Question

9.

Consider a 30-year bond paying 8.5% coupons per annum, payable semi-annually and which has a face value of $200. Assume that the yield curve is currently flat at 9.5% pa nominal. Based on exact bond pricing, if interest rates decrease by 100 basis points at all maturities, what is the percentage increase in the price of this bond?

Group of answer choices

9.876%

10.907%

12.388%

10.958%

11.810%

Answer 1

Given about a bond,

years to maturity = 30 years

coupon rate = 8.5% paid annually

face value = $200

yield = 9.5%

Annual coupon payment = 8.5% of 200 = $17

Price of the bond can be calculated on financial calculator using following values:

FV = 200

PMT = $17

N = 30

I/Y = 9.5

Compute for PV, we get PV = -180.33

So, the price of the bond at 9.5% yield = $180.33

When yield decrease by 100 basis points, new Yield = 8.5%

So, when yield equals to coupon rate, price of the bond = face value

=> New price = $200

So, percentage change in price = (New price - Old price)/old price = (200-180.33)/180.33 = 10.907%

So option B is correct.