A $1,000,000 face T-bill with 40 days to maturity is priced at $985,000. Compute the discount yield and the bond equivalent yield

To compute the discount yield and the bond equivalent yield, we need to understand the formulas and steps involved.

1. Discount Yield:
The discount yield represents the annualized rate of return on the investment, assuming the security is held until maturity. It is expressed as a percentage.

Formula:
Discount Yield = (Discount / Face Value) * (360 / Days to Maturity)

Steps:
1. Calculate the discount by subtracting the purchase price from the face value: Discount = Face Value - Purchase Price.
In this case, the discount would be $1,000,000 - $985,000 = $15,000.

2. Plug the values into the formula:
Discount Yield = ($15,000 / $1,000,000) * (360 / 40)

3. Simplify and calculate:
Discount Yield ≈ 0.015 * 9
Discount Yield ≈ 0.135

The discount yield is approximately 0.135 or 13.5%.

2. Bond Equivalent Yield:
The bond equivalent yield allows for a comparison with other fixed-income securities. It is also expressed as a percentage.

Formula:
Bond Equivalent Yield = (Discount Yield) * (365 / Days to Maturity)

Steps:
1. Plug the discount yield value calculated above into the formula:
Bond Equivalent Yield = 0.135 * (365 / 40)

2. Simplify and calculate:
Bond Equivalent Yield = 0.135 * 9.125
Bond Equivalent Yield ≈ 1.23

The bond equivalent yield is approximately 1.23% or 0.0123.