Depreciation & interest for medical equipment

What this vignette covers

• The formula and meaning of the annuity factor and the annual depreciation and interest charge.
• How to call depreciation_interest() and interpret its outputs.
• Edge cases: zero interest rate and validation checks.

Background & formulas

Let:

• \(k\) = annual depreciation and interest costs,
• \(V\) = replacement value,
• \(R\) = residual value at end of period,
• \(n\) = depreciation period (years),
• \(i\) = annual interest rate (decimal),
• \(a_{n,i}\) = annuity factor.

Annual depreciation + interest:

\(k = \frac{V - \frac{R}{(1 + i)^N}}{a_{n,i}}\).

Annuity factor:

\(a_{n,i} = \frac{1}{i}*\bigg(1-\frac{1}{(1 + i)^{n}}\bigg)\).

Quick starts

Default (returns a data frame)

depreciation_interest(
  v_replace_val = 50000, # replacement value 
  r_salvage_val = 5000   # salvage value at end of period 
)
#>   Annuity factor Yearly depreciation and interest costs
#> 1       8.752064                               5266.644

Only the annuity factor

depreciation_interest(
  v_replace_val = 50000,
  r_salvage_val = 5000,
  output = "annuity_factor"
)
#> [1] 8.752064

Only the annual cost (k)

depreciation_interest(
  v_replace_val = 50000,
  r_salvage_val = 5000,
  output = "annual_cost"
)
#> [1] 5266.644

Zero‑interest edge case

When \(i\) = 0, the function uses the mathematical limit:

• \(a = n\),
• \(k = (V - R)/n\).

depreciation_interest(
  v_replace_val = 50000,
  r_salvage_val = 5000,
  n_amortisation_period = 8,
  i_interest_rt = 0,
  output = "dataframe"
)
#>   Annuity factor Yearly depreciation and interest costs
#> 1              8                                   5625

Input validation & common messages

• v_replace_val must be a single positive number; r_salvage_val a non‑negative number.
• n_amortisation_period must be > 0; i_interest_rt must be ≥ 0.
• If salvage value exceeds replacement value, a warning is raised (allowed, but uncommon).

Example (triggers an error):

depreciation_interest(
  v_replace_val = 50000,
  r_salvage_val = -1
)
#> Error: `r_salvage_val` must be a single non-negative number.