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 $17,100 and that for the pulley system is $22,430. 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

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?

Answer 1

IRR	0.199991713
Year	0	1	2	3	4	5
Cash flow stream	-22430	7500	7500	7500	7500	7500
Discounting factor	1	1.199992	1.43998	1.727964	2.0735427	2.488234
Discounted cash flows project	-22430	6250.043	5208.405	4340.368	3616.9981	3014.186
NPV = Sum of discounted cash flows
NPV Pulley =	4.46061E-05
Where
Discounting factor =	(1 + IRR)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
IRR=	20%
Accept project as IRR is more than discount rate
c
Truck
Discount rate	0.14
Year	0	1	2	3	4	5
Cash flow stream	-17100	5100	5100	5100	5100	5100
Discounting factor	1	1.14	1.2996	1.481544	1.6889602	1.925415
Discounted cash flows project	-17100	4473.684	3924.284	3442.355	3019.6094	2648.78
NPV = Sum of discounted cash flows
NPV Truck =	408.71
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
Accept project as NPV is positive
Pulley
Discount rate	0.14
Year	0	1	2	3	4	5
Cash flow stream	-22430	7500	7500	7500	7500	7500
Discounting factor	1	1.14	1.2996	1.481544	1.6889602	1.925415
Discounted cash flows project	-22430	6578.947	5771.006	5062.286	4440.6021	3895.265
NPV = Sum of discounted cash flows
NPV Pulley =	3318.11
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
Accept project as NPV is positive
e
Truck
Combination approach
All negative cash flows are discounted back to the present and all positive cash flows are compounded out to the end of the project’s life
Thus year 5 modified cash flow=(8613.7)+(7555.87)+(6627.96)+(5814)+(5100)
=33711.53
Thus year 0 modified cash flow=-17100
=-17100
Discount rate	0.14
Year	0	1	2	3	4	5
Cash flow stream	-17100	5100	5100	5100	5100	5100
Discount factor	1	1.14	1.2996	1.481544	1.6889602	1.925415
Compound factor	1	1.68896	1.481544	1.2996	1.14	1
Discounted cash flows	-17100	0	0	0	0	0
Compounded cash flows	-5.84795E-05	8613.7	7555.87	6627.96	5814	5100
Modified cash flow	-17100	0	0	0	0	33711.53
Discounting factor (using MIRR)	1	1.145398	1.311937	1.50269	1.7211784	1.971435
Discounted cash flows	-17100	0	0	0	0	17100
NPV = Sum of discounted cash flows
NPV=	2.51306E-06
MIRR is the rate at which NPV = 0
MIRR=	14.54%
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
Compounding factor =	(1 + reinvestment rate)^(time of last CF-Corresponding period in years)
Compounded Cashflow=	Cash flow stream*compounding factor
Accept as MIRR is more than cost of capital
Pulley
Combination approach
All negative cash flows are discounted back to the present and all positive cash flows are compounded out to the end of the project’s life
Thus year 5 modified cash flow=(12667.2)+(11111.58)+(9747)+(8550)+(7500)
=49575.78
Thus year 0 modified cash flow=-22430
=-22430
Discount rate	0.14
Year	0	1	2	3	4	5
Cash flow stream	-22430	7500	7500	7500	7500	7500
Discount factor	1	1.14	1.2996	1.481544	1.6889602	1.925415
Compound factor	1	1.68896	1.481544	1.2996	1.14	1
Discounted cash flows	-22430	0	0	0	0	0
Compounded cash flows	-4.45831E-05	12667.2	11111.58	9747	8550	7500
Modified cash flow	-22430	0	0	0	0	49575.78
Discounting factor (using MIRR)	1	1.171893	1.373334	1.609401	1.8860458	2.210244
Discounted cash flows	-22430	0	0	0	0	22430
NPV = Sum of discounted cash flows
NPV=	7.90391E-05
MIRR is the rate at which NPV = 0
MIRR=	17.19%
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
Compounding factor =	(1 + reinvestment rate)^(time of last CF-Corresponding period in years)

Accept as MIRR is more than cost of capital