Courses · Business Mathematics · Week 13

Depreciation & Book Value

Week 13 of Business Mathematics, a fifteen-week course taught through Food Truck Wars, a live business simulation. Free to read; the practice boxes check your arithmetic as you go.

Your truck loses $100 of value every day, even on days it never leaves the lot. So why is the truck you started with still worth $5,000?

Learning objectives. After this week you can (1) compute straight-line depreciation for any truck you own; (2) apply the $5,000 floor and the dealer's 60% to get book value and resale price; and (3) compute your team's net worth.

Remember this: a truck loses $100 a day on paper, but its book value never drops below $5,000.

1) Assets wear out: the ledger should say so

Days owned = Today's day − Day you bought it
Straight-line value = $10,000 − $100 × Days owned

Depreciation spreads an asset's cost over its life. Your trucks lose the same $100 every day. A truck bought on day 60 is, on day 91, 91 − 60 = 31 days old, with a straight-line value of 10,000 − 3,100 = $6,900. Your founding truck was bought on day 0, so its days owned is just today's day number. (Outside the sim the same idea reads (Cost − Salvage) ÷ Life: a $12,000 oven with $2,000 salvage over 5 years loses $2,000 a year.)

Try it

A $10,000 truck loses $100 a day and you have owned it 30 days. It never falls below $5,000.

Book value = Cost − ($100 × Days), floored at $5,000

Fill in the boxes.

2) The sim's schedule: this is really happening to your trucks

Book value = the straight-line value, but never below $5,000
Dealer price = 60% of book value (10% if the truck is broken)

The straight line keeps falling. Book value stops at a $5,000 floor, which a truck reaches after 50 days. Same day, same truck, two numbers:

Days ownedStraight-line valueBook valueDealer pays (60%)
0$10,000$10,000$6,000
25$7,500$7,500$4,500
50$5,000$5,000$3,000
91$900$5,000$3,000

At 91 days the straight line says $900, but the truck is carried at $5,000. That gap is the floor at work. A broken truck, in the shop or gone for good, fetches only 10% of book. Your founding truck can never be sold, but you can still work out what the dealer would pay for it.

Try it

The dealer offers 60% of a $7,000 book value.

Dealer offer = Book value × 60%

Fill in the boxes.

3) Net worth: what the leaderboard really ranks

Net Worth = Cash + Book Value of all trucks owned

Cash $20,000 and trucks booked at $5,000 and $6,900: net worth is $31,900. Buying a truck moves $10,000 from cash into a truck booked at $10,000, so net worth does not change that day. Selling one booked at $8,000 brings in 0.60 × 8,000 = $4,800 cash, but the $8,000 truck is gone: net worth drops $3,200. Depreciation never shows up as a cost on your Daily Report. You see it only in net worth.

Quick self-check

You bought Truck 2 on day 22. Today is day 57. (a) Days owned? (b) Straight-line value? (c) Book value? (d) Dealer price if it is working? (Answers: 35; 10,000 − 3,500 = $6,500; $6,500, still above the floor; 0.60 × 6,500 = $3,900.)

Same truck, but it is permanently broken and sits idle. Why sell it for 10% of book instead of keeping it? (Answer: it earns nothing but still pays its idle costs every day. Selling stops that.)

Common mistakes

  • Thinking book value is the sale price. The dealer pays 60% of book, or 10% if broken.
  • Letting book value fall below $5,000. The straight line can; book value cannot.
  • Looking for depreciation on the Daily Report. It is not a cost there; it shows in net worth.

This week in the arena

Pick one truck you own. Write down the day you bought it and today's day, then work out its days owned, straight-line value, book value and dealer price. Then add up cash plus the book value of every truck. Does it match your net worth on the leaderboard?

In the course, the reading is where the week starts

Students who take Business Mathematics on Extrapoli run a business in Food Truck Wars all term. Each week pairs this reading with a quiz and a two-part assignment worked from the numbers their own team produced in the simulation, and the numbers are graded automatically against the simulation that team actually ran.