Question

Currently, Bruner Inc.'s bonds sell for $1,250. They pay a $120 annual coupon, have a 15-year maturity, and a $1,000 par value, but they can be called in 5 years at $1,050. Assume that no costs other than the call premium would be incurred to call and refund the bonds, and also assume that the yield curve is horizontal, with rates expected to remain at current levels on into the future. What is the difference between this bond's YTM and its YTC? (Subtract the YTC from the YTM.) 2.11% 2.32% 2.55% 2.80% 3.09%

Answer 1

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:

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

Coupon payment: $ 120

time 5 yeaars

rate 0.068070103 (solved with excel)

$120 \times \frac{1-(1+0.0680701028057608)^{-5} }{0.0680701028057608} = PV$

PV $494.5766

$\frac{Maturity}{(1 + rate)^{time} } = PV$  

Maturity: $ 1,050 (call price)

time   5.00

rate  0.068070103

$\frac{1050}{(1 + 0.0680701028057608)^{5} } = PV$  

PV   755.42

PV c $494.5766

PV m  $755.4235

Total $1,250.0002

YTM:

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

Cuopon payment: $ 120

time 15 years

rate 0.089142162 (solved with excel)

$120 \times \frac{1-(1+0.0891421622982136)^{-15} }{0.0891421622982136} = PV$

PV $972.2006

$\frac{Maturity}{(1 + rate)^{time} } = PV$  

Maturity $ 1,000.00

time   15 years

rate  0.089142162 (solved with excel)

$\frac{1000}{(1 + 0.0891421622982136)^{15} } = PV$  

PV   277.80

PV c $972.2006

PV m  $277.7995

Total $1,250.0001