Question

What is the discount yield, bond equivalent yield, and effective annual return on a $3 million commercial paper issue that currently sells at 97.50 percent of its face value and is 145 days from maturity?

Answer 1

The discount yield is 2.5%, the bond equivalent yield is 5%, and the effective annual return is 6.38%.

Step-by-step explanation:

The discount yield, bond equivalent yield, and effective annual return on a $3 million commercial paper issue that currently sells at 97.50 percent of its face value and is 145 days from maturity can be calculated as follows:

The discount yield is the difference between the face value of the commercial paper and its selling price, divided by the face value. In this case, the discount yield would be (100 - 97.50) / 100 = 0.025 or 2.5%.

1. The bond equivalent yield is a way to compare the yield of a commercial paper to the yield of a bond. It is calculated by doubling the discount yield. In this case, the bond equivalent yield would be 2 * 2.5% = 5%.
2. The effective annual return takes into account the compounding of interest over the course of a year. It is calculated using the formula: (1 + discount yield)^(365/number of days to maturity) - 1. In this case, the effective annual return would be (1 + 2.5%)^(365/145) - 1 = 6.38%.

Answer 2

(a) 6.206%

(b) 6.54%

(c) 6.58%

Step-by-step explanation:

Given that,

Commercial paper value = $3 million

Currently selling at 97.50 percent of its face value.

Days from maturity = 145

(a) Discount yield:

=
`((Face\ value - Current\ price))/(Face\ value)*(360)/(Days\ in\ maturity)`

=
`((100 - 97.50))/(100)*(360)/(145)`

= 0.025 × 2.4827

= 0.06206 or 6.206%

(b) Bond equivalent yield:

=
`((Face\ value - Current\ price))/(Current\ price)*(365)/(Days\ in\ maturity)`

=
`((100 - 97.50))/(97.50)*(365)/(145)`

= 0.026 × 2.52

= 0.0654 or 6.54%

(c) Effective annual return:

Future value = Present value ×
`(1+r)^(n)`

$100 = $97.50 ×
`(1+r)^{(145)/(365)}`

`((100)/(97.50))^{(365)/(145)} = 1+r`

1.0658 = 1 + r

0.0658 or 6.58% = r