Answer:
a) 500,000 // 466,450 // 536,800 //
b) 35,000 // 37,316 // 32,208
c) 35,000 // 35,000 // 35,000
d) 500,000 // 500,000 // 500,000
Explanation:
We should discount the bond coupon payment and maturity for the given discount rates of 6% 7% and 8%
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C 35,000.00
time 10
rate 0.06
[tex]35000 \times \frac{1-(1+0.06)^{-10} }{0.06} = PV\\[/tex]
PV $257,603.0468
[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]
Maturity 500,000.00
time 10.00
rate 0.06
[tex]\frac{500000}{(1 + 0.06)^{10} } = PV[/tex]
PV 279,197.39
PV c $257,603.0468
PV m $279,197.3885
Total $536,800.4353
interest expense:
536,800 x 0.06 = 32,208
When coupon and market rate are the same 7% face value and issuance is the same.
When market rate is 8%
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C 35,000.00
time 10
rate 0.08
[tex]35000 \times \frac{1-(1+0.08)^{-10} }{0.08} = PV\\[/tex]
PV $234,852.8490
[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]
Maturity 500,000.00
time 10.00
rate 0.08
[tex]\frac{500000}{(1 + 0.08)^{10} } = PV[/tex]
PV 231,596.74
PV c $234,852.8490
PV m $231,596.7440
Total $466,449.5930
interest expense:
466,450 x 0.08 = 37.316
The cash payment are indifirent to the maket rate what the market rate does is change the perception of the market. ower rate increase the price while higher rate decrease the price.
