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

Answer:

(a) 6.206%

(b) 6.54%

(c) 6.58%

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:

= $\frac{(Face\ value - Current\ price)}{Face\ value}\times\frac{360}{Days\ in\ maturity}$

= $\frac{(100 - 97.50)}{100}\times\frac{360}{145}$

= 0.025 × 2.4827

= 0.06206 or 6.206%

(b) Bond equivalent yield:

= $\frac{(Face\ value - Current\ price)}{Current\ price}\times\frac{365}{Days\ in\ maturity}$

= $\frac{(100 - 97.50)}{97.50}\times\frac{365}{145}$

= 0.026 × 2.52

= 0.0654 or 6.54%

(c) Effective annual return:

Future value = Present value × $(1+r)^{n}$

$100 = $97.50 × $(1+r)^{\frac{145}{365}}$

$(\frac{100}{97.50})^{\frac{365}{145}} = 1+r$

1.0658 = 1 + r

0.0658 or 6.58% = r