Discounted cash flow: present value of a single flow, net present value of a cash-flow stream, and a simple payback-period count

npv.cell

// Discounted cash flow: present value of a single flow, net present value
// of a cash-flow stream, and a simple payback-period count. Discounting
// over an index range, sum() of derived discounted flows.

cell DCF {
    face {
        signal present_value(cash: Float, rate: Float, period: Int) -> Float
        signal npv(rate: Float, flows: List) -> Float
        signal payback_period(flows: List) -> Int
        signal profitable(rate: Float, flows: List) -> Bool
    }

    // PV = CF / (1+r)^t
    on present_value(cash: Float, rate: Float, period: Int) {
        return cash / pow(1.0 + rate, period)
    }

    // NPV = sum_t CF_t / (1+r)^t, flows[0] at t=0 (usually the outlay)
    on npv(rate: Float, flows: List) {
        let total = 0.0
        for t in range(0, len(flows)) {
            total = total + present_value(flows[t], rate, t)
        }
        return total
    }

    // first period index where cumulative (undiscounted) flow turns non-negative
    on payback_period(flows: List) {
        let cum = 0.0
        let result = -1
        for t in range(0, len(flows)) {
            cum = cum + flows[t]
            if cum >= 0.0 && result == -1 {
                result = t
            }
        }
        return result
    }

    on profitable(rate: Float, flows: List) {
        return npv(rate, flows) > 0.0
    }
}

cell test DCFTests {
    rules {
        // PV of 110 one year out at 10% = 100
        assert abs(present_value(110.0, 0.10, 1) - 100.0) < 0.0001
        // invest 100 now, get 60 + 60 → positive NPV at 10%
        assert npv(0.10, list(-100.0, 60.0, 60.0)) > 0.0
        // a money-losing project
        assert profitable(0.10, list(-100.0, 30.0, 30.0)) == false
        // payback: -100, 60, 60 → cumulative crosses zero at period 2
        assert payback_period(list(-100.0, 60.0, 60.0)) == 2
    }
}