Question

A bond has a par value of $1,000, a time to maturity of 20 years, and a coupon rate of 7.40% with interest paid annually. If the current market price is $740, what will be the approximate capital gain of this bond over the next year if its yield to maturity remains unchanged? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

What will be the price of the bond next year if its YTM remains unchanged?

$

Capital gain            

$

Answer 1

First,we need to find the YTM , with the following input values :

Pmt.=Annual coupon amt.= $ 1000*7.40%= $ 74

r= YTM or effective annual rate of interest to be found out----?

n=No.of years to maturity,ie. 20

Face Value, FV= $ 1000

Plugging in the above values, in the Formula for price of the bond,ie.

Price=PV of futute cash flows from holding the bond(PV s of Coupons +Face value )=(Pmt.*(1-(1+r)^-n)+(FV/(1+r)^n)

& plugging in the values,

740=((1000*7.40%)*(1-(1+r)^-20)/r)+(1000/(1+r)^20)

Solving for r, in an online equation solver,

we get the annual r,ie. YTM as

10.57%

If the above YTM remains unchanged,

Price of the bond next year,ie. For the remaning 20-1= 19 yrs. Is

Price=((1000*7.40%)*(1-(1+10.57%)^-19)/10.57%)+(1000/(1+10.57%)^19)

744.54

ANSWER:

Price of the bond next year if its YTM remains unchanged= $ 744.54

Price after 1 yr= 744.54

Current price   = 740

Capital gain=(744.54-740)= 4.54

Capital gain % = 4.54/740=

0.61%

ANSWER:

Capital Gain= $ 4.54

CG%= 0.61%