Question

 

3. Find the price of a corporate bond maturing in 5 years
that has a 5 percent coupon (annual payments), a $1,000
face value, and an AA rating. A local newspaper’s financial
section reports that the yields on 5‐year bonds are AAA,
6 percent; AA, 7 percent; and A, 8 percent.

4. What is the yield‐to‐maturity of a corporate bond with
a 3‐year maturity, 5 percent coupon (semiannual payments),
and $1,000 face value if the bond sold for $978.30?

Answer 1

Pb 3:

Bond Price = PV of CFs from it.

Year	CF	PVF @7%	Disc CF
1	$      50.00	0.9346	$   46.73
2	$      50.00	0.8734	$   43.67
3	$      50.00	0.8163	$   40.81
4	$      50.00	0.7629	$   38.14
5	$      50.00	0.7130	$   35.65
5	$ 1,000.00	0.7130	$ 712.99
Price of Bond	$ 918.00

Pb 4:

YTM :
YTM is the rate at which PV of Cash inflows are equal to Bond price when the bond is held till maturity.

YTM = [ Rate at which least +ve NPV + [ NPV at that Rate / Change in NPV due to 0.5% inc in disc rate ] * 0.5% ] * 2

Period	CF	PVF @2.5%	Disc CF	PVF @3%	Disc CF
0	$ -978.30	1.0000	$ -978.30	1.0000	$ -978.30
1	$      25.00	0.9756	$    24.39	0.9709	$    24.27
2	$      25.00	0.9518	$    23.80	0.9426	$    23.56
3	$      25.00	0.9286	$    23.21	0.9151	$    22.88
4	$      25.00	0.9060	$    22.65	0.8885	$    22.21
5	$      25.00	0.8839	$    22.10	0.8626	$    21.57
6	$      25.00	0.8623	$    21.56	0.8375	$    20.94
6	$ 1,000.00	0.8623	$ 862.30	0.8375	$ 837.48
NPV	$    21.70		$     -5.39

YTM = [ Rate at which least +ve NPV + [ NPV at that Rate / Change in NPV due to 0.5% inc in disc rate ] * 0.5% ] * 2

= [ 2.5% + [ 21.70 / 27.09 ] * 0.5% ] * 2

= [ 2.5% + [ 0.80 ] * 0.5% ] * 2

= [ 2.5% + [ 0.4% ] ] * 2

= 2.90% * 2

= 5.80%