Question

Please show your work.

Suppose the annual coupon rate on TIPS is 4% and the annual inflation rate is 3.5%. An investor purchases a $200,000 (face value) bond on January 1. What is the dollar coupon that will be paid at the end of the first six months (June 30)?

Using the TIPS bond in the previous question, suppose for the next six months the annual inflation rate is 2%. Find the next coupon (on December 31).

Answer 1

a)	Annual Coupon Rate = 4% = 0.04
	Semi Annual Coupon Rate
	= Annual Coupon Rate * 6 Months / 12 Months
	= 0.04*6/12
	= 0.02
	Annual Inflation Rate = 3.5% = 0.035
	Semi Annual Inflation Rate
	= Annual Inflation Rate * 6 Months / 12 Months
	= 0.035*6/12
	= 0.0175
	Face Value Bonds = $200000
	Now,
	Inflation Adjusted Principal as on June 30
	= Face Value of Bonds * (1+Semi Annual Inflation Rate)
	= $200000 * (1 + 0.0175)
	= $200000 * (1.0175)
	= $203500
	Coupon Payment on June 30
	= Inflation Adjusted Principal as on June 30 * Semi Annual Coupon Rate
	= $203500 * 0.02
	= $4070
b)	If Annual Inflation Rate for next 6 months will be 2% i.e. 0.02
	Semi Annual Inflation Rate
	= Annual Inflation Rate * 6 Months / 12 Months
	= 0.02*6/12
	= 0.01
	Inflation Adjusted Principal as on December 31
	= Inflation Adjusted Principal on June 30 * (1+Semi Annual Inflation Rate)
	= $203500 * (1 + 0.01)
	= $203500 * (1.01)
	= $205535
	Coupon Payment on December 31
	= Inflation Adjusted Principal as on December 31 * Semi Annual Coupon Rate
	= $205535 * 0.02
	= $4110.70