True Interest Cost
In contrast, to the NIC, the true interest cost (TIC) incorporates the time value of money. The TIC is the interest rate necessary to discount the sum of the present value of interest payments and principal to the amount that the issuer will receive at closing (subtracting any discounts or fees). The TIC is equivalent to the internal rate of return (IRR) of the bond issue.
While most interest on bonds is paid semi-annually for simplicity we will assume that interest payments are paid once at the end of each year. So while this example will not be technically equivalent to the TIC, it will give you an idea of how it is calculated. The first year will have the highest interest payments because interest will need to be paid on all five maturities. At the end of the first year, there will be a total interest payment of $250,000 ($30,000 + $40,000 + $50,000 + $60,000 + $70,000 = $250,000) plus $2,000,000 in principal. The total outflow will be $2,250,000. This value will be discounted at the TIC. In the second year, the interest payments will be $220,000 because the first bond will have matured, so no interest payment is due on that bond. After the third year, $180,000 will be due, and after the fourth year, $130,000, and finally, at the end of the fifth year only $70,000 will be due.
The next step is to solve for a discount rate that makes the total discounted outflows equal to the proceeds to the issuer. This discount rate turns out to be around 3.542%. This would be the TIC.
|
Years to Maturity |
Principal Maturity |
Interest Payments Per Maturity* |
Total Outflows |
Interest Rate** |
Discounted Outflows*** |
|
1 |
$2,000,000 |
$250,000 |
$2,250,000 |