Problem 11-107 [LO 11-2] Fire Corp. is considering the purchase of a new piece o

ID: 2573289 • Letter: P

Question

Problem 11-107 [LO 11-2]

Fire Corp. is considering the purchase of a new piece of equipment. The equipment costs $50,000, and will have a salvage value of $5,000 after nine years. Using the new piece of equipment will increase Fire’s annual cash flows by $6,000.

a. What is the payback period for the new piece of equipment? (Round your answer to 2 decimal places.)

b. Suppose that the increase in cash flows were $10,000 in the first year, then decreased by $1,000 each year over the life of the equipment. What is the payback period for the equipment? (Round your answer to 2 decimal places.)

Explanation / Answer

Part a --- Payback Period

Payback period is the lenght of time within which company's initial investment is recovered back to the company.

Payback Period is calculated by two ways:

(i) In case Uniform Cash Flows

(ii) IN case different Cash Flows each year

In Part a of question, the cash flows is uniform

Payback Period (in case of Uniform Cash Flows) = INitial Investment in Equipment / Annual Cash Flows

= $50,000 / $6,000

= 8.33 Years

Part b --- Payback Period in case of different cash flows each year

In this case we need to prepare the Cumulative Cash Flow Statement

Year

Cash Flow

Cumulative Cash Flows

$10,000

$9,000

$19,000

$8,000

$27,000

$7,000

$34,000

$6,000

$40,000

$5,000

$45,000

$4,000

$49,000

$3,000

$52,000

$2,000

$54,000

From the above table, it is clear that Initial Investment $50,000 will be recovered back to the company between 7 and 8 year. Hence the Payback Period is between 7 and 8 year

Upto 7 years company recovers $49,000 and then in Year 8 Cash Flow is $3,000

Payback Period = 7 Years + (50,000 – 49,000) / $3,000

= 7 Years + 0.33 Years

= 7.33 Years

After 7 years, company need only $1,000 ($50,000 – 49,000 recovered upto 7 years) to recover all the initial investment.

Hence, In year 8 the company’s total cash flow is $3,000

So, we need to find out the time to recover $1,000

IN 1 year total recovery = $3,000

So the time to recover $1,000 = $1,000 / 3000 = 0.33

Hope the above calculations, working and explanations are clear to you and help you in understanding the concept of question.... please rate my answer...in case any doubt, post a comment and I will try to resolve the doubt ASAP…thank you