Cashflow Crate

Provides core utilities for basic discounted-cashflow analysis.

Present Value Calculations

Single Cashflow

The cal_pv function evaluates the present value of a single cashflow observed at time t, where t = 0 represents the present period.

PV = \frac{cashflow_t}{(1 + rate)^t}

Variables

• PV is the present value of the evaluated cashflow at t = 0
• cashflow_t is the cashflow received at timestep t
• rate is the discount rate applied to future cashflows

Multi-period Discounted Cashflow

The cal_pv_from_cf function evaluates the present value of a series of cashflows using a fixed discount rate.

PV = \sum_{t=0}^{T}{\frac{cashflow_t}{(1 + rate)^t}}

Variables

• PV is the total present value of the cashflow series at t = 0
• T is the final timestep in the series
• rate is the discount rate applied uniformly across the full horizon

The series is zero-indexed. The first element is therefore treated as the cashflow at t = 0.

Uniform Cashflow Required to Reach a Target Present Value

The pv_unispread function solves for a fixed nominal cashflow that produces a target present value across a payment horizon.

cashflow = target_PV_{t = 0} \times \left(\sum_{t = 0}^{T}{\frac{1}{(1 + rate)^t}}\right)^{-1}

Variables

• target_PV_{t = 0} is the desired present value at t = 0
• cashflow is the fixed nominal payment made at each timestep in the horizon
• T is the final timestep in the payment schedule
• rate is the discount rate applied to each payment

Notes

When calculating a uniform cashflow, an important modelling choice is whether to include an undiscounted payment at t = 0. The pv_unispread function exposes this as an option so the caller can decide whether the first period is included.