Answer:
a) 13.11%
b) as the price matches the bond rate it will be 12%
c) 11.31%
Explanation:
We should calcuate usig excel for the rate which makes the present value of the coupon payment and discounted maturity:
A) PV of the coupon payment (PV of an annuity)
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C $1,000 x 12% = 120.000
time 10
rate 0.1311 (finded with excel)
[tex]120 \times \frac{1-(1+0.1311)^{-10} }{0.1311} = PV\\[/tex]
PV $648.2804
PV of the maturity (PV of a lump sum)
[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]
Maturity 1,000.00
time 10.00
rate 0.1311(finded with excel)
[tex]\frac{1000}{(1 + 0.1311)^{10} } = PV[/tex]
PV 291.72
PV c $648.2804
PV m $291.7198
Total $940.0002
For C we do the same with a present value of 1,040 dollars
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C 120.000
time 10
rate 0.113118875
[tex]120 \times \frac{1-(1+0.113118874891792)^{-10} }{0.113118874891792} = PV\\[/tex]
PV $697.5599
[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]
Maturity 1,000.00
time 10.00
rate 0.113118875
[tex]\frac{1000}{(1 + 0.113118874891792)^{10} } = PV[/tex]
PV 342.44
PV c $697.5599
PV m $342.4400
Total $1,040.0000
