Discount Instruments
Instead of paying interest periodically or at maturity, some instruments do not pay interest at all in the traditional sense. Instead, they are sold at a discount to their face value and return their face value upon maturity. The difference between the instrument’s discounted price at purchase and its payment of face value at maturity represents the investor’s return.
The return of discounted instruments is quoted on a discounted basis. This means the discount rate is quoted instead of the instrument’s effective return. Unfortunately, quoting discounts tends to understate the investment’s true return, and this complicates the task of comparing the relative returns of investments that are interest-bearing with discounted instruments. Consider the following example:
A discounted investment with a 1-year maturity is priced at a 10% discount and is quoted on a 30/360 calendar. What would an interest-bearing instrument have to yield in order to offer the same return?
For instruments that are quoted on a discounted basis, the process for calculating the interest-bearing yield equivalent is:
Determine the discount:
Discount = Face Value × Rate × Time
In this example the discount would be:
Discount = $1MM × .10 × 360 / 360 = $100,000
So the purchase price is $1MM − $100,000 = $900,000
Determine the yield:
In this example, the investor earns $100,000 on a $900,000 investment. This equates to a return of:
$100,000 / $900,000 = 11.11%
Note the return is higher than an interest-bearing investment at 10% 30/360 because in an interest-bearing instrument the investor earns $100,000 on $1MM. In a discounted instrument, the investor earns $100,000 on just $900,000.
Let’s review some additional calculations before proceeding:
PROBLEM 3A
Convert a 7% 30/360 discount to an interest-bearing equivalent. Assume an FV of $1 and calculate the discount using the 7% rate.
ANSWER:
Discount = $1 × .07 × 360 / 360
Discount = $.07
Interest equivalent is: $.07 / .93 × 360 / 360 = .0752 = 7.52%
PROBLEM 3B
Convert a 6% A/360 discount yield to an interest-bearing equivalent.
ANSWER:
Discount = $1 × .06 × 365 / 360
Discount = $.0608 = 6.08%
Interest equivalent is: $.0608 / .9392 × 365 / 360 = .0656 = 6.56%