Home ownership is widely regarded as one of the key pillars of American dream and middle-class lifestyle. However, is it a good decision on purely financial considerations?
Read (and watch) the following articles from WSJ and elsewhere discussing that it is potentially more advantageous (financially) to rent rather than buy:
Assumptions:
Questions to answer:
it is financially better to buy. $1.18M net worth vs ≈ $0.85M for 30-yr buy and ≈ $0.52M for 15-yr buy
Is it better to choose a 15-year or 30-year mortgage (6.6%: $2,050 w/ 20% down ($80,000)) ?
yes, it is better to choose 30-year mortage
At what rent would a buyer/renter be indifferent between buying with a 15-year mortgage or renting?
2810 dollars/ month
At what interest rate would a buyer/renter be indifferent between buying with a 30-year mortgage or renting?
4.9 percent
400000*0.01## [1] 400050*30## [1] 1500# -----------------------------
# Car Scenario Setup
# -----------------------------
car_price <- 11000 # used car cost
fees_taxes <- 2000
total_cash_cost <- car_price + fees_taxes # if buying outright
loan_amount <- 13000 # if financing
loan_rate <- 0.08 # 8% APR
loan_term <- 5 # years
loan_months <- loan_term * 12
loan_payment <- 263.59 # given monthly payment
car_depreciation <- 0.05 # 5% per year
car_annual_cost <- 500 # owners hip costs
rent_price <- 442 # Turo monthly rent
inv_return <- 0.09 # 9% investment return
# Function to compute present value of a stream of payments
pv_annuity <- function(payment, rate, n) {
payment * (1 - (1 + rate)^(-n)) / rate
}
pv_rent <- pv_annuity(rent_price, inv_return/12, loan_months)
# PV of owning (car purchase now + annual costs + depreciation loss)
pv_own <- total_cash_cost + pv_annuity(car_annual_cost, inv_return, loan_term)
pv_rent## [1] 21292.63pv_own## [1] 14944.83#Q2
# PV of loan payments
pv_loan <- pv_annuity(loan_payment, inv_return/12, loan_months)
# Buying outright (lump sum)
pv_cash <- total_cash_cost
pv_cash## [1] 13000pv_loan## [1] 12698.02#question 3
# Solve for indifference rent
indifference_rent <- function(target_pv, rate, n) {
target_pv * rate / (1 - (1 + rate)^(-n))
}
rent_equal <- indifference_rent(pv_loan, inv_return/12, loan_months)
rent_equal## [1] 263.59#q4
# Future value if cash invested instead of buying
fv_invest <- total_cash_cost * (1 + inv_return)^loan_term
fv_invest## [1] 20002.11Assumptions:
Car: Used 2018 or 2019 Chevrolet Bolt EV LT
Price of used car: $11,000
Buying fees and taxes: $2,000 (loan would be $13k with $0 down)
Expected car depreciation: 5% per year
Possible loan term: 263.59 monthly for 5 years (60 months) with $0 down and assuming 8% interest
Car ownership costs: $500 per year
Alternative option to rent on Turo (in Denver, I found $442 per month with multiple month discount)
Assume any difference that is not used for rent or buying a home is invested in stock market with expected 9% return.
Questions to answer:
Is it financially better to buy or rent this car?
It’s financially better to buy this car outright. ( calculations are shown in the code)
Is it better to buy the car outright without a loan or have 6 year financing?
Having 6 years of financing is actually better as the money could be used to generate money in the stock market with an expected return of 9 percent.
# Assumptions
car_price <- 11000
fees <- 2000
total_cash <- car_price + fees # $13k upfront
depr_rate <- 0.05
loan_payment <- 263.59
loan_months <- 60
loan_rate <- 0.08
ownership_cost <- 500
rent_monthly <- 442
inv_return <- 0.09
years <- 5
# Depreciated resale value after 5 years
resale_value <- total_cash * (1 - depr_rate)^years
# Buying outright
buy_cost <- total_cash + ownership_cost * years - resale_value
# Financing total payments
loan_total <- loan_payment * loan_months
finance_cost <- loan_total + ownership_cost * years - resale_value
# Renting total
rent_cost <- rent_monthly * 12 * years
# Indifference rent price (monthly)
indifferent_rent <- finance_cost / (years * 12)
# Output
list(
resale_value = resale_value,
buy_cost = buy_cost,
finance_cost = finance_cost,
rent_cost = rent_cost,
indifferent_rent = indifferent_rent
)## $resale_value
## [1] 10059.15
##
## $buy_cost
## [1] 5440.848
##
## $finance_cost
## [1] 8256.248
##
## $rent_cost
## [1] 26520
##
## $indifferent_rent
## [1] 137.6041Under what rent price, would a consumer be indifferent between renting vs financing?
At $ 136/month , a consumer would be indifferent.
Does having more cash on hand at the beginning change your calculation and decision?
Yes. Having more cash available at the outset directly affects the choice. If a consumer has sufficient cash reserves, buying the car outright is generally preferable, as it avoids paying interest on a loan and simplifies ownership