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 $15,000 and that for the pulley system is $21,000. The firm's cost of capital is 11%. 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

1. Calculate the IRR for each project. Round your answers to two decimal places.

   Truck:  %
   
   What is the correct accept/reject decision for this project?
   -Select-AcceptRejectItem 2

   
   Pulley:  %
   
   What is the correct accept/reject decision for this project?
   -Select-AcceptRejectItem 4

2. 
   

3. Calculate the NPV for each project. Round your answers to the nearest dollar, if necessary. Enter each answer as a whole number. For example, do not enter 1,000,000 as 1 million.

   Truck: $  
   
   What is the correct accept/reject decision for this project?
   -Select-AcceptRejectItem 6

   
   Pulley: $  
   
   What is the correct accept/reject decision for this project?
   -Select-AcceptRejectItem 8

4. 
   

5. Calculate the MIRR for each project. Round your answers to two decimal places.

   Truck:  %
   
   What is the correct accept/reject decision for this project?
   -Select-AcceptRejectItem 10

   
   Pulley:  %
   
   What is the correct accept/reject decision for this project?
   -Select-AcceptRejectItem 12

Answer 1

a.

Computations of IRR using excel:

	A	B	C
1	Year	Cash Flow(Truck)	Cash Flow (Pulley)
2	0	($15,000)	($21,000)
3	1	$5,100	$7,500
4	2	$5,100	$7,500
5	3	$5,100	$7,500
6	4	$5,100	$7,500
7	5	$5,100	$7,500
8	IRR	20.76%	23.06%

Suppose the excel sheet looks like above table.

Insert formula in cell B8 as “=IRR(B2:B7) to get IRR for the project Truck as 20.76 %

Similarly to get IRR of Pulley inset formula “=IRR(C2:C7) in cell C8, which will display IRR as 23.06 %

IRR for Truck is 20.76 %

The Project should be accepted as IRR is higher than firm’s cost of capital 9 %.

b.

IRR for Pulley is 23.06 %

The Project should be accepted as IRR is higher than firm’s cost of capital 9 %.

c.

Computation of NPV:

Year	Computation of PV Factor	PV Factor @ 9 % (F)	Cash Flow (Truck) CT	Cash Flow (Pulley) CP	PV (Truck) (=F x CT)	PV (Pulley) (=F x CP)
0	1/(1+0.09)^0	1	($15,000)	($21,000)	($15,000.000000)	($21,000.000000)
1	1/(1+0.09)^1	0.91743119266	$5,100	$7,500	$4,678.899083	$6,880.733945
2	1/(1+0.09)^2	0.84167999327	$5,100	$7,500	$4,292.567966	$6,312.599949
3	1/(1+0.09)^3	0.77218348006	$5,100	$7,500	$3,938.135748	$5,791.376100
4	1/(1+0.09)^4	0.70842521107	$5,100	$7,500	$3,612.968576	$5,313.189083
5	1/(1+0.09)^5	0.64993138630	$5,100	$7,500	$3,314.650070	$4,874.485397
				NPV	$4,837.221443	$8,172.384475

NPV for Truck is $ 4,837

The Project should be accepted as NPV is positive.

d.

NPV for Pulley is $ 8,172

The Project should be accepted as NPV is positive.

e.

MIRR = ⁿ √ Terminal Value of Cash Inflow/Present Value of Cash Outflow – 1

n = No. of years of investment = 5

Year	Cash Flow (Truck) CT	Cash Flow (Pulley) CP	Computation of Future Value Factor	Future Value factor @ 9 % (F)	Future value Truck (F x CT)	Future value Pulley (F x CP)
1	$5,100	$7,500	(1.09)^4	1.41158161	$7,199.066211	$10,586.862075
2	$5,100	$7,500	(1.09)^3	1.295029	$6,604.647900	$9,712.717500
3	$5,100	$7,500	(1.09)^2	1.1881	$6,059.310000	$8,910.750000
4	$5,100	$7,500	(1.09)^1	1.09	$5,559.000000	$8,175.000000
5	$5,100	$7,500	(1.09)^0	1	$5,100.000000	$7,500.000000
				Terminal value	$30,522.024111	$44,885.329575

MIRR for Truck = ⁵ √ $30,522.024111 /$ 15,000 – 1

                           = [⁵ √ (2.03480160740)] – 1

                           = 1.152668471964 – 1

                      = 0.152668471964 or 15.27 %

Project Truck should be accepted as cost of capital is lower than MIRR.

MIRR for Pulley = ⁵ √ $44,885.329575 /$ 21,000 – 1

                           = [⁵ √ (2.13739664643)] – 1

                           = 1.164064445844 – 1

                          = 0.164064445844 or 16.41 %

Project Pulley should be accepted as cost of capital is lower than MIRR.