The Delivery Van: Two Financing Offers
Marcia runs a small bakery and needs a delivery van with a cash price of $48,000. She has $10,000 in savings and two written offers on the table.
Dealer A: pay a 20% deposit, then repay the balance plus simple interest at 12% per annum over 3 years in equal monthly instalments.
Bank (Dealer B): pay a 15% deposit, then repay the balance plus simple interest at 9.5% per annum over 4 years in equal monthly instalments, plus a once-only processing fee of $450.
Insurance and registration cost the same under both offers and are paid separately, so ignore them. Marcia estimates the van will lose 18% of its value each year on the reducing balance. Her takings, after all other costs, leave her about $1,600 a month to service a van payment. She intends to keep the van for at least four years and does not want to borrow any more than she must.
1. Calculate the total amount Marcia pays under each offer (including deposits and fees) and recommend an offer if cost alone is the criterion.
Read the worked answer
Dealer A Deposit = 20% × 48,000 = $9,600 Balance borrowed = 48,000 − 9,600 = $38,400 Interest = P × r × t = 38,400 × 0.12 × 3 = $13,824 Total credit repaid = 38,400 + 13,824 = $52,224 Monthly instalment = 52,224 ÷ 36 = $1,450.67 Total paid = 9,600 + 52,224 = $61,824
Bank (Dealer B) Deposit = 15% × 48,000 = $7,200 Balance = $40,800 Interest = 40,800 × 0.095 × 4 = $15,504 Total credit = 40,800 + 15,504 = $56,304 Monthly instalment = 56,304 ÷ 48 = $1,173.00 Total paid = 7,200 + 56,304 + 450 = $63,954
Comparison: Dealer A is cheaper by 63,954 − 61,824 = $2,130, so on cost alone choose Dealer A. Note the trade-off: the shorter term and smaller deposit make the monthly figure on A $277.67 higher, but it is still well inside her $1,600 capacity.
2. Marcia wants the monthly instalment on the Bank's offer to be no more than $1,000. Using her savings, how much extra deposit would she need to pay, and is the plan feasible?
Read the worked answer
Work backwards from the instalment.
Over 48 months the total credit she can repay is 1,000 × 48 = $48,000.
With simple interest at 9.5% for 4 years, the credit equals the borrowed amount × (1 + 0.095 × 4) = 1.38 × amount borrowed.
Amount borrowed = 48,000 ÷ 1.38 = $34,782.61
So her deposit must be 48,000 − 34,782.61 = $13,217.39.
Her required deposit is 15% = $7,200, so the extra needed is 13,217.39 − 7,200 = $6,017.39, i.e. about $6,020.
Feasibility: she has $10,000 in savings, so paying $6,017.39 extra leaves $3,982.61. From that remainder she must still find the $450 processing fee, leaving roughly $3,533 as a cash buffer. The plan works, but it drains most of her reserve - and because the extra deposit comes from savings rather than borrowing, it does not change the interest rate, only the amount on which interest is charged.
3. After exactly 2 years of payments under Dealer A, find the outstanding balance on the van and the van's book value, then comment on Marcia's position.
Read the worked answer
Outstanding balance (Dealer A) Total credit = $52,224; instalment = $1,450.67 Paid in 24 months = 24 × 1,450.67 = $34,816.08 Outstanding = 52,224 − 34,816.08 = $17,407.92 (If the lender rounds the instalment up to $1,451, the balance is about $17,400 - a difference of a few dollars.)
Book value after 2 years (18% depreciation on the reducing balance): Value = 48,000 × (1 − 0.18)² = 48,000 × 0.82² = 48,000 × 0.6724 = $32,275.20
Equity = value − amount owed = 32,275.20 − 17,407.92 = $14,867.28
Comment: Marcia is not 'underwater'. If she sold the van at book value she could clear the debt and keep about $14,867, which is a cushion against the risk of the bakery failing. This is a real argument in favour of the shorter, dearer Dealer A option: it builds equity nearly three times faster than the 4-year loan would. Note also that depreciation is an estimate, not a guarantee - a poor resale market would reduce the equity but would not change the amount owed.