Answer:
2.11%
YTM 0.089142162
YTC 0.068070103
Difference: 0.021072059 = 0.0211 = 2.11%
Explanation:
To calculate each rate we must solve for a rate at which the future coupon payment and maturity (or call value) equals the market price:
This is solve for excel and goal seek tool
It could also be solve with a financial calculator
YTC:
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
Coupon payment: $ 120
time 5 yeaars
rate 0.068070103 (solved with excel)
[tex]120 \times \frac{1-(1+0.0680701028057608)^{-5} }{0.0680701028057608} = PV\\[/tex]
PV $494.5766
[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]
Maturity: $ 1,050 (call price)
time 5.00
rate 0.068070103
[tex]\frac{1050}{(1 + 0.0680701028057608)^{5} } = PV[/tex]
PV 755.42
PV c $494.5766
PV m $755.4235
Total $1,250.0002
YTM:
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
Cuopon payment: $ 120
time 15 years
rate 0.089142162 (solved with excel)
[tex]120 \times \frac{1-(1+0.0891421622982136)^{-15} }{0.0891421622982136} = PV\\[/tex]
PV $972.2006
[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]
Maturity $ 1,000.00
time 15 years
rate 0.089142162 (solved with excel)
[tex]\frac{1000}{(1 + 0.0891421622982136)^{15} } = PV[/tex]
PV 277.80
PV c $972.2006
PV m $277.7995
Total $1,250.0001
