Deferred Payment Calculation Formula

The spectrum auctions in India allows an operator to make payment a certain portion of the auction value in a deferred mode after a certain moratorium period spread over a fixed number of years as defined in the NIA. Currently, the moratorium period is 2 years and payment period is 10 years. These are now been changed by IMG (Inter-Ministerial Group) to 2 years and 16 years respectively. The problem is that formulae to calculate the Easy Yearly Installments (EYI) is a little involved and not available as a standard formula in tools we generally use like Microsoft Excel. I have derived this formula using the financial theory of DCF (Discounting Cash Flow) and summing the resulting geometric series using standard sum formula. This purpose of this note is to layout the formula used for calculation of EYI which readers can use to evaluate different scenarios of input parameters (interest rates, moratorium period, deferred payment period etc).

EYI Formula Derivation

The following provides the derivation of the calculation for the EYI formula. This is only for those readers who are interested in diving a little deeper into the mechanics which led to its derivation. Since Linkedin editor does not allow an easy way of displaying mathematical jargons, I have embedded the calculations in a handwritten note in the picture below.

EYI Formula

Hence the formula for calculation of EYI is:-

EYI = [D x r (1+r)^(y+Y)]/[(1+r)^Y-1]

Total Deferred Payment (D) = Auction Value (A) - Upfront Payment (U)

r = Rate of Interest

y = Moratorium period in years.

Y = Duration of payment in years.

Therefore if Rs 100 is the Auction Value and Rs 50 is the Upfront Payment, the Total Deferred Payment is = 100 - 50 = Rs 50.

If Moratorium period (y) is 2 years, and Duration of payment (Y) is 16 years, and interest charged (r) is 8%, then Easy Yearly Installments is as under.

EYI = [50 x 0.08 (1+0.08)^(2+16)] / [(1+0.08)^16 - 1] = Rs 6.58

Hence, for 16 years the total outflow in absolute terms will be Rs 105.42, whereas in NPV terms the outflow will remain Rs 50, as all the future cash flows will get discounted by the interest rate of 8%.

Hope you will find this useful. Thanks.

(Views expressed are of my own and do not reflect that of my employer)

PS: Find the list of other relevant articles in the embedded link.