Question

One year ago, Alpha Supply issued 15-year bonds at par. The bonds have a coupon rate of 6.5 percent, paid semiannually, and a face value of $1,000. Today, the market yield on these bonds is 7.2 percent. What is the percentage change in the bond price over the past year?A) 5.94 percentB) 5.38 percentC) -6.11 percentD) -5.87 percentE) The bond price did not change

Answer 1

Answer:

option (C) - 6.11%

Explanation:

Data provided :

Coupon rate one year ago = 6.5% = 0.065

Semiannual coupon rate = $\frac{0.065}{2}$ = 0.0325

Face value = $1,000

Present market yield = 7.2% = 0.072

Semiannual Present market yield, r = $\frac{0.072}{2}$ = 0.036

Now,

With semiannual coupon rate bond price one year ago, C

= 0.0325 × $1,000

= $32.5

Total period in 15 years = 15 year - 1 year = 14 year

or

n = 14 × 2 = 28 semiannual periods

Therefore,

The present value = $C\times[\frac{(1-(1+r)^{-n})}{r}]+FV(1+r)^{-n}$

= $\ 32.5\times[\frac{(1-(1+0.036)^{-28})}{0.036}]+\ 1,000\times(1+0.036)^{-28}$

or

= $32.5 × 17.4591 + $1,000 × 0.37147

= $567.42 + $371.47

= $938.89

Hence,

The percent change in bond price = $\frac{\textup{Final price - Initial price}}{\textup{Initial price}}\times100\%$

= $\frac{\textup{938.89-1,000}}{\textup{1,000}}$

= - 6.11%

therefore,

the correct answer is option (C) - 6.11%