Question

a. Ten years ago today, Excel Corp issued a regular coupon bond that had original maturity of 15 years. The bond pays interest semiannually and had a coupon rate of 5%. The bond was originally issued at par. Since the bond was issued, market interest rates have generally moved down such that today the Yield to Maturity (YTM) on the bond is 4%. Estimate the price of the bond today. (5 points)

Answer 1

Answer:

Total $1,271.0564

Explanation:

We have bond of 10 years ago, so the bond is left with 5 years of life

we need to calculate the present value ofthe cuopon payment:

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

C 50 (1,000 x 5%)

time 10 (5 years 2 payment a year)

rate 0.02 (4% annual divide by 2 to get semiannually)

$50 \times \frac{1-(1+0.02)^{-10} }{0.02} = PV$

PV $449.1293

and the present value of the principal

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

Maturity 1000

time 5

rate 0.04

$\frac{1000}{(1 + 0.04)^{5} } = PV$

PV  $821.9271

We add both to get the present value ofthe bond

PV c $449.1293

PV m  $821.9271

Total $1,271.0564