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On Feb 1, 2019, the price of a T-bill maturing on July 31, 2019 is $96.98,...

On Feb 1, 2019, the price of a T-bill maturing on July 31, 2019 is $96.98, the price of a T-bill with maturity on Jan 31, 2020 is $97.11, and the price of a stripe with maturity on July 31 of 2020 is $97.76. A semiannual coupon treasury note that has the coupon rate 4.75% and will mature on July 31, 2020. What is the price of this T-note?

Solutions

Expert Solution

A B C D E F G H I J
2
3 Price of bond with face value F, years to maturity of n and yield of y can be written as follows:
4 Price of bond, P = F/ (1+y)n
5
6 For semi-annual bond,
7 Price of bond, P = F/ (1+y/2)2n
8
9 Using the above formula price of the bond P can be calculated as follows:
10
11 Year to maturity (n) Price Face Value Yield
12 0.5 $96.98 $100 6.23% =2*(((E12/D12)^(1/(2*C12)))-1)
13 1 $97.11 $100 2.95%
14 1.5 $97.76 $100 1.52%
15
16 Calculation of price of the coupon bond:
17
18 Face Value $1,000
19 Coupond rate 4.75%
20
21 Semi-annual coupon $47.50
22
23 Price of the T-note will be the present value of the future cash flows.
24
25 Cash Flow of the bond will be as follows:
26 Semi-annual period 0 1 2 3
27 Cash flow of the bond $47.50 $47.50 $1,047.50
28 Semi-annual yield 3.11% 1.48% 0.76%
29 Present Value of cash flows $46.07 $46.13 $1,024.04 =G27/((1+G28)^G26)
30 Price of the Bond $1,116.23 =SUM(E29:G29)
31
32 Hence the price of the bill is $1,116.23
33

Formula sheet

A B C D E F G H I J
2
3 Price of bond with face value F, years to maturity of n and yield of y can be written as follows:
4 Price of bond, P = F/ (1+y)n
5
6 For semi-annual bond,
7 Price of bond, P = F/ (1+y/2)2n
8
9 Using the above formula price of the bond P can be calculated as follows:
10
11 Year to maturity (n) Price Face Value Yield
12 0.5 96.98 100 =2*(((E12/D12)^(1/(2*C12)))-1) =getformula(F12)
13 1 97.11 100 =2*(((E13/D13)^(1/(2*C13)))-1)
14 1.5 97.76 100 =2*(((E14/D14)^(1/(2*C14)))-1)
15
16 Calculation of price of the coupon bond:
17
18 Face Value 1000
19 Coupond rate 0.0475
20
21 Semi-annual coupon =D18*D19
22
23 Price of the T-note will be the present value of the future cash flows.
24
25 Cash Flow of the bond will be as follows:
26 Semi-annual period 0 1 2 3
27 Cash flow of the bond =$D$21 =$D$21 =$D$21+D18
28 Semi-annual yield =F12/2 =F13/2 =F14/2
29 Present Value of cash flows =E27/((1+E28)^E26) =F27/((1+F28)^F26) =G27/((1+G28)^G26) =getformula(G29)
30 Price of the Bond =SUM(E29:G29) =getformula(D30)
31
32 Hence the price of the bill is =D30
33

jeff jeffy answered 1 year ago
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