Answer:
A)
before decrease in rates: 706,483
after rate decrease: 751,360
B)
interest expense 35,015.12
discount on BP 3,015.12
cash 32,000
--bonds first interest payment--
C)
interest expense 35,165.87
discount on BP 3,165.87
cash 32,000
--second interest payment--
D)
unrealized loss 44,877
discount on bonds payable 44,877
--to adjust bonds valuation--
Explanation:
First, we solve for the present value of the bond to get the proceeds from the issuance.
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C 32,000
time 20
rate 0.05
[tex]32000 \times \frac{1-(1+0.05)^{-20} }{0.05} = PV\\[/tex]
PV $398,790.7310
[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]
Maturity 800,000.00
time 20.00
rate 0.05
[tex]\frac{800000}{(1 + 0.05)^{20} } = PV[/tex]
PV 301,511.59
PV c $398,790.7310
PV m $301,511.5863
Total $700,302.3173
Now, we do the table for the first year:
# / Principal/ paid / interest / Amort/End. P
1 700,302 32000 35015.12 3015.12 703,317
2 703,317 32000 35165.87 3165.87 706,483
Now, we have to redo the calculations for the bonds market value considering a decrease in the market rate to 9%
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C 32,000
time 18
rate 0.045
[tex]32000 \times \frac{1-(1+0.045)^{-18} }{0.045} = PV\\[/tex]
PV $389,119.7377
[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]
Maturity 800,000.00
time 18.00
rate 0.045
[tex]\frac{800000}{(1 + 0.045)^{18} } = PV[/tex]
PV 362,240.30
PV c $389,119.7377
PV m $362,240.2951
Total $751,360.0328
We adjust for: 751,360 - 706,483 = 44,877
This will be an unrealized loss as the liability increases but, will be realized on the redemption of the bonds or at the end of the bonds' life.
