Suppose you purchased a $1,000 face value, 15-year bond one year ago. The bond has a 7.125% (annual) coupon rate - but the bonds pay coupons semiannually. You paid $974.24 for the bond last year. However, yields have increased 1%. What is the price of the bond today?
I guess I'm confused about what the yields increasing one percent changes, but if you could just show me how to set it up that would be great!
It is multiple choice so the answers are below:
A) $991.33
B) $955.78
C) $896.14
D) $912.85
E) $917.28
F) $1,000

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Respuesta :

beritop1089 beritop1089 · Answer 1 · 2019-11-26T21:30:31+01:00

Answer:

C) $896.14

Explanation:

First, find the YTM a year ago by entering the following inputs into your financial calculator;

N= 15*2 = 30 (semi-annual payments)

PV = $974.24

PMT = (7.125%/2)*1000 = $35.625

FV= 1000

then CPT I/Y = 3.706% (semiannual rate)

Initial YTM = 3.706%*2 = 7.4%

Current YTM = 7.412% +1% = 8.4%

Next,

Price today is the current price which is a year later since it was first bought.

Therefore, using your financial calculator, enter the following;

Total duration ;15-1= 14 years remaining to maturity, so

N = 14*2 = 28 (semi-annual payments)

I/Y = 8.4% /2 =4.2%

PMT = $35.625

FV= 1000

then CPT PV= 896.14