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:
= [tex]\frac{(Face\ value - Current\ price)}{Face\ value}\times\frac{360}{Days\ in\ maturity}[/tex]
= [tex]\frac{(100 - 97.50)}{100}\times\frac{360}{145}[/tex]
= 0.025 × 2.4827
= 0.06206 or 6.206%
(b) Bond equivalent yield:
= [tex]\frac{(Face\ value - Current\ price)}{Current\ price}\times\frac{365}{Days\ in\ maturity}[/tex]
= [tex]\frac{(100 - 97.50)}{97.50}\times\frac{365}{145}[/tex]
= 0.026 × 2.52
= 0.0654 or 6.54%
(c) Effective annual return:
Future value = Present value × [tex](1+r)^{n}[/tex]
$100 = $97.50 × [tex](1+r)^{\frac{145}{365}}[/tex]
[tex](\frac{100}{97.50})^{\frac{365}{145}} = 1+r[/tex]
1.0658 = 1 + r
0.0658 or 6.58% = r
