Net Present Value

This program calculates the Net Present Value (NPV) and Internal Rate of Return (IRR) for a capital investment project. It reads project parameters—initial cost, duration, periodic revenues, expenses, and a discount rate—from DATA statements, then computes discounted cash flows for each period. The IRR is found by iterating a discount rate from 0% to 100% in 0.5% steps until the NPV of cash flows falls to or below that rate. A sensitivity analysis loop allows the user to re-run calculations with a modified discount rate without restarting the program.

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Program Analysis

Program Structure

The program is divided into clearly separated phases, each handling a distinct part of the financial calculation:

1. Lines 2–18: Variable glossary display with a timed pause before clearing the screen.
2. Lines 19–90: Header output and data initialisation; reads initial cost C and project duration V from DATA, then dimensions six arrays of size V.
3. Lines 100–230: Reads and displays periodic revenues R(I), expenses D(I), residual value RO, and discount rate T.
4. Lines 260–340: Prints the raw forecast table (revenues, expenses, profit per period).
5. Lines 360–560: Computes and displays discounted present values for each period, plus the discounted residual value VR.
6. Lines 580–660: Prints final results: NPV of cash flow and a profitability index.
7. Lines 670–780: Iterative IRR search loop.
8. Lines 800–840: Sensitivity analysis prompt; loops back to line 220 if the user requests a new discount rate.
9. Lines 850–890: Subroutines — a horizontal rule printer and a column-header printer.
10. Lines 900–930: DATA block providing the sample project parameters.

Key Financial Calculations

The core discounting formula applied at line 440–460 is the standard present value formula:

• S(I) = R(I) * (1 + T/100)^(-I) — discounted revenue for period I
• E(I) = D(I) * (1 + T/100)^-I — discounted expense for period I
• C(I) = S(I) - E(I) — net discounted cash flow for period I
• VR = RO * (1 + T/100)^(-V-1) — residual value discounted one period beyond the project end (line 530)

The NPV (line 630) is B + VR - C, where B is the sum of discounted net cash flows, VR is the discounted residual, and C is the initial cost. The profitability index (line 660) is (RR + VR) / (DD + C) expressed as a percentage, rounded to two decimal places inline rather than using the FN A function.

IRR Search Algorithm

The Internal Rate of Return is found by a simple brute-force scan (lines 680–750). The outer loop variable O steps from 0 to 100 in 0.5% increments. For each candidate rate, the NPV X is recomputed using B(I) (pre-calculated net profits) plus the discounted residual, minus initial cost. The loop exits when X <= O, at which point O approximates the IRR.

There is a subtle bug in line 740: the exit condition IF X <= O compares the NPV against the current rate value rather than against zero (IF X <= 0). This means the loop exits slightly early—when NPV drops below the current percentage value rather than when it crosses zero—potentially overstating the IRR by a small margin. For typical project scales the error is minor but it is technically incorrect.

Variable Name Collision

A significant naming conflict exists: the scalar variable C (initial project cost, read at line 55) is overwritten at line 90 when DIM C(V) is declared, creating an array also named C. In Sinclair BASIC, a scalar and an array of the same name cannot coexist—declaring the array erases the scalar. After line 90, any reference to C as the initial cost (e.g., lines 630, 660, 730) would actually access C(0) (the zeroth element of the array, which defaults to zero), producing incorrect NPV and profitability results. This is a genuine bug in the program as listed.

Notable BASIC Idioms

• User-defined function: Line 19 defines FN A(X) = INT(100*X + 0.5)/100, a standard two-decimal-place rounding function used extensively in output formatting.
• Subroutine reuse: The horizontal rule subroutine at line 850 is called over ten times, keeping the separator output consistent and saving repeated PRINT statements.
• Sensitivity loop: Line 830 jumps back to line 220 (re-display of rate, then recalculation) rather than line 1, avoiding a full re-read of DATA and allowing repeated what-if analysis cleanly.
• TAB positioning: Column alignment throughout the output relies entirely on TAB() calls, producing a structured multi-column report without any screen editor tricks.

DATA Layout

Line	Values	Meaning
900	18000, 5	Initial cost C, duration V (5 periods)
910	5000, 5500, 5500, 5000, 5000	Revenue R(1)–R(5)
920	100, 1000, 1200, 1500, 1500	Expenses D(1)–D(5)
930	8000, 12	Residual value RO, discount rate T (%)