Question

Calvin and Andre both have bonds they bought at par value and pay 7% coupons. Calvin’s bond has ten years to maturity and Andre’s bond has 20 years to maturity. If interest rates suddenly rise to 9%, what is the approximate change in value of Calvin’s bond?

Multiple Choice

• 13.01%

• 14.95%

• -13.01%

• 19.79%

• -18.40%

• 14.21%

• -14.95%

Answer 1

Let the face value of the bond be 100
Coupon Rate = 7%
Coupon Amount = Face Value * Coupon Rate = 7
No of years to maturity = 10

For a bond trading at par, interest rate will be equal to the coupon rate of the bond.
Therefore current interest rate = 7%

Interest rate rises to 9% :
Face Value = 100
Coupon Amount = 7
Interest Rate = 9%
No of Years = 10

Calculation of bond price :

Value of Bond = Present Value of Coupons + PV of Principal Amount

                            = [PVAF (9%,10) * 7] + [PVIF (9%,10) * 100]

                           = (6.4177 * 7) + (0.4224 * 100)

                           = 44.92 + 42.24

                           = 87.16

Present Value Factor have been calculated as = (1/1+r)n

Where

r= Required rate of Return (Discount rate)

n= No of Periods

PVAF (9%,20) is calculated by adding the PV Factor of 9% for 20 years.

Change in bond Price = Bond price when int rate increase to 9% - Current bond price
                                       = 87.16 – 100
                                          = -12.84

% Change In bond Price = Change in bond Price/Current bond price * 100
                                           = -12.84/100 * 100
                                                = -12.84%

Since option c) i.e -13.01% is closest. Option c) is the answer.