Question

Each bond in the last 3 problems had the same structure: 10 year term and a $1000 face value. In problem #7, the required rate of return (YTM) on the bond selling at face value was 10%. In problem #8, the required rate of return (YTM) was increased and you calculated the present value of the bond. In problem #9, you were given the present value of the bond and you calculated the expected rate of return (YTM). Examine the present value of each of these bonds, and their required rates of return (YTM). Explain the relationship between what you see in bond prices (present value versus their yield to maturity (required rate of return).

Required Rate of Return, rd:	10%
Present Value  = PV:	1000

Required Rate of Return, rd:	13%
Present Value  = PV:	837.21

Required Rate of Return (YTM):	7%%
Present Value  = PV:	$   (1,211.00)

Answer 1

We shall check the price once more using a financial calculator:

N	10		N	10		N	10
I/Y	10.0000%		I/Y	13.0000%		I/Y	7.0000%
FV	1,000.00		FV	1,000.00		FV	1,000.00
PMT	$     100.00		PMT	$     100.00		PMT	$     100.00
CPT PV	$ 1,000.00		CPT PV	$     837.21		CPT PV	$ 1,210.71

As we can see that the present value is inversely proportional to the required rate of return. That is when the rate of return is less, present value is high and when the required return is more, the present value is low. At 10%, since required return is equal to the coupon percentage, the bond sells at par.

When the interest falls, the prices rise and vice versa. I shall graph the result using more interest rates for better understanding.