Question

The treasurer of a large corporation wants to invest $24 million in excess short-term cash in a particular money market investment. The prospectus quotes the instrument at a true yield of 3.52 percent; that is, the EAR for this investment is 3.52 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 96 days, what is the percentage discount yields on this investment

Answer 1

First we need to understand what Money market yield and discount yield means.

Money market Yield- It is the rate of return on highly liquid money market instruments whose maturity is less than a year or 365 days. It is also known as Bond Equivalent Yield. It is computed on the Purchase Price

Money Market yield= (Face Value- Purchase Price)/Purchase Price * 360/Time to maturity

Discount Yield- It is the rate of return on the bond when it is sold at a discount to its face value. It is calculated on Discount-based instruments such as T-Bills, Commercial paper,etc. It is computed on the Face Value.

Discount Yield= (Face Value- Purchase Price)/ Face Value* 360/ Time to Maturity

From the above question, the following information is provided-

Purchase Price= $24 million

EAR= 3.52%

Time to maturity= 96 days

Now we have to find the Face Value

Face value = Purchase Price (1+ EAR)^^{Time to maturity/365}

= 24(1+3.52%)^^96/365

⁼ 24(1.00913)= $24.21 million

1) Money Market Yield=   (Face Value- Purchase Price)/Purchase Price * 360/Time to maturity

= (24.21- 24)/ 24 * 360/96

= 0.21/24 * 3.75 = 0.0328 %

2) Discount Yield= (Face Value- Purchase Price)/ Face Value* 360/ Time to Maturity

= (24.21- 24)/24.21 * 360/96

= 0.21/24.21 * 3.75 = 0.0325%