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Bond Equivalent Yield Financial Markets
Accountancy (University of Northern Philippines)
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BOND EQUIVALENT YIELD, DISCOUNT YIELD AND EFFECTIVE ANNUAL RETURN
Assignment
1. What is the discount yield, bond equivalent yield, and effective annual return on a 1 million
Treasury bill that currently sells at 99.375 percent of its face value and is 65 days from
maturity?
Pf = Php1,000,000
P0 = Php1,000,000 (0.99375) = Php993,750 n
= 65
Discount yield
Id= (1,000,000 - 993,750) x 360
1,000,000
65
= 3.4615%
Bond equivalent yield
Ibe = (1,000,000 - 993,750) x 365
993,750
65
= 3.5317%
Effective annual return
EAR = [ 1 + 3.5317% ]365/65 - 1
365/65
= 3.5833%
2. What is the discount yield, bond equivalent yield, and effective annual return on a 5 million
Treasury bill that currently sells at 98.625 percent of its face value and is 136 days from
maturity?
Pf = Php5,000,000
P0 = Php5,000,000 (0.98625) = Php4,931,250 n
= 136
Discount yield
Id= (5,000,000 – 4,931,250) x 360
5,000,000
136
= 3.6397%
Bond equivalent yield
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Ibe = (5,000,000 – 4,931,250) x 365
4,931,250
136
= 3.7417%
Effective annual return
EAR = [ 1 + 3.7417% ]365/136 - 1
365/136
= 3.7858%
3. Calculate the bond equivalent yield and effective annual return on a negotiable CD that is
115 days from maturity and has a quoted nominal yield of 6.56 percent.
Bond Equivalent Yield
= Id x (365/360)
= 6.56% x (365/360)
= 6.6511%
Effective Annual Rate
= [ 1 + 6.6511% ]365/115 - 1
365/115
= 6.8038%
4. Calculate the bond equivalent yield and effective annual return on fed funds that are 3
days from maturity and have a quotes yield of 0.25 percent.
Bond equivalent yield
= Id x (365/360)
= 0.25% x (365/360)
= 0.2535%
Effective Annual Rate
= [1 + 0.2535% ]365/25 - 1
365/25
= 0.2538%
5. You would like to purchase a Treasury bill that has a 10,000 face value and is 68 days from
maturity. The current price of the Treasury bill is 9,875. Calculate the discount yield on
this Treasury bill.
Discount yield
Id= (10,000 – 9,875) x 360
10,000
68
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= 6.6176%
6. Suppose you purchase a T-bill that is 125 days from maturity from 9,765. The T
a face value of 10,000. a. Calculate the T-bill's quoted discount yield.
bill has
a. Calculate the T-bill's quoted discount yield.
Discount yield
Id= (10,000 – 9,765) x 360
10,000
125
= 6.768%
b. Calculate T-bill's bond equivalent yield Bond
equivalent yield
Ibe = (10,000 – 9,765) x 365
9,765
125
= 7.0271%
7. You can purchase a T-bill that is 95 days from maturity from 9,965. The T-bill has a face
value of 10,000.
a. Calculate the T-bill's quoted yield
Discount yield
Id = (10,000 – 9,965) x 360
10,000
95
= 1.3263%
b. Calculate the T-bill's bond equivalent yield
Bond equivalent yield
Ibe = (10,000 – 9,965) x 365
9,965
95
= 1.3495%
c. Calculate the T-bill's EAR
Effective Annual Rate
= 1 + 1.3495% ]365/95 - 1
365/95
= 1.3562%
8. A T-bill that is 225 days from maturity is selling for 98,850 the T-bill has a face value of
100,000.
a. Calculate the discount yield, bond equivalent yield and EAR on the T-bill,
Discount yield
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Id = (100,000 – 98,850) x 360
100,000
225
= 1.84%
Bond equivalent yield
Ibe = (100,000 – 98,850) x 360
98,850
225
= 1.8872%
Effective Annual Rate
= 1 + 1.8872% ]365/225 - 1
365/225
= 1.8941%
b. Calculate the discount yield, bond equivalent yield and EAR on the T-bill if it matures
in 300 days.
Discount yield
Id = (100,000 – 98,850) x 360
100,000
300
= 1.38%
Bond equivalent yield
Ibe = (100,000 – 98,850) x 365
98,850
300
= 1.4154%
Effective Annual Rate
= 1 + 1.4154% ]365/225 - 1
365/225
= 1.4172%
9. If the overnight fed funds rate is quoted as 0.75 percent, what is the bond equivalent rate
calculate the bond equivalent rate on fed funds if the quoted rate is 1.00 percent.
a. Bond equivalent yield
= Id x (365/360)
= 0.75% x (365/360)
= 0.7604%
b. Bond equivalent yield
= Id x (365/360)
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= 1% x (365/360)
= 1.0139%
10. The overnight fed funds rate on May 20,2016 was 0.37 percent. Compute the bond
equivalent rate and the equivalent annual return on the fed funds as of May 20, 2016.
Bond equivalent yield
= Id x (365/360)
= 0.37% x (365/360)
= 0.3751%
Effective Annual Rate
= 1 + 0.3751% ]365/1 - 1
365/1
= 0.3758%
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