Question

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.)

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%

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