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Homework answers / question archive / Eliza buys a 180-day bank bill for $98,676 and sells it with 40 days remaining for $98,245

Eliza buys a 180-day bank bill for $98,676 and sells it with 40 days remaining for $98,245

Finance

  1. Eliza buys a 180-day bank bill for $98,676 and sells it with 40 days remaining for $98,245. What has her annualized holding period return been? A. -1.1496 O B.-0.4496 OC.-2.1596 OD.-3.99%
    Jim buys a 120-day bill with a face value of $1,000 000 at a yield of 0.88% pa, when it is initially issued. What is his buying price? A. $997,838 B. $997,115 C. $998,802 D. $998,383

  2. Sandy buys a 10-year commonwealth year bond with a face value of $100 and a coupon of 6% pa (paid semi-annually) at a yield of 4% pa, when it is initially issued. What is the buying price? A. $118.44 OB. $116.22 O C. $100 OD. $116.35

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1 

(1) Option (A) -1.14%

Purchase Price of 180-day Bank Bill = $ 98,676
Sale Proceeds of the bond before 40 Days to Maturity = $ 98,245
Holding Period = 180 - 40 days = 140 days
Holding Period Return = ($ 98,245 - $ 98,676) / $ 98,676
Holding Period Return = - $ 431 / $ 98,676
Holding Period Return = -0.44% (for 140 Days)
 
Annualised Holding Period Return = -0.44%/140 * 365 days
Annualised Holding Period Return = -1.14%

(2) Option (B)

Let 'P' be the Issue Price of 120-day Bill.
Face Value = $1,000,000
Yield = 0.88%
Then, P + (P * 0.88% * 120/365) = $ 1,000,000
Then, P(1 + 0.0029) = $ 1,000,000
P * 1.0029 = $ 1,000,000
P = $ 1,000,000 / 1.0029
P = $ 997,115

 

2 

Periods Coupon @ 3% Discount factor @ 2% Present Value
1 $3.00 0.9804 $2.94
2 $3.00 0.9612 $2.88
3 $3.00 0.9423 $2.83
4 $3.00 0.9238 $2.77
5 $3.00 0.9057 $2.72
6 $3.00 0.8880 $2.66
7 $3.00 0.8706 $2.61
8 $3.00 0.8535 $2.56
9 $3.00 0.8368 $2.51
10 $3.00 0.8203 $2.46
11 $3.00 0.8043 $2.41
12 $3.00 0.7885 $2.37
13 $3.00 0.7730 $2.32
14 $3.00 0.7579 $2.27
15 $3.00 0.7430 $2.23
16 $3.00 0.7284 $2.19
17 $3.00 0.7142 $2.14
18 $3.00 0.7002 $2.10
19 $3.00 0.6864 $2.06
20 $3.00 0.6730 $2.02
20 $100.00 0.6730 $67.30
      $116.35
Notes:          
1) As the coupon payments are made semi annually for 10 years, there are 20 payments during
the bond period.        
2) The bond is assumed to be redeemed at par upon maturity at the end of 10th year/20th period.
3) As the coupon rate is 6% per annum, semiannually it becomes 3%.  
4) As the yield is 4% per annum, semi annually it becomes 2%.

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