Car purchase: Auto Loan vs Cash Purchase - Capital Allocation

capital.py

# Auto loan cost comparison
# When debt can be obtained at low interest rates, using cheap debt 
# and investing the cash that would have been used otherwise) can be 
# more tactical, than just deploying cash where cheap debt can suffice.
import math 

auto_rate_table = [
    0.0219, 0.0429, # Old vs New Rates, Credit Union 1
    0.0289, 0.0319, # Old vs New Rates, Credit Uni$on 2
    0.0449, 0.0524 # Old vs New Rates, National Bank
]

def auto_loan_cost(auto_cost, months, compound_rate=0.03):
  # 10-year Treasury yield is currently at 3.2%~. Assuming this holds, 
  # reinvesting interest coupons from US Treasury bonds ("risk-free" investment 
  # issued by US government, which also issues US dollars), we can get a 3% CAGR~
  fig, fig_ax1 = plt.subplots()
  num_months = np.arange(months) + 1

  for interest_rate in auto_rate_table:
    # Auto loan is simple, not compounded interest (interest calculated monthly)
    # auto_loan_interest[x] = total paid interest up to that point, on month x
    auto_loan_interest = np.cumsum(numpy_financial.ipmt(
        rate=interest_rate/12, per=num_months, nper=months, pv=-1*auto_cost,
    ))

    # Option A: Don't buy the car in cash. Instead, invest the cash that would 
    # have been used for car purchase (preventing capital from being locked in)
    # Net profit after taking into account the downsides of auto loan: 
    # * Monthly payment interest could have been invested over time
    # * Principal of debt owed against bank
    option_a = numpy_financial.fv(
        compound_rate/12, nper=num_months, 
        pmt=0, pv=-1*auto_cost
    ) - (
        auto_loan_interest * np.full(
            months, 1+compound_rate/12
        ) ** np.arange(months)
    ) - auto_cost
    fig_ax1.plot(
        num_months, option_a, '--', 
        label='{0}% interest'.format(np.round(interest_rate*100, 2))
    )
    
  # Option B: Buy the car in cash outright, no investable money as our capital 
  # was locked in a cash-based car purchase
  fig_ax1.plot(num_months, np.zeros(months), '-', label='Cash Purchase')

  fig_ax1.set_xlabel('Months')
  fig_ax1.set_ylabel('Net Profit, $')
  fig_ax1.set_title('Car Purchase: Auto Loan vs Cash\n3% CAGR on investments')
  fig_ax1.legend()
  fig_ax1.yaxis.set_major_formatter(ticker.FormatStrFormatter('$%.0f'))

auto_loan_cost(15000, 72)