Question

Yield to Maturity and Required Returns

The Brownstone Corporation's bonds have 5 years remaining to maturity. Interest is paid annually, the bonds have a $1,000 par value, and the coupon interest rate is 9%.

1. What is the yield to maturity at a current market price of $832? Round your answer to two decimal places.
   %
   
2. What is the yield to maturity at a current market price of $1,093? Round your answer to two decimal places.
   %

Answer 1

		13.00%						14.00%
Year	Cash Flow	PV fatctor = 1/ (1+r)^t	PV					PV fatctor = 1/ (1+r)^t	PV
0	(832)	1.000	(832.00)					1.000	(832.00)
1	90	0.885	79.65					0.877	78.95
2	90	0.783	70.48					0.769	69.25
3	90	0.693	62.37					0.675	60.75
4	90	0.613	55.20					0.592	53.29
5	90	0.543	48.85					0.519	46.74
5	1,000	0.543	542.76					0.519	519.37
			27.31						(3.65)
NPV @ 0.13	27.31
NPV @ 0.14	(3.65)
Difference in both	30.96
YTM	=Lower rate + Difference in rates*(NPV at lower rate)/(Lower rate NPV-Higher rate NPV)
	'=0.13+ (0.14-0.13)*(27.310/(27.310+3.6540)
YTM	0.1388
YTM	13.88%

		6.00%						7.00%
Year	Cash Flow	PV fatctor = 1/ (1+r)^t	PV					PV fatctor = 1/ (1+r)^t	PV
0	(1,093)	1.000	(1,093.00)					1.000	(1,093.00)
1	90	0.943	84.91					0.935	84.11
2	90	0.890	80.10					0.873	78.61
3	90	0.840	75.57					0.816	73.47
4	90	0.792	71.29					0.763	68.66
5	90	0.747	67.25					0.713	64.17
5	1,000	0.747	747.26					0.713	712.99
			33.37						(11.00)
NPV @ 0.06	33.37
NPV @ 0.07	(11.00)
Difference in both	44.37
YTM	=Lower rate + Difference in rates*(NPV at lower rate)/(Lower rate NPV-Higher rate NPV)
	'=0.06+ (0.07-0.06)*(33.370/(33.370+10.996)
YTM	0.0675
YTM	6.75%