Question

A farm owner is considering replacing his obsolete tractor with one of two new state-of-the-tractors. This new machine would cost $125,000 and would have a ten-year useful life. Unfortunately, the new machine would have no salvage value but would result in annual cost savings of $23,000 per year. The current old tractor can be sold now for $10,000. The farm owner’s Cost of Capital is 10%. The farm owner uses the straight line method of depreciation (this depreciation information is needed only for calculating the “Simple Rate of Return” in Question #3).

a.) Calculate the Net Present Value of replacing the tractor .

b.) Based on this method of comparison, would you recommend replacing the tractor? Why?

Question #3

Based on the above information for Question #2 and your solution to that question,

calculate the following associated with replacing the tractor:

c.) The Profitability Index

d.) The Payback Period

e.) Simple Rate of Return

Answer 1

Solution:

Part a – Net Present Value

Step 1 -	Calculation of Initial Cash Outflow required
		$$
	Cost of New Machine	$125,000
	Less: Anticipated Sale Proceeds from Old Tractor	($10,000)
	Net Initial Cash Outflow required	$115,000

Step 2 -	Calculation of Net Present Value
Year		Cash Flow	PV factor @ 10%	Present Value
0	Initial Cash Outflow	($115,000)	1.000	($115,000)
1	Annual Cost Saving (Annual Inflow)	$23,000	0.909	$20,909
2	Annual Cost Saving (Annual Inflow)	$23,000	0.826	$19,008
3	Annual Cost Saving (Annual Inflow)	$23,000	0.751	$17,280
4	Annual Cost Saving (Annual Inflow)	$23,000	0.683	$15,709
5	Annual Cost Saving (Annual Inflow)	$23,000	0.621	$14,281
6	Annual Cost Saving (Annual Inflow)	$23,000	0.564	$12,983
7	Annual Cost Saving (Annual Inflow)	$23,000	0.513	$11,803
8	Annual Cost Saving (Annual Inflow)	$23,000	0.467	$10,730
9	Annual Cost Saving (Annual Inflow)	$23,000	0.424	$9,754
10	Annual Cost Saving (Annual Inflow)	$23,000	0.386	$8,867
	Net Present Value			$26,325

Net Present Value = $26,325

Part b – Yes, it is recommended to replace the tractor, since the NPV from New Machine is positive.

Part c –

Profitability Index = Present Value of Cash Inflow / Initial Cash Outflow

Present Value of Cash Inflow = Net Present Value + Initial Cash Outflow

= $26,325 + $115,000

= $141,325

Profitability Index = Present Value of Cash Inflow 141,325 / Initial Cash Outflow115,000

= 1.23

Part d –

Payback Period is the length of time within which initial investment or cost is returned back to the company.

Payback Period = Initial Cash Outflow / Annual Cash Flow

= $115,000 / $23,000

= 5 Years

Part e – Simple Rate of Return

Simple Rate of Return = Net Income after tax and depreciation / Initial Investment x 100

Net Income After Depreciation and Tax

Annual Cost saving	$23,000
Less: Annual Depreciation ($125,000 Cost of Machine – Salvage Value 0) / Useful life 10)	($12,500)
Net Income	$10,500

Simple Rate of Return = Net Income after tax and depreciation $10,500 / Initial Investment $115,000 x 100

= 9.13%

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