Present value of cash flows using spot rates

Discounts deterministic cash flows using spot rates matched to their maturities.

Usage

pv_spot_cashflows(
  amounts,
  times,
  spot,
  compounding = c("annual", "semiannual")
)

Arguments

amounts

Numeric vector of cash flow amounts.

times

Numeric vector of payment times in years.

spot

Numeric vector of spot rates matched elementwise to times. Use 0 for any time-0 entry.

compounding

Either "annual" or "semiannual".

Value

A numeric scalar.

Details

For annual compounding, each positive-time cash flow at time \(t\) is discounted by \((1+z_t)^{-t}\).

For semiannual nominal compounding, each positive-time cash flow at time \(t\) is discounted by \((1+z_t/2)^{-2t}\).

Time-0 cash flows are left undiscounted.

Examples

pv_spot_cashflows(
  amounts = c(200000, 50000, 50000, 100000),
  times   = c(0, 0.5, 1, 2),
  spot    = c(0, 0.02440, 0.02601, 0.02936),
  compounding = "semiannual"
)
#> [1] 392459.1