For a given contract, find the optimal payment terms. Conditions for optimality are:
Payment terms assert the time frame in which payment for services need to be transferred. The standard notation is shown below:
NET 30
Here, the payment needs to be transferred within thirty days of receiving the invoice. If a discount is contracted, the standard notation is as follows:
2/10 NET 120
Here, if the payment is received within 10 days, a 2% discount is applied. If the payment is received within 11-120 days, the full amount is due. Generally, interest is applied if the payment is late.
We would like to maximize the time before payment (NET), as it gives the purchaser the ability to obtain returns by acquiring short-term financial instruments (think MMI or Repo) between invoice receival and the final payment date. We would like to maximize the discount, as it helps us lower the total payment.
There exists a tradeoff in receiving the discount and delaying the payment. If the return from the financial instrument is greater than the discount, the purchaser should delay the payment (and vice versa).
We can calculate the discount for a given contract as the supplier's forgone returns if paid on the final day of the discount period, subtracted from the supplier's forgone returns if paid on the final payment due date. Forgone returns are defined as the expected return for the supplier if they were to receive the payment the day the buyer received the invoice. Therefore, the discount is equal to the supplier's expected return for the period of time between the final day the discount is available and the final payment due date.
I use the standard exponential growth approximation to accomodate for returns that are modeled as percentage changes.
The discount rate calculation is as follows:
$ D = Pd = Pe^{rN_e} - (P-D)e^{rN_d}$
Where $D$ is the discount in dollar terms. $P$ is the payment value and $d$ is the discount rate. $r$ is the daily rate of return of the supplier. $N_e$ is the expected (mean, if normally distributed) number of days until payment is due (NET). $N_d$ is the contracted number of days that the payment must be transferred to receive the discount.
I see that $D$ appears on both sides of the equation above $-$ we need to perform some algebraic manipulation to find the reduced form.
$ D = Pe^{rN_e} - Pe^{rN_d} + De^{rN_d}$
Next, I apply a natural logarithm to each term:
$\ln D = rN_e \ln P - rN_d \ln P + rN_d \ln D$
$\ln D - rN_d \ln D = rN_e \ln P - rN_d \ln P$
$\ln D (1 - rN_d) = rN_e \ln P - rN_d \ln P$
$\ln D = \cfrac{rN_e \ln P - rN_d \ln P}{(1 - rN_d)}$
Then, I apply $e$ to each term to obtain the reduced-form equation for $D$:
$ D = e^{\cfrac{rN_e \ln P - rN_d \ln P}{(1 - rN_d)}}$
If the discount rate $d$ is desired, we can then solve:
$d = \cfrac{D}{P}$
We only need to estimate two values to make this calculation: $N_e$ and $r$.
In the absence of data, $N_e$ can be estimated using a benchmark. For example, a production company shoots a TV advertisement for us. The benchmark would indicate the average contract NET value in the production industry. We then set $N_e$ as the benchmark.
We may be able to access payment delay data: The Hackett Group appears to hold this information on the largest 1000 US companies, as per this article.
In this case, $N_e$ is estimated using the probability distribution of NET days for each payment, which can be inferred from the frequency distribution provided by the data.
$N_e = \sum_{1}^{N} X_i p(X_i)$
Where $N_e$ is the expected NET value, and $X_i$ is one observation of a past NET value. $p(X_i)$ contains the probability/frequency of said NET value.
The daily rate of return for these firms is affected by many factors. More modeling is necessary to estimate an accurate daily rate of return for any given supplier.