Respuesta :
Answer:
a) 17.53%
b) $41 x 40% = $ 16.40
815.25 - 728.48 = 86.77 capital gain x 30% = $ 26.03
Total: 26.03 + 16.40 = $ 42.43 income tax expense
c) (815.25 + 41 - 42.43) / 728.48 - 1 = 0.1171425 = 11.71%
d)
we recalculate the price of the bond with 13 years left to maturity
holding period return 26.94%
e)
tax expense:
(41x1.02 + 41) x 0.4 = 33.14
(841.87 - 728.48) x 0.3 = 34.02
tax expense: 67.16
after tax return:
(841.87 + 41x1.021 + 41 - 67.16) /728.48 - 1 = 0.177209379 = 17.72%
Explanation:
We need to determinate the value of the bond at yield of 7.1% and at yield of 6.1% which is the sum of the present value of the maturity and coupon payment:
Purchase price:
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
Coupon payment = 1,000 x 0.041 = 41.00
time 15 years
rate 0.071
[tex]41 \times \frac{1-(1+0.071)^{-15} }{0.071} = PV\\[/tex]
PV $371.0773
[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]
Maturity 1,000.00
time 15.00
rate 0.071
[tex]\frac{1000}{(1 + 0.071)^{15} } = PV[/tex]
PV 357.40
PV c $ 371.0773
PV m $ 357.4028
Total $ 728.4801
Selling Price
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C 41.00
time 14 (one-year past so maturity is more closer)
rate 0.061
[tex]41 \times \frac{1-(1+0.061)^{-14} }{0.061} = PV\\[/tex]
PV $378.7456
[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]
Maturity 1,000.00
time 14.00
rate 0.061
[tex]\frac{1000}{(1 + 0.061)^{14} } = PV[/tex]
PV 436.50
PV c $378.7456
PV m $436.5004
Total $815.2460
Holding period return:
return / investment - 1
(815.25 + 41) / 728.48 - 1 = 0.175387059 = 17.53%
d)
we recalculate the price of the bond with 13 years left to maturity
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C 41.00
time 14
rate 0.061
[tex]41 \times \frac{1-(1+0.061)^{-14} }{0.061} = PV\\[/tex]
PV $378.7456
[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]
Maturity 1,000.00
time 13.00
rate 0.061
[tex]\frac{1000}{(1 + 0.061)^{13} } = PV[/tex]
PV 463.13
PV c $378.7456
PV m $463.1269
Total $841.8725
and redo the return, tax and after-tax return:
(841.87 + 41x1.021 + 41) /728.48 - 1 = 0.269401333