Question

Bonds

There is an inverse relationship between bond prices and yields. This inverse relationship will be demonstrated by calculating bond prices to show that interest rates move inversely: if yields rise, then bond prices fall. Bonds will be sold either at a premium or a discount. With this in mind respond to the following question.

You currently own a 30 year Treasury Bond paying a 4% annual coupon rate. The market interest rates for like securities rose to 5%. Would your bond sell for a premium or a discount? Why?

What would the market value of your bond be? Prove your answer by showing your work, the appropriate factors, or the factors that would be used for the fx calculator.

Answer 1

Price of Bond = PV of Cfs from it.

If Coupon rate > required Rate ( YTM), Bond will trade at Premium.

If Coupon rate = required Rate ( YTM), Bond will trade at Par.

If Coupon rate < required Rate ( YTM), Bond will trade at Discount.

Int Given case Coupon rate (4% ) < required Rate ( 5% ), Hence Bond will trade at Discount.

Ex:

Assuming Face Value of Bond is $ 1000.

Particulars	Amount
Coupon Amount	$         40.00
Maturity Value	$    1,000.00
Disc Rate	5.000%
Starting	1
Ending on	30

Year	Cash Flow	PVF/ PVAF @5 %	Disc CF
'1 - 30	$      40.00	15.3725	$    614.90
'30	$ 1,000.00	0.2314	$    231.38
Bond Price			$    846.28

PVAF = Sum [ PVF(r%, n) ]
PVF = 1 / ( 1 + r)^n
Where r is int rate per Anum
Where n is No. of Years

PVAF using Excel:
+PV(Rate,NPER,-1)
Rate = Disc rate
Nper = No. of Periods

Bond price is 846.28 < 1000. Hence trading at discount.