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NPV & Payback

level 40 course

Is an investment worth it once timing is counted? Payback versus net present value.

Pen and paper is fine · no calculator needed why?

Opens at level 40.

Builds on: Present Value (not open yet)

the lesson

The idea, the techniques and a tip for each skill, right here. The Learn page adds worked examples for every skill and untimed practice.

Read the lesson · about 3 minutes

The idea

Two questions decide whether an investment pays. Simple payback asks how many years the savings take to repay the cost. It is quick, but it treats a dollar in year 4 like a dollar today, and it ignores everything after the cost is back.

Net present value (NPV) discounts each future cash flow to today at a stated discount rate, adds them up, and subtracts the cost paid now. A positive NPV means the project beats that rate; a negative one means it falls short. It is an estimate, not a promise.

When the two disagree, go with NPV: it counts every dollar and when it arrives.

Techniques

Payback: cost over yearly savings

How long until savings repay a cost.

Divide the cost by the yearly savings.
The answer is in years, and half years count.

worked example

Example: A print shop buys a machine for $9,000 that saves $2,000 a year. What is the simple payback period in years?

$9,000 ÷ $2,000 = 4.5 years.

Answer: 4.5

Discount each flow, then subtract

NPV with one or two future payoffs.

Divide a payoff one year out by 1 plus the rate.
Divide a payoff two years out by that factor twice.
Add the present values and subtract the cost. A negative NPV takes a minus sign.

worked example

Example: A café project costs $2,200 now, then pays $1,100 after one year and $1,815 after two years. Assume a 10% annual discount rate. What is its NPV?

$1,100 ÷ 1.1 = $1,000.
$1,815 ÷ 1.21 = $1,500.
$1,000 + $1,500 − $2,200 = $300.

Answer: $300

Tips by skill

TipSimple payback period: Cost ÷ yearly savings. The cost, the bigger number, goes on top.
TipNPV with one future payoff: Divide the payoff by 1 plus the rate, then subtract the cost. It can be negative.
TipNPV with two payoffs: Discount the year-1 payoff once and the year-2 payoff twice, add them, then subtract the cost.
TipPayback or NPV?: More value means the higher NPV, even when its payback is slower.

Watch out for

Dividing the savings by the cost. Payback puts the cost on top.
Subtracting the cost from the raw payoffs without discounting them.
Dividing a year-2 payoff by 1 plus the rate only once.
Choosing the faster payback when its NPV is lower. Payback ignores everything after the cost comes back.

skills · practice stats

From rounds of this course only: box, review and test-out answers are left out. Once a skill has 40 tries, it compares your first 20 tries with your last 20.

Simple payback period par 13 s not tried yet
worked example
A machine costs $48,000 and saves $8,000 a year. What is the simple payback period in years?

Answer: 6
1. Payback = cost ÷ yearly savings = $48,000 ÷ $8,000 = 6 years.
2. It ignores the time value of money and everything after payback.
NPV with one future payoff par 20 s not tried yet
worked example
A project costs $3,700 now and pays $4,125 one year later. Assume a 25% annual discount rate. What is its NPV? (Use a minus sign if negative.)

Answer: -$400.00
1. Today's value of the payoff: $4,125 ÷ 1.25 = $3,300.
2. NPV = $3,300 − $3,700 = −$400.
NPV with two payoffs par 30 s not tried yet
worked example
A project costs $9,700 now, then pays $990 after one year and $11,858 after two years. Assume a 10% annual discount rate. What is its NPV? (Use a minus sign if negative.)

Answer: $1,000.00
1. Year 1: $990 ÷ 1.1 = $900.
2. Year 2: $11,858 ÷ 1.21 = $9,800.
3. NPV = $900 + $9,800 − $9,700 = $1,000.
Payback or NPV? par 22 s not tried yet
worked example
Project A pays back in 4 years and has an NPV of $3,400. Project B pays back in 2 years and has an NPV of $4,900, at the same discount rate. Which creates more value?
1. Project B
2. Neither can be judged without payback
3. Project A
4. They create the same value
Answer: Project B
1. NPV counts every cash flow and when it arrives; payback only asks how fast the cost comes back and ignores the rest.
2. Project B's NPV ($4,900) is higher than Project A's ($3,400), so B creates more value.

rest ladder

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