# Compounding:

• When we determine the present value of Rupee in terms of future value, the method is called compounding, and the money is known as compounded money.
• Simply, what is the future value of the present investment?
• Compounding is the process of finding the future value of a single amount.

Formula: Vn = Vo (1 + r)n
Or; Compound value = a × (1 + r)n
(Where a or Va is what’s value is being determined, n is no of years, and r is the rate of interest)

# Discounting:

• The process of reducing the future value to present equivalent
• It means what is the present value of the future investment.

Formula: Vo = Vn  / (1 + r)n
(Where; Va is present value, Vn is future value)

• Eg what is the total produce in a plantation; we will calculate all the revenues and costs.
• In every forest, we have to do expenditure in every year. The procedure should be:
 Year Operation Cost Discounting yr Present value Plants, labor, digging, etc 20 Rs/- 0 20 Restocking, digging, etc 10 (1 + r)-1 1 — Some operations 5 (1 + r)-5 2 — — — — — — — — — Thinning 7 (1 + r)-7 5
• In short, all the costs are discounted at the same schedule and they are added.
• Moreover, we have revenues during, the course of rotation, they will also be reckoned. Eg
 Cost Revenue Operations Rs. 50 Rs. 30 Planting, restocking, etc 20 35 Thinning – I 25 100 Thinning – II 30 150 Thinning – III 200 3000 Final Felling
• All the costs will be added but firstly they discounted individually.
• Same is the case with revenues. Now both are compared and if the cost is less than revenues the project is accepted otherwise sacked.
• The special thing in this regard was that if cost is spent today, the revenue will be available after a number of years during which the value of rupee will have got a decrease. To compensate this (interest), all costs and revenues incurred or bagged at different stages of the crop are brought either in terms of value at the time of planning or taken to the value at the time of harvesting the crop.
• Thing act of bringing cost of revenues to the start will be called discounting and that of dragging it to the felling stage will be compounding.
• However, the term present and future value has been developed for the value of money is falling day by day whereas the prices of goods and services, in turn, are rising fast. Thus we get the Net Present Value (NPV).
• Today the bank interest rate is 11%, if it turns 10, after one or two years, we will count it as 10%. In Pakistan, the analysis was done and a 14% discount rate was applied. In the UK it is 3%, Australia 3%, and in the USA 4%.
• In forestry, there are two opinions. One says we should not discount more than 4% while the other is of the view that discounting should be done a more, however, they have done it at 14% in Pakistan. 