Question

Q: The bond equivalent yield on a T-bill matures in 45 days, priced at $99.00 with a $100 face value, is ____:

A: BEY = 1.01% * 8.111 = 8.19%

Above is the question and the solution but, I am confused about how they came to this solution. I'm not sure where the 1.01% or 8.111 came from?? Any help would be appreciated!

Answer 1

In the question, it is provided that bond equivalent yield is missing. Bond Equivalent implies that coupon rate/interest rate is equal to the Yield Rate.

Yield to maturity can be calculated by using the following formula, also called approximation method

Kd = [Interest + (Maturity Value - Issue Value) / n ] / [ (Maturity Value + Issue Value) / 2 ]

where, Kd is the Yield Rate, let it be Y

Interest = Face Value x Coupon Rate = $100 x Y%  (Since Y = Coupon Rate = Yield Rate)

  = $100 x Y/100 = Y

Maturity Value or Face Value = $100

Issue Price or Current Price = $99

n = Years to Maturity = 45/365 = 0.12328767123

Putting the above values in the equation

Y = [ Y + (100 - 99) / 0.12328767123 ] / [ (100 + 99) / 2 ]

Y = [ Y + (1) / 0.12328767123 ] / [ (199) / 2 ]

Y = [ Y + 8.1111 ] / [ 99.5 ]

99.5Y = Y + 8.1111

99.5Y - Y = 8.1111

98.5Y = 8.1111

Y = 8.1111/98.5

Y = 0.08235 or 8.24%

Check - $100 discount at 8.24% for 45 days should be equal to $99

In other words, Prevent value of $100 at discount rate of 8.24% annually should be equal to $99

Discount Rate for 45 days = 8.24 x 45/365 = 0.01015%

Present Value = Face Value x (1 / (1 + r))

99 = 100 x (1 / 1 + 0.01015)

99 = 100 x ( 1 / 1.01015 )

99 = 100/1.01015

99 = 98.99 (approx)

LHS = RHS, Hence Proved.

For any query or clarification, please leave a comment.