Question

Please solve the below showing all work (no excel, no financial cal.). Thanks.

0. An asset is expected to make single cash flow payment in 20 years. Calculate its %change in price from a 4% to a 5% yield.

1. A 20-year annuity pays 5 annually. What is its price at a 4% yield? At 5%? Calculate the %change in price between the two market situations.

2. Consider a 20-year bond, annual coupon=5. What is its price at a 4% yield? 5%? Calculate the %change in price between the two market situations. How does your answer relate to those in Question 0 and Question 1?

Answer 1

The solution is provided below:

An asset is expected to make single cash flow payment of 100 in 20 years. Calculate its %change in price from a 4% to a 5% yield.
=(100/1.05^20)/(100/1.04^20)-1=-17.419%

A 20-year annuity pays 5 annually. What is its price at a 4% yield?
=5/4%*(1-1/1.04^20)=67.95163172

At 5%?
=5/5%*(1-1/1.05^20)=62.31105171

Calculate the %change in price between the two market situations.
=(5/5%*(1-1/1.05^20))/(5/4%*(1-1/1.04^20))-1=-8.301%

Consider a 20-year bond, annual coupon=5. What is its price at a 4% yield?
=5/4%*(1-1/1.04^20)+100/1.04^20=113.5903263

At 5%?
=5/5%*(1-1/1.05^20)+100/1.05^20=100

Calculate the %change in price between the two market situations.
=100/113.5903263-1
=-11.964%

How does your answer relate to those in Question 0 and Question 1?