Question

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

Answer 1

[AI-generated answer — Explain Bot]

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.