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
$
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% |
A bond has a par value of $1,000, a time to maturity of 20 years, and...
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.) Capital gain $
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