Question

You bought a bond one year ago for $1,070.85. This bond pays a semi-annual coupon at the rate of 8.4% and matures 19 years from today. What is the percentage change in price from last year until today if interest rate have fallen and a fair yield for this bond is now 7.2%? (a) + 10.34% (b) + 4.89% (c) - 17.16% (d) + 4.66% (e) - 4.66%

Answer 1

Answer:

(b) + 4.89%

Explanation:

Price of bond is the present value of future cash flows. The coupon payment and cash flow at maturity is discounted to calculate the value of the bond.

Assuming the face value of the bond is $1,000

As per given data

Coupon payment = $1,000 x 8.4% = $84 annually = $42 semiannually

Number of periods = n = 19 years x 2 = 38 periods

Yield to maturity = 7.2% annually = 3.6% semiannually

To calculate Price of the bond use following formula

Price of the Bond = C x [ ( 1 - ( 1 + r )^-n ) / r ] + [ F / ( 1 + r )^n ]

Price of the Bond =$42 x [ ( 1 - ( 1 + 3.6% )^-38 ) / 3.6% ] + [ $1,000 / ( 1 + 3.6% )^38 ]

Price of the Bond = $42 x [ ( 1 - ( 1.036 )^-38 ) / 0.036 ] + [ $1,000 / ( 1.036 )^38 ]

Price of the Bond = $862.38 + $260.81

Price of the Bond = $1,123.19

There is an increase in selling price

Change in price = $1,123.19 - $1,070.85 = 52.34

Percentage change = 52.34 / $1,070.85 = 4.89%