Question

Consider a 10 year bond with face value $1,000 that pays a 6.8% coupon semi-annually and has a yield-to-maturity of 8.4%. What is the approximate percentage change in the price of bond if interest rates in the economy are expected to decrease by 0.60% per year? Submit your answer as a percentage and round to two decimal places. (Hint: What is the expected price of the bond before and after the change in interest rates?)

To answer the question:

(1) Describe and interpret the assumptions related to the problem.

(2) Apply the appropriate mathematical model to solve the problem.

(3) Calculate the correct solution to the problem.

Answer 1

(1) The problem assumes that the face value of the bond is $1000. The bond will pay a semi-annual coupon of 6.8% i.e., coupon or interest amount of $68 is assumed to paid every year. It also assumes that investors currently required to decrease by 0.60% on investments with similar risk characteristics. The use of bond valuation concept is appropriate to calculate the true value of these bonds. The accuracy of the solution depends on the correctness of the assumptions on face value, coupon payments and required rate of return assumption.

(2) The use of bond valuation concept which suggests that the true value of a bondis the present value of its future coupon and face value discounted at investorsrequired rate of return is appropriate to calculate the true value of these bonds.We are required to compute the change in price which represents the true valueof the bond, new price-old price/old price

(3)

Bond 1 Rate = 8.4%/2; N = 10*2; PMT = $68/2; FV = $1000; Computed PV =$893.18

Bond 2 Rate =(8.4% - 0.6%) 7.8%/2; N = 10*2; PMT = $68/2; FV = $1000; Computed PV =$931.44

Percentage change 893.18/931.44 = .9589, 1-.9589 = .0411 = 4.11%

Calculate valuation of a bond concept which can be solves by using below the PV function formula in excel

Syntax

=PV (rate, nper, pmt, [fv], [type])

Arguments

• rate - The interest rate per period.
• nper - The total number of payment periods.
• pmt - The payment made each period.
• fv - [optional] A cash balance you want to attain after the last payment is made. If omitted, assumed to be zero.
• type - [optional] When payments are due. 0 = end of period, 1 = beginning of period. Default is 0.

Face Value = $1,000 Annual Coupon Rate = 6.80% Semiannual Coupon Rate = 3.40% Semiannual Coupon = 3.40% * $1,000 Semiannual Coupon = $34