Discounted Cash Flow

You will understand that to obtain a sum of money now instead of in the future is important. This is because when you get money in the present time you could invest it at a particular interest rate. The amount of money would grow into the future.

Say that you were promised an amount of money and that it was worth K 10,000 now. You are given the option of receiving it in 5 years into the future. You know that you could invest it now a current rate of interest of 10 per cent per annum. If you waited for 5 years the amount that you would receive would be less at K 6,209.21.

The same process is involved in investment analysis. To get an idea of what a future stream of cash was worth as a lump sum today you would have to calculate its Net Present Value. This can be achieved by applying the following equation.

Where:

= Sum of

C_t = Net cash inflow for the period t

Co = the initial investment

r = the discount rate

t = the number periods (years)

Note that NPVs are an assessment of wealth.

It is a common experience for commercial farmers to increase their wealth by renting land rather than by purchasing it. The reason is that they obtain economies of scale. That is, the extra land will attract a rental fee, but the overhead or fixed costs will be held to a minimum.

The Maambo Family have been offered the rental of 200 hectares of land that borders their farm. The amount of annual rent will be K 6,250 for 10 years.

The Maambo Family want an earning rate on capital invested of 20 % per annum. That is, the discount rate will be 20% per annum.

They will have to invest on day one an extra K 900,000 for machinery. The salvage value at the end of year 10 has been estimated at K 350,000. That amount is not discounted. b. That is, depreciation is not a fixed expense.

Five years of the rotation repeated for a further five years are shown below. Also displayed are yields per hectare for the various crops with estimated prices per tonne and extra variable costs.

All items are in nominal values that include inflation. Extra income is per annum is multiplied by a productivity increase of 15% per annum. Inflation is also 15% per annum per annum charged on total extra cost per annum to get extra costs after inflation.

Calculate NPV and IRR for the investment analysis and comment on the Maambo Familys decision to carry out the investment.

See attachment for the layout as an Excel spreadsheet.

Note: The value of the extra NPV is equal to the sum of the annual discounted value of extra net benefits after inflation plus the salvage value of machinery.

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Net Present Value T Ct NPV = - .Co t-1 (1+r)t Item Year 2 3 4 5 Crop Soybeans Maize Sunflower Maize Cassava Area Yield/ha Hectares tomes 200 3.0 200 5.0 200 2.5 200 5.0 200 10.5 Price/ tonne K 4.200 2,500 4.700 2,500 1.200 Extra Variable Costs/ha K 5,980 4.250 4.280 4.250 5,280 Item Year 1 2 3 4 5 Crop Soyabeans Maize Sunflower Maize Cassava 200 200 200 200 200 kg/ha K K 15% 15% 15% 15% 15% Area Yield Price per tonne Extra income Increase in productivity Extra income Extra machinery Extra variable costs/ha Lease/ha Extra costs per ha K -900,000 K K K K K 15% 15% 15% 15% 15% K K 30% 30% 30% 30% 30% Total extra cost Inflation Extra costs after inflatior Extra net benefits Tax on extra benefits Tax on extra benefits Extra benefits after tax Discount rate Discounted value Add Salvage value K K 20% 20% 20% 20% 20% K K 350,000 NPV IRR % Net Present Value T Ct NPV = - .Co t-1 (1+r)t Item Year 2 3 4 5 Crop Soybeans Maize Sunflower Maize Cassava Area Yield/ha Hectares tomes 200 3.0 200 5.0 200 2.5 200 5.0 200 10.5 Price/ tonne K 4.200 2,500 4.700 2,500 1.200 Extra Variable Costs/ha K 5,980 4.250 4.280 4.250 5,280 Item Year 1 2 3 4 5 Crop Soyabeans Maize Sunflower Maize Cassava 200 200 200 200 200 kg/ha K K 15% 15% 15% 15% 15% Area Yield Price per tonne Extra income Increase in productivity Extra income Extra machinery Extra variable costs/ha Lease/ha Extra costs per ha K -900,000 K K K K K 15% 15% 15% 15% 15% K K 30% 30% 30% 30% 30% Total extra cost Inflation Extra costs after inflatior Extra net benefits Tax on extra benefits Tax on extra benefits Extra benefits after tax Discount rate Discounted value Add Salvage value K K 20% 20% 20% 20% 20% K K 350,000 NPV IRR %