Question

Calculate the current yield on a $1000 face value bond under the following conditions. Assume bond coupons are paid semiannually. Round the answers to 2 decimal places Coupon Rate Time Until Maturity Current Market Rate Current Yield 15 years

Answer 1

Par/Face value	1000
Annual Coupon rate	0.13
Annual coupon	130
semi-annual coupon	65
Present Value = Future value/[(1+(r/m))^mt]
r is the interest rate that is 10%.
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
r/2	0.05
mt	1	2	3	30
future cash flow	65	65	65	1065
present value	61.9047619	58.9569161	56.14944	246.417
sum of present values	1230.59
Price of the bond	1230.59
Current yield	Annual cash inflow/Price of the bond
Current yield	130/1230.59
Current yield	10.56%

Par/Face value	1000
Annual Coupon rate	0.07
Annual coupon	70
semi-annual coupon	35
Present Value = Future value/[(1+(r/m))^mt]
r is the interest rate that is 12%.
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
r/2	0.06
mt	1	2	3	4	10
future cash flow	35	35	35	35	1035
present value	33.01887	31.14988	29.38667	27.72328	577.9386
sum of present values	816.00
Price of the bond	816
Current yield	Annual cash inflow/Price of the bond
Current yield	70/816
Current yield	8.58%

Par/Face value	1000
Annual Coupon rate	0.09
Annual coupon	90
semi-annual coupon	45
Present Value = Future value/[(1+(r/m))^mt]
r is the interest rate that is 6%.
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
r/2	0.03
mt	1	2	3	4	50
future cash flow	45	45	45	45	1045
present value	43.6893204	42.41682	41.18137	39.98192	238.3719
sum of present values	1385.95
Price of the bond	1385.95
Current yield	Annual cash inflow/Price of the bond
Current yield	90/1385.95
Current yield	6.49%

Par/Face value	1000
Annual Coupon rate	0.14
Annual coupon	140
semi-annual coupon	70
Present Value = Future value/[(1+(r/m))^mt]
r is the interest rate that is 9%.
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
r/2	0.045
mt	1	2	3	4	60
future cash flow	70	70	70	70	1070
present value	66.98564593	64.1011	61.34076	58.69929	76.27924
sum of present values	1515.95
Price of the bond	1515.95
Current yield	Annual cash inflow/Price of the bond
Current yield	140/1515.95
Current yield	9.24%

Par/Face value	1000
Annual Coupon rate	0.05
Annual coupon	50
semi-annual coupon	25
Present Value = Future value/[(1+(r/m))^mt]
r is the interest rate that is 8%.
m is the compounding period that is 2
mt is the time period.
r/2	0.04
mt	1	2	3	4	12
future cash flow	25	25	25	25	1025
present value	24.03846	23.11391	22.22491	21.3701	640.212
sum of present values	859.22
Price of the bond	859.22
Current yield	Annual cash inflow/Price of the bond
Current yield	50/859.22
Current yield	5.82%

COUPON RATE (%)	TIME UNTIL MATURITY	CURRENT MARKET RATE (%)	CURRENT YIELD
13	15	10	10.56%
7	5	12	8.58%
9	25	6	6.49%
14	30	9	9.24%
5	6	8	5.82%