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Model : npv1
Simile version : 4.0
Date added : 20041021
Keywords :
System Dynamics ;
Business model ;
Simile techniques ;
Many markets for agricultural products and other commodities are locked in a cycle of boom and bust. Overinvestment when prices are high leads to an excess of capacity and a price slump. Low prices lead to shutdowns, a withdrawal of capacity and eventually a new wave of high prices.
Stock prices of companies in cyclical markets follow the same upsanddowns.
At first glance, this appears irrational. Why should investors be willing to sell shares at a low price in bad times, when they surely know that in a few years, the good times will come again? And why should investors be willing to pay high prices for shares in good times, when they surely know that in a few years time, another slump will follow?
Rational companies make investment decisions on the basis of the project’s net present value (NPV). Projects with a positve NPV are undertaken; projects with a negative NPV are rejected. The net present value is calculated as the sum of all future cash flows from the project, net of expenses, discounted for the fact that cash is received at different points in time. Cash received today is more valuable than the same amount of cash received next year, because in the meantime one can invest it, earning interest. When calculating the net present value, the future payments are discounted to the equivalent value that would be the same as a payment received today.
The formula for discounting a payment P received at time t is:
P/(1+r)^{t}
where r is the discount rate. The discount rate is the riskadjusted real interest rate applicable to the project. It is often about 10 per cent.
This model implements this simple formula to calculate the net present value of a hypothetical project in a cyclical market. The assumed net cash flows from the project follow a sinusoidal curve, typical resulting from boomandbust commodity prices and fixed expenses.
The model contains one slider, which is used to adjust the point of the cycle at which the project begins. It is thus possible to compare projects begun during the slump in prices with projects begun during the good times. Since these are the same hypothetical project, differing only in start date, the duration of the project and the net cash received over its entire life are the same whenever it starts.
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npvcycle.sml  Base model 
The sinusioidal variation of net income with time is given by:
(1+sin(time()/10+(offset_to_cycle*pi())))
where offset_to_cycle is controlled by a slider to vary between 0 and 1.
The summation of discounted income is performed by the compartment representing NPV. Each period the discounted income flows into the compartment. The discounted income is calculated from the real income using the formula:
income/((1+discount_rate)^time())
Each model run simulates a single project, with a particular start date. To compare the effect of choosing a different start date, at a different point in the cycle, it is necessary to run the model again. To get a complete picture, it is therefore necessary to run the model several times. The most convenient way to do this, is to use SimileScript.
similescript::ModelWindow mw mw Open "../Examples/npvcycle.sml" mw Run similescript::RunControl rc set table {} foreach i {0.0 0.25 0.5 0.75 1.0} { rc SetValue "/offset to cycle" $i rc Reset rc Start lappend table [rc GetValue "/NPV"] } put $table
The interesting thing to note about the results, is how dependent the project’s NPV is on the stage of the cycle at which the project is begun. The highest NPV (and hence the most attractive time to invest) is just before the peak of the cycle. This rationalises the empirical observations of cyclical markets discussed in the opening paragraph of this example.
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