Question

NPVs, IRRs, and MIRRs for Independent Projects

Edelman Engineering is considering including two pieces of equipment, a truck and an overhead pulley system, in this year's capital budget. The projects are independent. The cash outlay for the truck is $18,000, and that for the pulley system is $22,000. The firm's cost of capital is 14%. After-tax cash flows, including depreciation, are as follows:

Year	Truck		Pulley
1	$5,100		$7,500
2	5,100		7,500
3	5,100		7,500
4	5,100		7,500
5	5,100		7,500

Calculate the IRR, the NPV, and the MIRR for each project, and indicate the correct accept/reject decision for each. Do not round intermediate calculations. Round the monetary values to the nearest dollar and percentage values to two decimal places. Use a minus sign to enter negative values, if any.

	Truck			Pulley
	Value	Decision		Value	Decision
IRR	%	-Select-AcceptRejectItem 2		%	-Select-AcceptReject
NPV	$	-Select-AcceptRejectItem 6		$	-Select-AcceptReject
MIRR	%	-Select-AcceptRejectItem 10		%	-Select-AcceptReject

Answer 1

Computation of Net Present value of Truck and Pulley System

Truck
Year	Cash flows	Disc @ 14%	Discounted Cash flow
0	($18,000)	1	($18,000)
1	$5,100	0.877192982	$4,474
2	$5,100	0.769467528	$3,924
3	$5,100	0.674971516	$3,442
4	$5,100	0.592080277	$3,020
5	$5,100	0.519368664	$2,649
		Total	($491)

NPV for Truck is ( $ 491). Since NPV is negitive reject the Project.

Pulley
Year	Cash flows	Disc @ 14%	Discounted Cash flow
0	($22,000)	1	($22,000)
1	$7,500	0.877193	$6,579
2	$7,500	0.769468	$5,771
3	$7,500	0.674972	$5,062
4	$7,500	0.59208	$4,441
5	$7,500	0.519369	$3,895
		Total	$3,748

NPV for Pulley is $ 3748.Since NPV is positive accept the Project.

Computation of IRR for Truck

Let the Discount rate be 12% and 13%( Trial and Error method)

Year	Cash flows	Sisc @ 12%	Discounted Cash flow	Disc @ 13%	Discounted Cash flow
0	($18,000)	1	($18,000)	1	($18,000)
1	$5,100	0.892857	$4,554	0.8849558	$4,513
2	$5,100	0.797194	$4,066	0.7831467	$3,994
3	$5,100	0.71178	$3,630	0.6930502	$3,535
4	$5,100	0.635518	$3,241	0.6133187	$3,128
5	$5,100	0.567427	$2,894	0.5427599	$2,768
			$384		($62)

We know that at IRR , NPV should be 0.

From the above table we can observe that NPV lies between 12%% and 13% rate.

By using the interpolation technique we can find the IRR.

Disc rate	NPV
12%	$384
13%	($62)

For 1% Change in Diiscount rate NPV turns from $ 384 to ( $ 62)

So Change in NPV is $ 384-($62) = $ 446

Change in Disc	Change in NPV
1%	$446
X	$384

X = $ 384/$ 446

X = 0.8609

Hence the IRR is 12.8609 %.Since the Cost of Capital is 14% which is greater than IRR.SO we have to turndown the Project.

Computation of IRR for pulley

Pulley
Year	Cash flows	Disc @ 14%	Discounted Cash flow	Disc @ 20%		Disc @ 21%
0	($22,000)	1	($22,000)	1	($22,000)	1	($22,000)
1	$7,500	0.877193	$6,579	0.8333333	$6,250	0.826446	$6,198
2	$7,500	0.769468	$5,771	0.6944444	$5,208	0.683013	$5,123
3	$7,500	0.674972	$5,062	0.5787037	$4,340	0.564474	$4,234
4	$7,500	0.59208	$4,441	0.4822531	$3,617	0.466507	$3,499
5	$7,500	0.519369	$3,895	0.4018776	$3,014	0.385543	$2,892
		Total	$3,748		$430		($55)

We know that at IRR , NPV should be 0.

From the above table we can observe that NPV lies between 20% and 21% rate.

By using the interpolation technique we can find the IRR.

Disc rate	NPV
20%	$430
21%	($55)

For 1% Change in Diiscount rate NPV turns from $ 430 to ( $ 55)

So Change in NPV is $ 430-($55) = $ 485.

Change in Disc	Change in NPV
1%	$485
X	$430

X = $ 430/$ 485

X = 0.8865

Hence the IRR is 20.8865 %.Since the Cost of Capital is 14% which is less than IRR.SO we can accept the Project.

Computation of the MIRR for Truck

Truck
Year	Cash flows	Future value factor	Future value factor	Terminal values
1	$5,100	( 1.14)^4	1.6890	$8,613.70
2	$5,100	(1.14)^3	1.4815	$7,555.87
3	$5,100	( 1.14)^2	1.2996	$6,627.96
4	$5,100	( 1.14)^1	1.1400	$5,814.00
5	$5,100	( 1.14)^0	1.0000	$5,100.00
	Total			$33,711.53

We know that

At MIRR, Present value of terminal cash inflow is equal to the Outflow

$ 33711.53/( 1+i)^5 = $ 18000

$ 33711.53/$ 18000= ( 1+i)^5

( 1+i)^5 = 1.872862

1+I = ( 1.872862)^0.2

1+I = 1.133708

I = 13.3708%

Since MIRR is less than Cost of Capital , reject the project.

Computation of MIRR for pulley

Pulley
Year	Cash flows	Future value factor	Future value factor	Terminal values
1	$7,500	( 1.14)^4	1.6890	$12,667.20
2	$7,500	(1.14)^3	1.4815	$11,111.58
3	$7,500	( 1.14)^2	1.2996	$9,747.00
4	$7,500	( 1.14)^1	1.1400	$8,550.00
5	$7,500	( 1.14)^0	1.00	$7,500.00
		Total		$ 49575.78

We know that

At MIRR, Present value of terminal cash inflow is equal to the Outflow

$ 49575.78/( 1+i)^5 = $ 22000

$ 49575.78/$ 22000= ( 1+i)^5

( 1+i)^5 = 2.25344

1+I = ( 2.25344)^ 0.2

1+I = 1.176438

I = 17.6438%

Since MIRR is greater than Cost of Capital , accept the project.

	Truck		Pulley
	Value	Decision		Value	Decision
IRR	12.86%	Reject the Project		20.88%	Accept the Project.
NPV	($491)	Reject the Project		$3,748	Accept the Project.
MIRR	13.37%	Reject the Project		17.64%	Accept the Project.