Question

A firm is considering an investment in a new machine with a price of $16.1 million to replace its existing machine. The current machine has a book value of $5.8 million and a market value of $4.5 million. The new machine is expected to have a 4-year life, and the old machine has four years left in which it can be used. If the firm replaces the old machine with the new machine, it expects to save $6.5 million in operating costs each year over the next four years. Both machines will have no salvage value in four years. If the firm purchases the new machine, it will also need an investment of $290,000 in net working capital. The required return on the investment is 12 percent and the tax rate is 24 percent. The company uses straight-line depreciation.

     

What is the NPV of the decision to purchase a new machine? (Do not round intermediate calculations and enter your answer in dollars, not millions, rounded to 2 decimal places, e.g., 1,234,567.89.)

What is the IRR of the decision to purchase a new machine? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

What is the NPV of the decision to purchase the old machine? (A negative amount should be indicated by a minus sign. Do not round intermediate calculations and enter your answer in dollars, not millions, rounded to 2 decimal places, e.g., 1,234,567.89.)

What is the IRR of the decision to purchase the old machine? (A negative amount should be indicated by a minus sign. Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16. )

Answer 1

Option- 1 Buy New machine

In this question after reading is confusing that company have old machine or not so we calculate NPV and IRR of ner projecta with both way.

(1) Company have old machine (So sold old machine and buy new machine)

Calculation of NPV
Year	Cashflow	DF @12%	PV
0	($11,578,000)	1.0000	($11,578,000.00)
1	$5,906,000	0.8929	$5,273,214.29
2	$5,906,000	0.7972	$4,708,227.04
3	$5,906,000	0.7118	$4,203,774.14
4	$6,196,000	0.6355	$3,937,670.01
Net Present Value	$6,544,885.48

Calculation of cashflow of New machine
Year	0	1	2	3	4
Saving in operating cost	-	$6,500,000	$6,500,000	$6,500,000	$6,500,000
Less : Depreciation	-	$4,025,000	$4,025,000	$4,025,000	$4,025,000
Saving before tax	-	$2,475,000	$2,475,000	$2,475,000	$2,475,000
Less : Tax @ 24%	-	$594,000	$594,000	$594,000	$594,000
Saving after tax	-	$1,881,000	$1,881,000	$1,881,000	$1,881,000
Add : Depreciation	-	$4,025,000	$4,025,000	$4,025,000	$4,025,000
Cashflow from Saving	-	$5,906,000	$5,906,000	$5,906,000	$5,906,000
Add : Salvage value	$4,812,000	-	-	-	-
Less : Increase in working capital	$290,000	-	-	-	-
Add : Release of working capital	-	-	-	-	$290,000
Less : Initial Investment	$16,100,000	-	-	-	-
Net Cashflow from New machine	($11,578,000)	$5,906,000	$5,906,000	$5,906,000	$6,196,000

Calculation of Salvage value
Book Value	$5,800,000
Less : Market Value	$4,500,000
Capital Loss	$1,300,000
Save Tax on above @24%	$312,000
Net Inflow from salvage
Market value	$4,500,000
Add : Saving on Tax	$312,000
Salvage Value of old machine	$4,812,000

Now calculating IRR

IRR of project means Present Value of cashinflow = Present value of Cash outflow or in other way say that Net Present Value should be '0' (Zero).

So we use two discounting factor, One factor will provide positive NPV mean NPV>0 and second factor will provide Negative NPV mean NPV<0 and interpolate both to get NPV '0' (Zero).

Calculation of NPV @ DF 35%			Calculation of NPV @ DF 37%
Year	Cashflow	DF @35%	PV		Year	Cashflow	DF @37%	PV
0	($11,578,000)	1.0000	($11,578,000.00)		0	($11,578,000)	1.0000	($11,578,000.00)
1	$5,906,000	0.7407	$4,374,814.81		1	$5,906,000	0.7299	$4,310,948.91
2	$5,906,000	0.5487	$3,240,603.57		2	$5,906,000	0.5328	$3,146,678.03
3	$5,906,000	0.4064	$2,400,447.09		3	$5,906,000	0.3889	$2,296,845.28
4	$6,196,000	0.3011	$1,865,418.74		4	$6,196,000	0.2839	$1,758,851.37
Net Present Value	$303,284.21		Net Present Value	($64,676.42)

= 35% + [$303,284.21 / {$303,284.21 - (-$64,676.42)}] x 2%

= 35% + ($303,284.21 / $367,960.63) x 2%

= 35% + 1.6485%

= 36.65%

(2) Company not have old machine

Calculation of NPV
Year	Cashflow	DF @12%	PV
0	($16,390,000)	1.0000	($16,390,000.00)
1	$5,906,000	0.8929	$5,273,214.29
2	$5,906,000	0.7972	$4,708,227.04
3	$5,906,000	0.7118	$4,203,774.14
4	$6,196,000	0.6355	$3,937,670.01
Net Present Value	$1,732,885.48

Calculation of cashflow of New machine
Year	0	1	2	3	4
Saving in operating cost	-	$6,500,000	$6,500,000	$6,500,000	$6,500,000
Less : Depreciation	-	$4,025,000	$4,025,000	$4,025,000	$4,025,000
Saving before tax	-	$2,475,000	$2,475,000	$2,475,000	$2,475,000
Less : Tax @ 24%	-	$594,000	$594,000	$594,000	$594,000
Saving after tax	-	$1,881,000	$1,881,000	$1,881,000	$1,881,000
Add : Depreciation	-	$4,025,000	$4,025,000	$4,025,000	$4,025,000
Cashflow from Saving	-	$5,906,000	$5,906,000	$5,906,000	$5,906,000
Less : Increase in working capital	$290,000	-	-	-	-
Add : Release of working capital	-	-	-	-	$290,000
Less : Initial Investment	$16,100,000	-	-	-	-
Net Cashflow from New machine	($16,390,000)	$5,906,000	$5,906,000	$5,906,000	$6,196,000

Now calculate IRR

Calculation of NPV @ DF 15%			Calculation of NPV @ DF 17%
Year	Cashflow	DF @15%	PV		Year	Cashflow	DF @37%	PV
0	($16,390,000)	1.0000	($16,390,000.00)		0	($16,390,000)	1.0000	($16,390,000.00)
1	$5,906,000	0.8696	$5,135,652.17		1	$5,906,000	0.8547	$5,047,863.25
2	$5,906,000	0.7561	$4,465,784.50		2	$5,906,000	0.7305	$4,314,413.03
3	$5,906,000	0.6575	$3,883,290.87		3	$5,906,000	0.6244	$3,687,532.51
4	$6,196,000	0.5718	$3,542,583.11		4	$6,196,000	0.5337	$3,306,495.70
Net Present Value	$637,310.65		Net Present Value	($33,695.51)

= 15% + [$637,310.65 / {$637,310.65 - (-$33,695.51)}] x 2%

= 15% + ($637,310.65 / $671,006.16) x 2%

= 15% + 1.8996%

= 16.8996% or say 16.90%

Wn:1 Depreciation = Cost of new machine / 4 = $16.1 Million / 4 = $4.025 million

Assume that working capital invested in year 0 or beginning of year-1 and release it at the end of year-4 or beginning of year -5.

Based IRR new machine recommend.

Option -2 Buy old machine

Calculation of NPV
Year	Cashflow	DF @12%	PV
0	($4,500,000)	1.0000	($4,500,000.00)
1	$348,000	0.8929	$310,714.29
2	$348,000	0.7972	$277,423.47
3	$348,000	0.7118	$247,699.53
4	$348,000	0.6355	$221,160.29
Net Present Value	($3,443,002.43)

Calculation of cashflow of New machine
Year	0	1	2	3	4
Saving in operating cost	-	-	-	-	-
Less : Depreciation	-	$1,450,000	$1,450,000	$1,450,000	$1,450,000
Saving before tax	-	($1,450,000)	($1,450,000)	($1,450,000)	($1,450,000)
Less : Tax @ 24%	-	($348,000)	($348,000)	($348,000)	($348,000)
Saving after tax	-	($1,102,000)	($1,102,000)	($1,102,000)	($1,102,000)
Add : Depreciation	-	$1,450,000	$1,450,000	$1,450,000	$1,450,000
Cashflow from Saving of Tax	-	$348,000	$348,000	$348,000	$348,000
Less : Initial Investment	$4,500,000	-	-	-	-
Net Cashflow from New Old	($4,500,000)	$348,000	$348,000	$348,000	$348,000

WN-1 : Depreciation = Book Value / 4 = $5.8 Million / 4 = $1.45 Million

Assume that depreciation for tax purpose on book value.

Calculation of IRR

Calculation of NPV @ DF -51%			Calculation of NPV @ DF -53%
Year	Cashflow	DF @-51%	PV		Year	Cashflow	DF @-53%	PV
0	($4,500,000)	1.0000	($4,500,000.00)		0	($4,500,000)	1.0000	($4,500,000.00)
1	$348,000	1.5100	$525,480.00		1	$348,000	1.5300	$532,440.00
2	$348,000	2.2801	$793,474.80		2	$348,000	2.3409	$814,633.20
3	$348,000	3.4430	$1,198,146.95		3	$348,000	3.5816	$1,246,388.80
4	$348,000	5.1989	$1,809,201.89		4	$348,000	5.4798	$1,906,974.86
Net Present Value	($173,696.36)		Net Present Value	$436.85

= -51% + [-$173,696.36 / {(-$173,696.36) - $436.85}] x -2%

= -51% + (-$173,696.36 / -$174,133.21) x -2%

= -51% - 1.99498%

= -52.995% or say -53.00%

Calculation of NPV
Year	Cashflow	DF @12%	PV
0	($4,500,000)	1.0000	($4,500,000.00)
1	$270,000	0.8929	$241,071.43
2	$270,000	0.7972	$215,242.35
3	$270,000	0.7118	$192,180.67
4	$270,000	0.6355	$171,589.88
Net Present Value	($3,679,915.68)

Calculation of cashflow of New machine
Year	0	1	2	3	4
Saving in operating cost	-	-	-	-	-
Less : Depreciation	-	$1,125,000	$1,125,000	$1,125,000	$1,125,000
Saving before tax	-	($1,125,000)	($1,125,000)	($1,125,000)	($1,125,000)
Less : Tax @ 24%	-	($270,000)	($270,000)	($270,000)	($270,000)
Saving after tax	-	($855,000)	($855,000)	($855,000)	($855,000)
Add : Depreciation	-	$1,125,000	$1,125,000	$1,125,000	$1,125,000
Cashflow from Saving of Tax	-	$270,000	$270,000	$270,000	$270,000
Less : Initial Investment	$4,500,000	-	-	-	-
Net Cashflow from New Old	($4,500,000)	$270,000	$270,000	$270,000	$270,000

WN-1 : Depreciation = Book Value / 4 = $4.5 Million / 4 = $1.125 Million

Assume that depreciation for tax purpose on buying price i.e. market value.

Calculation of NPV @ DF -65%			Calculation of NPV @ DF -68%
Year	Cashflow	DF @-65%	PV		Year	Cashflow	DF @-68%	PV
0	($4,500,000)	1.0000	($4,500,000.00)		0	($4,500,000)	1.0000	($4,500,000.00)
1	$270,000	1.6500	$445,500.00		1	$270,000	1.6800	$453,600.00
2	$270,000	2.7225	$735,075.00		2	$270,000	2.8224	$762,048.00
3	$270,000	4.4921	$1,212,873.75		3	$270,000	4.7416	$1,280,240.64
4	$270,000	7.4120	$2,001,241.69		4	$270,000	7.9659	$2,150,804.28
Net Present Value	($105,309.56)		Net Present Value	$146,692.92

= -65% + [-$105,309.56 / {(-$105,309.56) - $146,692.92}] x -3%

= -65% + (-$105,309.56 / -$252,002.48) x -3%

= -65% - 1.2537%

= -66.2537% or say -66.25%

Based on IRR old machine not recommend.

If any help require please comment i will help you.