Question

You have been offered a 6% 5 year Medical Lake water bond priced at $1150 and a 8% 7 year Cheney sewer bond priced at $1200.

a. Which bond would you purchase if the current interest rate is 3%?

b. Which bond has the greatest interest rate risk when the rate increases to 6%?

Answer 1

First we need to find out the intrinsic value of both the stocks at the current interest rate.

This can be found out by solving the following equations:

Here r = current interest rate and n = maturity

Par value of both the bonds = 1000

So the intrinsic value of the 5 year bond is:

Year	CF	Discount Factor		Discounted CF
0	$              -	1/(1+0.03)^0=	1	1*0=	$              -
1	$       60.00	1/(1+0.03)^1=	0.970873786	0.970873786407767*60=	$       58.25
2	$       60.00	1/(1+0.03)^2=	0.942595909	0.942595909133754*60=	$       56.56
3	$       60.00	1/(1+0.03)^3=	0.915141659	0.91514165935316*60=	$       54.91
4	$       60.00	1/(1+0.03)^4=	0.888487048	0.888487047915689*60=	$       53.31
5	$       60.00	1/(1+0.03)^5=	0.862608784	0.862608784384164*60=	$       51.76
5	$ 1,000.00	1/(1+0.03)^5=	0.862608784	0.862608784384164*1000=	$     862.61
				intrinsic value	$ 1,137.39

So the intrinsic value of the 7 year bond is:

Year	CF	Discount Factor		Discounted CF
0	$	1/(1+0.03)^0=	1	1*0=	$              -
1	$       80.00	1/(1+0.03)^1=	0.970873786	0.970873786407767*80=	$       77.67
2	$       80.00	1/(1+0.03)^2=	0.942595909	0.942595909133754*80=	$       75.41
3	$       80.00	1/(1+0.03)^3=	0.915141659	0.91514165935316*80=	$       73.21
4	$       80.00	1/(1+0.03)^4=	0.888487048	0.888487047915689*80=	$       71.08
5	$       80.00	1/(1+0.03)^5=	0.862608784	0.862608784384164*80=	$       69.01
6	$       80.00	1/(1+0.03)^6=	0.837484257	0.837484256683654*80=	$       67.00
7	$       80.00	1/(1+0.03)^7=	0.813091511	0.813091511343354*80=	$       65.05
7	$ 1,000.00	1/(1+0.03)^7=	0.813091511	0.813091511343354*1000=	$     813.09
				intrinsic Value =	$ 1,311.51

So the 5 year bond is overpriced at 1150 as its intrinsic value is 1137 while the 7 year bond is under priced at 1200 as the intrinsic value is 1311.51 so it is worth buying the 7 year bond and not the 5 year bond if the interest rate is 3%

At 6% interest rate the 5 year bond has less interest rate risk due to lower coupon and smaller time to maturity while bond with 7 year has higher interest rate risk