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NPV & Payback

lesson · about 3 minutes

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

Pen and paper is fine · no calculator needed why?

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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.

  1. Divide the cost by the yearly savings.
  2. 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?

  1. $9,000 ÷ $2,000 = 4.5 years.

Answer: 4.5

Discount each flow, then subtract

NPV with one or two future payoffs.

  1. Divide a payoff one year out by 1 plus the rate.
  2. Divide a payoff two years out by that factor twice.
  3. 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. $1,100 ÷ 1.1 = $1,000.
  2. $1,815 ÷ 1.21 = $1,500.
  3. $1,000 + $1,500 − $2,200 = $300.

Answer: $300

watch out for

practice

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Simple payback period

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

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

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?

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.

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