# Resolving interest during construction (IDC) circular references using algebra

For financing large infrastructure, long-term industrial projects or public services, it may be structured as “project finance” which is a non-recourse or limited recourse financial structure. Project financing relies primarily on the project’s cash flow for servicing debt and paying back equity.

Typically, large projects have long construction period which require large amount of funds. After the construction completed, the operation period begins where the project starts to earn revenue. The bank understands and agrees not to require that loan interest and principal repayment be paid during the construction period. However, the bank still requires that interest is charged during this time and combined into loan principal. Loan principal will accumulate during the construction period, and interest payment and principal repayment will start after the operation period started (where the project start to have revenue).

In contrast to typical loan where interest that incurs from a loan is immediately paid and recorded as expense which is tax deductible, for project financing, Interest During Construction (IDC) is capitalized and added to the cost of the asset.

#### Modeling interest during construction (IDC)

Generally, specific cost items during construction are known. A portion of these costs will be funded by equity, and the rest by debt. However, any debt drawdown will incur IDC which should be covered by the debt drawdown itself. In other words, the debt drawdown should be extra from what is required for the specific cost items. For example, let’s assume for a given period (in construction period) the followings:

• Initial debt drawdown required to fund construction is \$100M
• Let’s say the loan interest is 10% per this given period, so the interest incurred equals \$10M
• The project cannot pay \$10M at this time, so the project owes additional \$10M
• Since additional \$10M is rolled into principal, it should incur additional interest of \$1M
• (The drawdown so far has accumulated to \$100M + \$10M = \$110M, and there is \$1M interest to pay)
• Again, the project cannot pay \$1M at this time, so the project requires additional \$1M drawdown
• Therefore \$1M is rolled into principal, and it will incur additional \$0.1M interest
• The loop goes on

We could model this nature of project finance using MS Excel’s circular references capability. However, circular reference adds heavy load to Excel calculation. It also makes the model unstable and might fail at any instance.

The most common workarounds to avoid circular references are such as (i) running a fixed number of iterative calculations to arrive at a good enough result, or (ii) using copy-and-paste macro to break away circular loops. The first one can be inaccurate at times, and the latter introduces discontinuity into calculation flow which prohibits more advanced analysis such as using data tables for sensitivity analysis.

[An example of how “copy-and-paste” macro is widely adopted as a workaround for project finance modeling, see section “Dealing with circularities” on page 4 of this document: https://go.ey.com/2RNGr11]

Let’s develop a more noble approach to tackle this.

#### Let’s talk algebra

Let’s look at an example period of time in the above illustration.

• At the beginning of the period the debt outstanding is A, and additional debt B is drawn during the period making the closing debt outstanding equals A + B
• Loop #1: debt A & B will incur interest of AI and BI/2 during the period, where I is interest rate for the given period
• Loop #2: Interest AI and BI/2 will then roll into principal and incur additional interest of AI x (I/2) and BI/2 x (I/2)
• Loop #3: In similar fashion, interest AI x (I/2) and BI/2 x (I/2) will incur additional interest of AI x (I/2)^2 and BI/2 x (I/2)^2
• Loop #n: Going on and on, loop #n will incur additional interest of AI x (I/2)^(n-1) and BI/2 x (I/2)^(n-1)

Total IDC therefore equals IDC #1 + IDC #2 + IDC #3 + … + IDC #n.

Then, derive a simple formula to determine IDC.

Here’s a formula that determines IDC directly from the construction costs (the portion that requires debt funding) and hence avoid having circular references.

Note this approach to IDC works when IDC is the only financial cost during construction period. For more complex conditions, for example, financial costs also include commitment fee (where a fee is charged to undrawn committed amount), the formula will need to be revised.