The treasurer of a large corporation wants to invest $47 million in excess short-term cash in a particular money market investment. The prospectus quotes the instrument at a true yield of 3.83 percent; that is, the EAR for this investment is 3.83 percent. However, the treasurer wants to know the money market yield on this instrument to make it comparable to the T-bills and CDs she has already bought. If the term of the instrument is 109 days, what are the bond equivalent and discount yields on this investment

Bond equivalent = 3.78%

Discount yield = 3.73%

Explanation:

Explanation:

Given the following :

Current price = $47 million

Effective annual rate (EAR) = 3.83% = 0.0383

TERM of instrument = 109 days

Bond equivalent yield formula:

[(face value - Current price) /current price] × 365/term

Face value= current price × (1 + EAR)^term/365

= $47,000,000×(1+0.0383)^(109/365)

= $47,000,000 × (1.0383)^0.298630

= $47,530,496.

Bond equivalent yield :

[(47,530,496 - 47,000,000)/47,000,000]×(365/109)

=[$530,496 / $47,000,000] × 3.34862385

= 0.0377964

= 3.78%

Discount yield :

Discount yield uses 30-days a month which equals 360-days a year.

Discount yield formula:

[(face value - Current price) /current price] × 360/term

Discount yield :

[(47,530,496 - 47,000,000)/47,000,000]×(360/109)

=[$530,496 / $47,000,000] × 3.3027522

= 0.0372786

= 3.73%

= 3.73%

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