Question

What is the discount yield, bond equivalent yield, and effective annual return on a $1 million T-bill that currently sells at 97.375 percent of its face value and is 75 days from maturity? (Use 360 days for discount yield and 365 days in a year for bond equivalent yield and effective annual return. Do not round intermediate calculations. Round your answers to 3 decimal places. (e.g., 32.161))

Answer 1

Solution :

a. Calculation of T-Bill’s discount yield:                                   

The formula for calculation of discount yield of a T-bill when the No. of days in a year = 360

= [ (Face value – Purchase Price)/ Face value ] * ( 360 / No. of days to maturity )

As per the Information given in the question we have

Face Value = $ 1 Million   ; Purchase Price = ( $ 1 Million * 97.375 % ) = $ 0.97375 Million ;

No. of days to maturity = 75

Applying the above values in the formula we have

= [ ( 1 – 0.97375 ) / 1 ] * ( 360 / 75 )

= 0.02625 * 4.8

= 0.126 = 12.600 %

Thus the Discount Yield is = 12.6 %

b. Calculation of the T-Bill’s Bond Equivalent yield:           

The formula for calculation of Bond equivalent yield of a T-Bill when the No. of days in a year = 365

= [ (Face value – Purchase Price)/ Purchase Price ] * ( 365 / No. of days to Maturity)

As per the Information given in the question we have

Face Value = $ 1 Million   ; Purchase Price = ( $ 1 Million * 97.375 % ) = $ 0.97375 Million ;

No. of days to maturity = 75

Applying the above values in the formula we have

= [ ( 1 – 0.97375 ) / 1 ] * ( 365 / 75 )

= 0.02625 * 4.8667

= 0.12775 = 12.775 %

Thus the Bond Equivalent Yield is = 12.775 %

c. Calculation of Effective annual return :

Effective annual return is calculated using the following formula:

EAR = ( 1 + ( r/n) )ⁿ – 1

Where r = Bond equivalent yield

n = 365 / No. of days to maturity

As per the information given in the question and the above calculation we have

r = 12.775 %

No. of days to maturity = 75

Applying the above values in the formula we have

= ( 1 + ( 0.12775 / ( 365 / 75 )) ) ^{( 365 / 75 )} - 1

= ( 1 + ( 0.12775 / 4.8667 ) ) ^4.8667 - 1

= ( 1 + 0.02625 ) ^4.8667 - 1

= ( 1.02625 ) ^4.8667 - 1

= 1.13440 – 1

= 0.13440

= 13.440 %

Thus the Effective annual Return = 13.440 %

Note : ( 1.02625) ^4.8667 is calculated using the excel formula

=POWER(Number,Power) = POWER(1.02625,4.8667) = 1.13440