Treasury spot interest rates are as follows: Maturity (years) 1 2 3 4 Spot rate (EAR) 1.4% 2.8% 3.6% 4.5% What is the price of a
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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.
C 32,000
time 20
rate 0.05
PV $398,790.7310
Maturity 800,000.00
time 20.00
rate 0.05
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%
C 32,000
time 18
rate 0.045
PV $389,119.7377
Maturity 800,000.00
time 18.00
rate 0.045
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.