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
1
$10,000
$10,000
2
$9,000
$19,000
3
$8,000
$27,000
4
$7,000
$34,000
5
$6,000
$40,000
6
$5,000
$45,000
7
$4,000
$49,000
8
$3,000
$52,000
9
$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
Year
Cash Flow
Cumulative Cash Flows
1
$10,000
$10,000
2
$9,000
$19,000
3
$8,000
$27,000
4
$7,000
$34,000
5
$6,000
$40,000
6
$5,000
$45,000
7
$4,000
$49,000
8
$3,000
$52,000
9
$2,000
$54,000