What is the discount yield bond equivalent yield and effecti

What is the discount yield, bond equivalent yield, and effective annual return on a $5 million Treasury bill that currently sells at 94.875 percent of its face value and is 88 days from maturity? (LG 5-1)

Solution

Discount yield = (Par value - Purchase price) / Par Value *360/Days to maturity
Purchase price = $5,000,000 * 94.875% = $4,743,750
Discount yield = ($5,000,000 - $4,743,750) / $5,000,000 * 360 / 88
= $256,250 / $5,000,000 * 360 /88 = 0.2096 or 20.96%

Bond Equivalent yield = (Par value – Purchase Price)/Purchase Price × (365/Days to maturity)
= ($256,250 / $4,743,750) * (365/88)
= 0.2240 or 22.41%

Effective annual return = (1+ (Par – Price)/Price)^ (365/n) - 1
= (1+ $256,250 / $4,743,750) ^ (365/88) - 1
= 0.2438 or 24.38%