Question

The table provides the prices of 5 zero-coupon bonds:

Maturity	Price per 100 of par
1	96.9672
2	90.3364
3	80.7259
4	76.5899
5	64.0297

Determine the value of the annual effective forward rate applicable from time 2 to time 3.

A. 12.3%

B. 11.9%

C. 23.7%

D. 19.2%

E. 17.8%

Answer 1

YTM is the Rate at which PV of Cash Inflows are equal to PV of Cash Outflows.

YTM of Year 3 Bond:

Year	CF	PVF @7%	Disc CF	PVF @8%	Disc CF
0	$ -80.73	1.0000	$ -80.73	1.0000	$ -80.73
3	$ 100.00	0.8163	$   81.63	0.7938	$   79.38
NPV			$      0.90		$    -1.34

YTM = Rate at which least +ve NPV + [ NPV at that rate / Change in NPV due to 1% inc in disc rate] * 1%

= 7% + [ 0.9 / 2.25 ] * 1 %

= 7 % + 0.4%

= 7.4%

YTM of Year 2 Bond:

Year	CF	PVF @5%	Disc CF	PVF @6%	Disc CF
0	$ -90.34	1.0000	$ -90.34	1.0000	$ -90.34
3	$ 100.00	0.9070	$   90.70	0.8900	$   89.00
NPV			$      0.37		$    -1.34

YTM = Rate at which least +ve NPV + [ NPV at that rate / Change in NPV due to 1% inc in disc rate] * 1%

= 5% + [ 0.37 / 1.70 ] * 1 %

= 5 % + 0.22%

= 5.22%

1 Year Fwd Rate 2 to 3 Years = [ (1+YTM of 3year Bond)^3 / ( 1+YTM of 2Year Bond)^2 ] - 1

= [ ( 1 + 0.074)^3 / ( 1 + 0.0522)^2 ] - 1

= [ (1.074^3 ) / ( 1.0522^2) ] - 1

= [ 1.2388 / 1.1071 ] - 1

= 1.1190 - 1

= 0.1190 i.e 11.90%