Question

In late September 2016, the US Treasury issued three T-Bills, and they had issued a one-year T-Bill on September 15, 2016:

	4-Week	13-Week	26-Week	52-Week
Issue Date	9/29/2016	9/29/2016	9/29/2016	9/15/2016
Maturity Date	10/27/2016	12/29/2016	3/30/2017	9/14/2017
Face Value per $100	100	100	100	100
Price per $100	99.987556	99.936806	99.787667	99.363000

1. Calculate the bank discount rate for each security using the formula given in the chapter (=(FV – Price)/FV * 360/M, where M is the number of days until maturity) and using the DISC function.
2. Calculate the bond equivalent yield for each security using the formula given in the chapter (=(FV – Price)/Price * 365/M, where M is the number of days until maturity) and using the YieldDisc function.

a) What is the Bank Discount Rate (rounded to 4 decimals) for the 52-week security?

b) Using the DISC formula, do you get the same answer as the Bank Discount Rate?

c) What is the Bond Equivalent Yield for the 26-week security?

d) Using the YieldDisc function, do you get the same answer as the Bond Equivalent Yield?

Thank you in advance

Answer 1

(A)

Calculation of Bank Discount Rate for each security (using Formula given) :

	4 Week	13 Week	26 Week	52 Week
FV	100	100	100	100
Price	99.987556	99.936806	99.787667	99.363
Issue Date	9/29/2016	9/29/2016	9/29/2016	9/15/2016
Maturity Date	10/27/2016	12/29/2016	3/30/2017	9/14/2017
No of days until Maturity (M)	28	91	182	364
FV - Price ----- (A)	0.012444	0.063194	0.212333	0.637
[(FV - Price)/FV] ----- (B)	0.000124	0.000632	0.002123	0.006370
360/M ----- (C)	12.8571	3.9560	1.9780	0.9890
Bank Discount Rate (B*C) (%)	0.1600%	0.2500%	0.4200%	0.6300%

Calculation of Bank Discount Rate for each security (using DISC Function) :

	4 Week	13 Week	26 Week	52 Week
Issue (Settlement) Date	9/29/2016	9/29/2016	9/29/2016	9/15/2016
Maturity Date	10/27/2016	12/29/2016	3/30/2017	9/14/2017
Redemption (Face Value)	100	100	100	100
Price	99.987556	99.936806	99.787667	99.363
Bank Discount Rate (%)	0.1600%	0.2528%	0.4223%	0.6388%

(B)

Calculation of Bond Equivalent Yield for each security (using Formula given) :

	4 Week	13 Week	26 Week	52 Week
FV	100	100	100	100
Price	99.987556	99.936806	99.787667	99.363
Issue Date	9/29/2016	9/29/2016	9/29/2016	9/15/2016
Maturity Date	10/27/2016	12/29/2016	3/30/2017	9/14/2017
No of days until Maturity (M)	28	91	182	364
FV - Price ----- (A)	0.012444	0.063194	0.212333	0.637
[(FV - Price)/Price] ----- (B)	0.000124	0.000632	0.002128	0.006411
365/M ----- (C)	13.0357	4.0110	2.0055	1.0027
Bond Equivalent Yield (B*C) (%)	0.1622%	0.2536%	0.4267%	0.6428%

Calculation of Bond Equivalent Yield for each security (using YIELDDISC Function) :

	4 Week	13 Week	26 Week	52 Week
Issue (Settlement) Date	9/29/2016	9/29/2016	9/29/2016	9/15/2016
Maturity Date	10/27/2016	12/29/2016	3/30/2017	9/14/2017
Redemption (Face Value)	100	100	100	100
Price	99.987556	99.936806	99.787667	99.363
Bond Equivalent Yield (%)	0.1600%	0.2529%	0.4232%	0.6429%

(a)

Bank Discount Rate (4 decimal places) for 52-week Security

Using Formula given : 0.6300%

(b)

Bank Discount Rate (4 decimal places) for 52-week Security

Using DISC Function : 0.6388%

The Bank Discount Rate is not the same for 52 week security. The difference is marginal (0.0088%)

The same is true for 13-week and 26 week security. The difference is marginal. However, the rates will be same if the Bank Discount rate is taken at 2 decimal places.
In the case of the 4-week security, however, the rate is exactly the same using both the methods.

(c)

Bond Equivalent Yield for 26-week security

Using Formula given : 0.4267%

(d)

Bond Equivalent Yield for 26-week security

Using YIELDDISC Function : 0.4232%

The Bond Equivalent Yield is not the same for 26-week security. The difference is marginal (0.0035%)

The same is true for 4-week,13-week and 52-week security. The difference is marginal. However, the rates of these 3 securities will be same in both the methods if the Bond Equivalent Yield is taken at 2 decimal places.