Question

1-

What is the discount yield, bond equivalent yield, and effective annual return on a $1 million T-bill that currently sells at 96.375 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))

  

Discount yield		%
Bond equivalent yield		%
Effective annual return		%

2-  Calculate the bond equivalent yield and effective annual return on fed funds that are 25 days from maturity and have a quoted yield of 0.21 percent. (Use 365 days in a year. Do not round intermediate calculations. Round your answers to 4 decimal places. (e.g., 32.1616))

Bond equivalent yield		%
Effective annual return		%

Answer 1

1. a). Discount Yield = [(par value - purchase price)/par value] * 360/days to maturity

= [($1,000,000 - $963,750) / $1,000,000] * 360/75

= [$36,250/$1,000,000] * 4.8

= 0.03625 * 4.8 = 0.174, or 17.4%

b). Bond Equivalent Yield = [(par value - purchase price)/purchase price] * 365/days to maturity

= [($1,000,000 - $963,750) / $963,750] * 365/75

= [$36,250/$963,750] * 4.87

= 0.03761 * 4.8 = 0.18305, or 18.305%

c). Effective annual return = [1 + {BEY / (365/days to maturity)}]^{(365/days to maturity)} - 1

= [1 + {0.18305 / (365/75)}]^(365/75) - 1

= [1.03761]^4.8667 - 1 = 1.19685 - 1 = 0.19685, or 19.685%

2). a). BEY = Nominal Yield(365/360)

= 0.21%(365/360) = 0.2129%

b). Effective annual return = [1 + {BEY / (365/days to maturity)}]^{(365/days to maturity)} - 1

= [1 + {0.002129 / (365/25)}]^(365/25) - 1

    = [1.000146]^14.6 - 1 = 1.002131 - 1 = 0.002131, or 0.2131%