Question

A 20 year, 4%, $1000 face value bond paying annual coupons is callable at par at the end of any year from 15 on.

a) How much should an investor pay if they want to earn at least 6% until the bond is called (or matures).

b) How much should an investor pay if they want to earn at least 3% until the bond is called (or matures).

explain fully please

Answer 1

Coupon sale – 4% face value = $ 1000 So annual Coupon = $1000 44% = $40 Redemption value = $1000 If bond is called after 15 years value is PIFA (M= 15,8=6%) = 9.7122 PVF (n=15, 8=64.) = 0.4173 So fair value of bond – $40x9 1122+ $100 x 0.47 Brestment on bond E$8050788 If bond is called after 16 years value à PYIFA (n=16, Y=64.) = 10.1059 PVF (n=16, 8=6% = 0.3936. faů value of bond = $ 40 x 10.1059+ $1000 0-3756 =$797.836 If bond & called after it years vales i PRIFA (n=14, 8264.) = 10.4773 PVF (n=11, r= 64.) = 0.3714 Bond ralece = $ 40 X 10.4773 + $1000 x 0.3714 $ 790.992

If bond & called after 18 year value is PUEFA (n=18, 26-) = 10,8276 PUF (n=18, 2264.) = 0.3503 Bond value = $40 x 10.8276 + 42000 x 0.3 - 183.4048 It bond is called after 19 years value is 194 PYIFA (n= 264.) = 11.158/ PVF (n=19, 8=64.) = 0.3305 Bond value = $40 x 11. 1561 + $1000 x 0.3305 =$776.824 If bond is called after 20 yeage value it PRIFA (n=20 = 67.) = 11.4699 PVF (n=20, s. 6.) = 0.3118 11.4699 Bond value = $40 X 838 + $ 1000 x 0.3118 = $770. 596
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- 3years If bond & called after 15 years value a PVIFA (n=15, 8-3%) = 11.9319 PVF (n=15, r=3x) - 0.6419 Bond value = $40 x 11.9379+ $1000 x 0.6619 - $ 1119.416 If bond i called after 16 years value is PVIFA (+216,0=34) = 12.561) PVF (n=16, 2234) = 0.6232 Bond valere = $ 40 x 12.5611 + $ 1000 x 0.6232 $ 1125.646 If bond is called after 17 years value is PVIFA (n=17,7-3+) = 13.1661 PVP (n=11, 8-37.) = 0.6050 land Value = $40 x 13-1661 + $1000X0-6050 - $91131.666

If bond u called after 18 yeage value a PRIFA (n=18, 8=34) = 13.1535 pur (n = 18, 8= 3%) = 0.5874 Bond value = $40 x 13.7535 + $ 1000 X 0.5874 & 1137.54 If bond & called after 19 years vabee is PVIFA (n = 19, 8=34) = 14.3238 PrF (n=19, 8=37) = 0.5703 Bond Kalvee = $40 x 19.3238 + $1000 X 0.5703 = $ 1143-252 If bond is called after 20 years value is PRIFA (1220, 8-34-) = 14.8775 PVF (n=20,83%) = 0.5537 Bond value = & 40 x 14.8775 + $ 1000 Xossit = $ 1148.8