A commercial paper note with a $1 million par value and maturing in 60 days has an expected discount return (DR) at maturity of 6 percent. What was its purchase price? What is this note’s expected coupon-equivalent (investment return) yield (IR)?
To calculate the purchase price of the commercial paper note, we need to understand that the discount return (DR) represents the difference between the face value of the note and its purchase price.
Step 1: Convert the discount rate to a decimal. In this case, the discount rate is 6%, so we convert it to 0.06.
Step 2: Calculate the discount value. The discount value is the amount deducted from the face value of the note to determine the purchase price. It can be calculated using the formula:
Discount Value = Par Value * Discount Rate
In this case, the par value is $1 million, and the discount rate is 0.06. Therefore,
Discount Value = $1,000,000 * 0.06 = $60,000
Step 3: Calculate the purchase price. The purchase price can be obtained by subtracting the discount value from the par value.
Purchase Price = Par Value - Discount Value
Purchase Price = $1,000,000 - $60,000 = $940,000
Therefore, the purchase price of the commercial paper note is $940,000.
Now, let's calculate the note's expected coupon-equivalent yield (IR).
The coupon-equivalent yield (IR) represents the interest rate that would provide the same return if the investor bought a bond with the face value and held it until maturity. It helps to compare the yield of different investments.
The formula to calculate the coupon-equivalent yield is:
IR = (Discount Rate / (1 - Discount Rate)) * (365 / Days to Maturity)
In this case, the discount rate is 6% (0.06) and the number of days to maturity is 60.
IR = (0.06 / (1 - 0.06)) * (365 / 60)
IR = (0.06 / 0.94) * 6.083333333333333
IR ≈ 0.064009
Therefore, the note's expected coupon-equivalent yield (IR) is approximately 6.4009%.