Question

The following is a list of prices for zero-coupon bonds with different maturities but same par value of $1,000: the 1-year zero bond sells at $1000, the 2-year zero bond sells at $862.57, the 3-year zero bond sells at $788.66, and the 4-year zero bond sells at $711.00. You have purchased a 4-year maturity bond with a 9% coupon rate paid annually. The bond has a par value of $1,000. What would be the price of the bond one year from now if the implied forward rates stay the same?

Answer 1

First we calculate forward rates by the formula

	1000	862.57	788.66	711
Forward Rate((Initial/Final) - 1)		0.1593262	0.093716	0.109226
		15.93%	9.37%	10.92%

Now, we convert these forward rates to present value factor of 1$.

Year	Forward Rates	Present Value Factor
0	-	1
1	15.93%	0.86257
2	9.37%	0.78866
3	10.92%	0.711

To Calculate the price of the bond we bring cash flow from each year to the present value and we discount future cash flows with the rates calculated above.

Cash Flows	Present Value Factor	Present Value of CF
90	1	90
90	0.86257	77.6313
90	0.78866	70.9794
1090	0.711	774.99
	Price of the bond at the beginning	1013.6007

This price is in the beginning. However, the question is asking the price for 1 year from now.

I am assuming two point of views, you can choose answer from any 1 and if you have doubt you can ask me in the comment section.

Case 1 : Price of the bond one year from now for the person who purchased in year 0 will be sum of year 1, year 2, year 3 cash flows discounted to PV i.e 77.6313 + 70.9794 + 774.99 = 923.60

Case 2 : If that person who purchases the bond in year 0 is selling in the next year, then the price will be new cause present value be changed to future values

	1000	862.57	788.66	711
Forward Rate((Initial/Final) - 1)		1	0.093716	0.109226
			9.37	10.92

Cash Flows	Present Value Factor	Present Value of CF
90		0
90	1	90
90	0.914314201	82.28827805
1090	0.824280928	898.4662114
	Price of the bond after 1 year	1070.754489

Again if you have any doubt, please ask me in the comment section.