Components of Bond Returns

Components of Bond Returns – Q36 Page 197

Current Yield for Bond P

First, find the price of the bond ie. Current price. @9%, coupon = $90, say maturity value is $1,000 Bond value = Present value of coupons + Present value of the face amount. P0 = C x [1-1/(1+r)t]/r + F/(1+r)t P0 = $90 x [1-1/(1+0.07)5]/0.07 + $1000/(1+0.07)5 P0 = $90 x [1-1/1.403] /0.07 + $1000/1.403 P0 = $90 x 4.10 + $712.76 P0 = $369 + $712.76 P0 = $1081.76 Current yield for Bond P: Current yield = $90/$1081.76 = 0.0832 or 8.32%

Current Yield for Bond D

First, find the price of the bond ie. Current price. @5%, coupon = $50, say maturity value is $1,000 Bond value = Present value of coupons + Present value of the face amount. P0 = C x [1-1/(1+r)t]/r + F/(1+r)t P0 = $50 x [1-1/(1+0.07)5]/0.07 + $1000/(1+0.07)5 P0 = $50 x [1-1/1.403]/0.07 + $1000/1.403 P0 = $50 x 4.10 + $712.76 P0 = $205 + $712.76 P0 = $917.76 Current yield for Bond D: Current yield = $50/$917.76 = 0.0545 or 5.45%

Components of Bond Returns – Q36 Page 197

Expected Capital Gain in 1 Yr – Bond P

P0 = $1,081.76, coupon rate $90 Maturity value = $1,000 P1 = C x [1-1/(1+r)t]/r + F/(1+r)t P1 = $90 x [1-1/(1+0.07)4]/0.07 + $1000/(1+0.07)4 P1 = $90 x [1-1/1.311]/0.07 + $1000/1.311 P1 = $90 x 3.386 + $762.78 P1 = $304.74+ $762.78 P1 = $1067.52 Capital gains yield = (New price – Original price)/Original price. CGY1 = ($1067.88 - $1081.76)/$1081.76 CGY1 = - 0.0132 or -1.32%

Expected Capital Gain in 1 Yr – Bond D

P0 = $917.76, coupon rate $50 Maturity value = $1,000 P1 = C x [1-1/(1+r)t]/r + F/(1+r)t P1 = $50 x [1-1/(1+0.07)4]/0.07 + $1000/(1+0.07)4 P1 = $50 x [1-1/1.311]/0.07 + $1000/1.311 P1 = $50 x 3.386 + $762.78 P1 = $169.30 + $762.78 P1 = $932.08 Capital gains yield = (New price – Original price)/Original price. CGY1 = ($932.08 - $917.76)/$917.76 CGY1 = 0.0156 or 1.56%

Premium bonds pay higher current income with price depreciating as maturity year nears. Discount bonds do not pay high current income, but price...