# How to Calculate Treasury Bill Profit in Nigeria

Sometimes the Federal Government may need to borrow money from the public to fund independent operations and special projects. To achieve this, the Central Bank of Nigeria, on a bi-weekly basis, conducts auctions to sell treasury bills to the public at a discount price. Although treasury bills are low-yield investments, they are suitable for investors seeking to stash their money for a brief period (a maximum of 364 days) with the guarantee of repayment at maturity. In this article, we’d explain all you ever wanted to know about treasury bills in Nigeria, including how to calculate the profit.

How to calculate treasury bill profit in Nigeria would be discussed below:

• ## What are Treasury Bills?

Treasury bills are short-term securities backed by the government and issued to the public through a bi-weekly auction conducted by the Central Bank of Nigeria (CBN). T-bills, as they are often called, are sold to the public at a discount from their face value and have a maturity period of 91 days, 182 days, or 364 days.

On the same day that an investor buys a t-bill at the discounted price from CBN, he is paid the interest on the investment upfront. Next, he holds on to the treasury bills he’s purchased until the maturity date, of which he would eventually be paid the full price of the face value of the t-bill. For example, if an investor intends to purchase N200,000 worth of treasury bills at a discount rate of 10% and a 364-day tenor. CBN would only debit his account with N180,000 (the discounted price of the t-bill) – as such his N20,000 interest is paid upfront. After 364 days when the tenor of the bill expires, the investor would be paid N200,000, which is the full price of the t-bill.

• ## How Does Treasury Bill Work?

As stated earlier, CBN sells treasury bills to the public through a bi-weekly Dutch auction system. A Dutch auction system refers to a type of auction that works by receiving all bids for an item before the highest price at which the item would be sold is determined.

Before we proceed to discuss how the auction for treasury bills is conducted by CBN works, we should state that the minimum amount one can purchase t-bills from the CBN is N50,000,000. However, investors who do not have up to the minimum N50 million required by the CBN can buy t-bills through CBN-licensed brokers or banks, for as low as N100,000 (even lesser). Banks and licensed brokers will have to pool money from their customers to meet or exceed the N50 million required and invest into a portfolio on their behalf.

Having established that an investor may buy treasury bills through CBN, brokers, or banks, let’s move on to explaining how CBN performs the bi-weekly auction for t-bills. During the auction of treasury bills, CBN allows investors to quote the discount rate they are willing to pay for each tenor of t-bills. When all the bids are received, CBN begins by accepting the lowest bids first, then climbing higher until the total amount it seeks to raise for the issued treasury bills is met. The highest quote accepted by CBN from the total bids received is then selected to be the maximum discount price (also known as stop rate), meaning quotes above this selected stop rate would be rejected. Consequently, CBN offers all successful bidders the highest accepted bid rate as the discount margin on the t-bills issued.

Here’s an example that illustrates how CBN  conducts auctions for t-bills. Let’s assume CBN wants to raise N500 million for a single treasury bills issues and the following quotes were received for a 364-day tenor:

N50 million @ 5.85%

N75 million @ 5.98%

N50 million @ 6%

N125 million @ 6.25%

N100 million @ 6.47%

N150 million @ 6.95%

N250 million @ 6.95%

CBN will accept the lowest bid until it meets the N500 million it seeks to raise, which will fall within the 6.95% quote. However, only N100 million will be accepted from the 6.95% bid while quote higher than 6.95% are outbid/rejected. Therefore, all investors who quoted 6.95% and below would receive a discount rate of 6.95%.

• ## How Does Interest Rate on Treasury Bills in Nigeria Work?

The interest on treasury bills is the difference between the price an investor pays to buy a T-bill and the bill’s face value, which is the amount received at maturity. To explain this better, let’s assume you purchased N50 million worth of treasury bills for a 364-tenor at a discount rate of 6.95%. We would find out what your interest on the t-bill would be and the discounted rate at which you would buy the t-bill.

Solution

The formula used to determine the interest rate on tertiary bills in Nigeria is:

(Tenor/364 days) × face value of treasury bill × discount rate

where Tenor = duration of maturity (could be 91 days, 182 days, or 364 days, depending on the tenor or the treasury bill)

Face value of treasury bill = the value of the security as stated by its issue (i.e. the full price)

Now, let’s determine the interest rate on N50 million worth of treasury bills for a 364-tenor at a discount rate of 6.95%:

Interest rate = (364/364) × 50,000,000 × 6.95%

=  1 × 50,000,000 × 0.0695

= 3,475,000

The interest rate is N3,475,000. This means, on the day you purchase the t-bill, CBN will debit your account with N46,525,000 million – as such your N3,475,000 interest is paid upfront. And upon maturity of the t-bills (i.e. 364 days),  CBN will pay you N50,000,000, which is the face value of the t-bill you purchased.

The profit on the treasury bill you purchased is the interest, which is the difference between the price you paid to buy a T-bill and the bill’s face value, which is the amount received at maturity. From the example above, the profit is N3,475,000.

This is how you calculate treasury bill profit in Nigeria.