Answer:
Holding Period return 19.54%
Explanation:
We purchase to get a yield of 8%
so we sovle for the present value of the bond (market value) which is the amount at which we adquire the bond:
PV of the coupon payment:
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C ($1,000 x 5%) 50.000
time 20 years
rate 0.08
[tex]50 \times \frac{1-(1+0.08)^{-20} }{0.08} = PV\\[/tex]
PV $490.9074
Pv of maturity:
[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]
Maturity 1,000.00
time 20.00
rate 0.08
[tex]\frac{1000}{(1 + 0.08)^{20} } = PV[/tex]
PV 214.55
PV c $490.9074
PV m $214.5482
Total $705.4556
Then, we solve for the price that 7% YTM after a year:
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C 50.000
time 19
rate 0.07
[tex]50 \times \frac{1-(1+0.07)^{-19} }{0.07} = PV\\[/tex]
PV $516.7798
[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]
Maturity 1,000.00
time 19.00
rate 0.07
[tex]\frac{1000}{(1 + 0.07)^{19} } = PV[/tex]
PV 276.51
PV c $516.7798
PV m $276.5083
Total $793.2881
Now we compare to get hte capital gain:
year-end less beginning value
$793.29 - $705.46 = $87.83
The coupon is also a return:
$1,000 x 5% = $50
Total return $137.83
Investment $705.46
Holding-period return
137.83/705.46 = 0,195376 = 19.54%
