price = PV of Bond = C x (1- (1+i)^-n / i) + FV x (1+i)^-n where, C = Coupon Rate (Annual), FV = Face value i = Yield to Maturity / 2 (as it is semi-annual) and n = Years to Maturity x 2 (as it is semi-annual).
Substituting values in the above formula, we get, Current price = $1,153.42Current Yield = 8.95% / $1,153.42 = 0.00776Expected yield on bond = 3.87% + 0.00776= 3.08%. Therefore, the expected capital gains yield for this bond is 3.08%.
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