# Theory of Credit Spreads in Project Finance

This page discusses how credit spreads should in theory be derived from an analysis of probability of default and loss given default. In evaluating credit spreads, I compute the implied probably of default given assumptions about the loss given default and the timing of default. For debt that has a tenure of more than a couple of years, I demonstrate that the compounding of credit spreads produces very high implied default rates when the credit spread is above 3%.

There are a few files that work through the theory of credit spreads using the Merton model and formulas for computing the credit spread.

## Interest and Fees Over Time Period from Borrowing to Repaying Money

The fourth lesson set deals with a subject that I sometimes become emotional about, the rate of return that is required to compensate a financial institution or another investor for taking risk. It may seem that as long as the all-in interest rate (that I define as the debt IRR), then you should not care too much about the credit spread. But high credit spreads earned over long-term debt tenures can result in a lot of money for lenders simply because of compounding of the return. These high spreads lead to very high implied probability of default even if the loss given default is high as explained in a couple of the videos. Further, in project finance since the equity risks and returns have a lot of debt characteristics, similar analysis of the probability of contract abrogation and the loss associated with contract abrogation can be applied to equity. Therefore, there are a couple of videos and associated files that address the implied probability of default associated with equity investors. I go a bit crazy when I compute the implied probability of default in IFC or other multi-lateral institutions’ credit spreads for countries in Africa and South Asia, and/or the risk premiums computed by Damarodan for developing countries.

Lesson set 4 also includes some more boring issues associated with whether it is better to ask for fees paid up-front or for credit spreads over the life of the debt. The general answer to this question depends on whether a debt constraint or a DSCR constraint applies. If a debt to capital constraint applies, it seems that the debt increases when fees are paid up front and this is beneficial from an equity IRR perspective. However, as fees are paid in cash, they require more cash equity contribution (even if the fees are capitalized). This hurts the IRR and leads to a simple rule that anytime something increases cash equity requirements, it hurts. The situation is aggravated when debt is defined by the DSCR. In this case even if the debt IRR is the same, the Equity IRR is reduced from paying fees up-front.

## Videos Associated with Credit Spread and Probability of Default Analysis

Technical aspects of videos associated with lesson set 3 involve a lot of goal seeks with macros to derive the implied probability of default in different circumstances. In most of the videos cash flows from increased risk are compared to cash flows that supposedly have lower risk. Then the cash flows with higher risk are divided into a default case and a non-default case. The default case is attributed an arbitrary probability that is fixed and then a goal seek is used to derive what default probability makes the risky flows (e.g. from Nigeria) become equivalent to the lower risk cash flows (e.g. Germany). Macros are attached to the goal seeks and spinner buttons are used to test alternative loss given default and default timing.

## Required Return to Compensate Lenders and Equity Providers for Taking Risk

I designed the files for lesson set 3 with exercises that force you to compute the implied probability of default for loans with a high credit spread and/or equity investments with a country risk premium. I desperately want you to see how unfair the high credit spreads and equity risk premiums are to developing countries. When the credit spread and required return on a solar project is high, then prices are high and GDP growth is spent on giving money to foreign investors (including the World Bank). Because this is such an emotional issue for me I have decided to drop any fee for this lesson set. This means that if you go to the files and complete the yellow blanks and see for yourself how much money a 5% credit spread or an 15% equity IRR really mean, you can get your name on the list of completed files and also receive a nice badge and a diploma.

23. Carrying Charge Analysis Revised.xlsm