# Exposure At Default: Calculating the present value

In this numerical example, I can't figure out with which numbers (when using the PV formula) to calculate exposure at default (EAD) as shown in the table.

The EAD is the value of the discounted future cashflows (CF) at the time of default.

With my calculations I do not get the EAD shown there starting from t=2. How do I replicate the the EAD in the table?

The following parameters are given in the calculation:

nominal amount: 1000
Duration: 6 years
Interest rate: 10%.
Effective interest rate: 10%.
Date of payment of interest: Annual
Credit structure: maturing loan


I can see that you provided an answer on your own question, but let me provide the general procedure.

We are standing at time $$t=0$$, we have just issued a loan (bond) with notional $$N=1000$$ to our counterparty (borrower). In return we will collect $$K=0.1 N=100$$ every year in interest payments, where interest rate is $$r=10\%$$. At the end of the final term (6 years), we will collect our last interest rate payment, as well as the full notional. If the borrower defaults at time $$t=\tau$$, we will neither receive our payment due on this date, nor any other future payments thereafter.

That is, if the borrower defaults at time $$t=\tau$$, before any cashflows due on this date have been exchanged, our value exposure today ($$\mathcal{F}_0$$) will be

\begin{align} EAD(t)|\mathcal{F}_0 &= \sum_{k=t}^6 \frac{r N}{(1+r)^k} + \frac{N}{(1+r)^6} \\ &= \sum_{k=t}^6 \frac{10\% \cdot 1000}{(1+10\%)^k} + \frac{1000}{(1+10\%)^6}. \end{align}

I would like to share with you the answer from saulspatz, from math.stackexchange

They are computing the present value, at the time fo the loan of the defaulted payments, using the same rate as the rate of the loan. If the debtor defaults on the last payment, the present value is

$$1100*1.1^{-6}=620.92$$

If he default at the end of year 5 that will add another

$$100*1.1^{-5}=62.09$$

bringing the total to 683.01.