Question

1) New Markets has $1,000 face value bonds outstanding that pay interest semiannually, mature in 20 years, and have a 5.8 percent coupon. The current price is quoted at 103.25. What is the yield to maturity?

2)   American Hat has $1,000 face value bonds outstanding with a market price of $1,150. The bonds pay interest semiannually, mature in 8 years, and have a yield to maturity of 5.98 percent. What is the current yield?

Please explain with simple formula

Answer 1

1)	Par/Face value	1000
	Annual Coupon rate	0.058
	Annual coupon	58
	semi-annual coupon	29
	Present Value = Future value/[(1+(r/m))^mt]
	r is the interest rate.
	m is the compounding period that is 2
	mt is the time period.
	price of the bond = sum of present values of future cash flows
	price of the bond = 1032.5
	Use excel to find r
	r/2	0.02765	r	0.0553
	mt	1	2	3	4	5	6	7	8	9	10
	future cash flow	29	29	29	29	29	29	29	29	29	29
	present value	28.21972	27.46044	26.72159	26.00262	25.30299	24.62219	23.9597	23.31504	22.68773	22.07729
	sum of present values	1032
	The yield to maturity is 5.53%.

2)	Par/Face value	1000
	Use excel to find the coupon payment
	Annual Coupon rate	0.0837
	Annual coupon	83.7
	semi-annual coupon	41.85
	Present Value = Future value/[(1+(r/m))^mt]
	r is the interest rate that is 5.98%.
	m is the compounding period that is 2
	mt is the time period.
	price of the bond = sum of present values of future cash flows
	price of the bond = 1150
	Use excel to find the coupon payment
	r/2	0.0299
	mt	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16
	future cash flow	41.85	41.85	41.85	41.85	41.85	41.85	41.85	41.85	41.85	41.85	41.85	41.85	41.85	41.85	41.85	1041.85
	present value	40.63501	39.4553	38.30984	37.19763	36.11771	35.06914	34.05101	33.06245	32.10258	31.17058	30.26564	29.38697	28.53381	27.70541	26.90107	650.2558
	sum of present values	0
	Current yield = Annual cash inflow/Market price
	Annual cash inflow	41.85
	Market price	1150
	Current yield	41.85/1150
	Current yield	0.036391
	The current yield is 3.64%.