Example Payback period of a new machine Let’s say that the owner of Perfect Images Salon is considering the purchase of a new tanning bed. It costs $10,000 and is likely to bring in after-tax cash inflows of $4,000 in the first year, $4,500 in the second year, $10,000 in the 3rd year, and $8,000 in the 4th The firm has a policy of buying equipment only if the payback period is 2 years or less. Calculate the payback period of the tanning bed and state whether the owner would buy it or not. Calculate the discounted payback period of the tanning bed, stated in Example 1 above, by using a discount rate of 10%.

Payback period = Year before payback + Amount left to be paid back / Cashflow in year of payback

In year 2, the bed would have paid back:

= 4,000 + 4,500

= $8,500

Would be left with:

= 10,000 - 8,500

= $1,500

Payback period = 2 + 1,500 / 10,000

= 2.15 years

Company will not buy as payback period is more than 2 years.

Discount the cashflows first:

Year 1 = 4.000 / 1.1 = $3,636.36

Year 2 = 4,500 / 1.1² = $3,719

Year 3 = 10,000 / 1.1³ = $7,513.15

Year 4 = 8,000 / 1.1⁴ = $5,464.11

Discounted payback period = Year before payback + Amount left to be paid back / Cashflow in year of payback

= 2 + (10,000 - 3,636.36 - 3,719) / 7,513.15

= 2 + 2,644.64 / 7,513.15

= 2.35 years

odd consecutive integers are odd integers that follow each other. they have a difference of 2 between every two numbers. if n is an odd integer, then n, n+2, n+4 and n+6 will be odd consecutive integers. the first number in the pattern is always the variable on its own or in this case, "n". examples.

u = 30

continuing your method

= +

subtract from both sides

= - thus

= -

= ⇒ u = 30