Question

Filkins Fabric Company is considering the replacement of its old, fully depreciated knitting machine. Two new models are available: Machine 190-3, which has a cost of $190,000, a 3-year expected life, and after-tax cash flows (labor savings and depreciation) of $87,000 per year; and Machine 360-6, which has a cost of $360,000, a 6-year life, and after-tax cash flows of $98,300 per year. Knitting machine prices are not expected to rise, because inflation will be offset by cheaper components (microprocessors) used in the machines.

Assume that Filkins' cost of capital is 14%. Calculate the two projects' NPVs. Round your answers to the nearest cent.

Machine 190-3    $   

Machine 360-6    $   

Should the firm replace its old knitting machine, and, if so, which new machine should it use?
-Select-Yes. Machine 190-3Yes. Machine 360-6NoItem 3

By how much would the value of the company increase if it accepted the better machine? Round your answer to the nearest cent.
$  

What is the equivalent annual annuity for each machine? Round your answer to the nearest cent.

Machine 190-3	$
Machine 360-6	$

Answer 1

Net Present Value (NPV) of Machine 190-3   

Year	Annual cash flows ($)	Present Value Factor (PVF) at 14.00%	Present Value of annual cash flows ($) [Annual cash flow x PVF]
1	87,000	0.8771930	76,315.79
2	87,000	0.7694675	66,943.67
3	87,000	0.6749715	58,722.52
TOTAL	2.3216320	201,981.99

Net Present Value = Present Value of annual cash inflows – Initial Investment

= $201,981.99 - $190,000

= $11,981.99

Net Present Value (NPV) of Machine 360-6

Year	Annual cash flows ($)	Present Value Factor (PVF) at 14.00%	Present Value of annual cash flows ($) [Annual cash flow x PVF]
1	98,300	0.8771930	86,228.07
2	98,300	0.7694675	75,638.66
3	98,300	0.6749715	66,349.70
4	98,300	0.5920803	58,201.49
5	98,300	0.5193687	51,053.94
6	98,300	0.4555865	44,784.16
TOTAL	3.8886675	3,82,256.02

Net Present Value = Present Value of annual cash inflows – Initial Investment

= $382,256.02 - $360,000

= $22,256.02

DECISION

“YES”. The firm should replace its old knitting machine and they should use the “Machine 360-6”, since it has the higher NPV of $22,256.02.

Increase in the Value of the Company

Increase in the Value of the Company = NPV of Machine 360-6 – NPV of Machine 190.3

= $22,256.02 - $11,981.99

= $10,274.03

The Equivalent Annual Annuity (EAA) for the Machine 190-3

The Equivalent Annual Annuity (EAA) = NPV / [PVIFA 14.00%, 3 Years]

= $11,981.99 / 2.3216320

= $5,161.02

The Equivalent Annual Annuity (EAA) for the Machine 360-6

The Equivalent Annual Annuity (EAA) = NPV / [PVIFA 14.00%, 6 Years]

= $22,256.02 / 3.8886675

= $5,723.30

NOTE    

The Formula for calculating the Present Value Factor is [1/(1 + r)n], Where “r” is the Discount/Interest Rate and “n” is the number of years.