Question

how do u calculate value of a bond

You consider purchasing $1000 face value 7 year annual coupon bond which currently sells for $975.20 at the bond market the annual coupon payments are $70 given that your annual required rate of return to purchase his bond is 8%

a)What is the value of the bond to you a potential investor?

b) What is your expected rate of return should you purchase the barn today and hold it to maturity

c) would u buy the bond

Answer 1

Part A:

Value of Bond = PV of CFs from it.

Year	CF	PVF @8%	Disc CF
1	$      70.00	0.9259	$   64.81
2	$      70.00	0.8573	$   60.01
3	$      70.00	0.7938	$   55.57
4	$      70.00	0.7350	$   51.45
5	$      70.00	0.6806	$   47.64
6	$      70.00	0.6302	$   44.11
7	$      70.00	0.5835	$   40.84
7	$ 1,000.00	0.5835	$ 583.49
Price of Bond			$ 947.94

Part B:

YTM is the rate at which PV of Cash Inflows are equal to Bond price.

Year	CF	PVF @7%	Disc CF	PVF @8%	Disc CF
0	$ -975.20	1.0000	$ -975.20	1.0000	$ -975.20
1	$      70.00	0.9346	$    65.42	0.925926	$    64.81
2	$      70.00	0.8734	$    61.14	0.857339	$    60.01
3	$      70.00	0.8163	$    57.14	0.793832	$    55.57
4	$      70.00	0.7629	$    53.40	0.73503	$    51.45
5	$      70.00	0.7130	$    49.91	0.680583	$    47.64
6	$      70.00	0.6663	$    46.64	0.63017	$    44.11
7	$      70.00	0.6227	$    43.59	0.58349	$    40.84
7	$ 1,000.00	0.6227	$ 622.75	0.58349	$ 583.49
NPV			$    24.80		$   -27.26

YTM = Rate at which least +ve NPV + [ NPV at that Rate / chnage in NPV due to 1% in inc in DIsc Rata ] * 1%

= 7% + [ 24.80 / 52.06 ] * 1%

= 7% + 0.48%

= 7.48%

Part C:

YTM < Required Ret, Hence Bond is not adviced to buy.