Sum of the Present Value, by time at which the calculation is performed (tzero input to dynpv())
Arguments
- df
Tibble of class "dynpv" created by
dynpv()orfuturepv()
Details
The Present Value of a cashflow \(p_k\) for the \(u_j\) patients who began treatment at time \(j\) and who are in their \(k\)th timestep of treatment is as follows $$PV(j,k,l) = u_j \cdot p_k \cdot R_{j+k+l-1} \cdot (1+i)^{2-j-k}$$ where \(i\) is the risk-free discount rate per timestep, \(p_k\) is the cashflow amount in today’s money, and \(p_k \cdot R_{j+k+l-1}\) is the nominal amount of the cashflow at the time it is incurred, allowing for an offset of \(l = tzero\).
The total present value by time at which the calculation is performed, \(TPV(l)\), is therefore the sum of \(PV(j,k,l)\) over all \(j\) and \(k\) within the time horizon \(T\), namely: $$TPV(l) = \sum_{j=1}^{T} \sum_{k=1}^{T-j+1} PV(j,k, l) \\ \; = \sum_{j=1}^{T} \sum_{k=1}^{T-j+1} u_j \cdot p_k \cdot R_{l+j+k-1} \cdot (1+i)^{2-j-k}$$