Question

Instructions:

You are required to use a financial calculator or spreadsheet (Excel) to solve related to the risk and return, stocks and bonds valuation. You are required to show the following 3 steps for each problem (sample questions and solutions are provided for guidance):

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

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

(iii) Calculate the correct solution to the problem.

PROBLEM:

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?)

Answer 1

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 the bond if interest rates in the economy are expected to decrease by 0.60% per year?

Solution: Given that,

n = time period = 10 years, FV = Face value = $1000, Coupon rate = p

Semi Annually, YTM = 8.4% = 0.084

The price of bond is computed using the formula as below:

Case 1: Coupon rate = p = 6.8%/2 = 0.068/2 = 0.034

Coupon value = 0.034 x 1000 = 34

Bond Value = (C/R) x {1-[1/(1+R)^T] } + (FV/(1+R)^T

= 34/(0.042) x {1-[1/(1+0.042)²⁰]} + (1000/(1+0.042)²⁰

= (809.524 x 0.5608) + 439.1831

= 893.1641

Case 2: Coupon rate = p = 6.2% / 2 = 0.062/2 = 0.031

Coupon value = 0.031 x 1000 = 31

Bond Value = (C/R) x {1-[1/(1+R)^T] } + (FV/(1+R)^T

= (31 / 0.042) x {1-[1/(1+0.042)²⁰] } + (1000/(1+0.042)²⁰

= (738.0952 x 0.5608) + (439.1831)

= $853.1069

Change in Bond price = 893.1641 - 853.1069 = $40.06 (approx)