Question

8. 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

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 one) Accept/Reject		__ %	(select one)Accept/Reject
NPV	$__	(select one) Accept/Reject		$ __	(select one) Accept/Reject
MIRR	__%	(select one) Accept/Reject		__%	(select one)Accept/Reject

Answer 1

NPV

It is the difference between the present values of cash inflows and the present value of cash outflows.

IRR

IRR is the discount rate that makes NPV = 0

MRR

MIRR of modified internal rate of return is an advanced version of IRR which rectifies the limitation of the IRR method of project appraisal. In this method, it is assumed that positive cash flows are reinvested at the cost of capital, but negative cash flows (cash outflow) are funded at the current cost of capital.

Consider for the truck:

Initial cost = $15,000

Annual cash flow = $5,100

NPV(11%) = $5,100*PVIFA (11%, 5 years) - $15,000

=$5,100* 3.696 - $15,000

= $3,849.1

NPV = 0 = $5,100*PVIFA (IRR%, 5 years) - $15,000 ...................................(1)

Solving the equation (1) we get

IRR = 20.76%

MIRR = (Future value of cash flows/Present value of initial cash ouflow)^(1/n) -1

=16.19%

We can do this similarly for Pulley.

For Pulley

Initial cost = $ 21,000

Annual cash flow = $7,500

NPV(14%) = $7,500*PVIFA (11%, 5 years) - $ 21,000

=$7,500* 3.696 - $ 21,000

= $6,719.2

We calculate IRR as the discount rate that makes NPV = 0

NPV = 0 = $7,500*PVIFA (IRR%, 5 years) - $21,000 ...............................(2)

Solving the equation (2) we get

IRR = 23.06%

MIRR = (Future value of cash flows/Present value of initial cash outflow)^(1/n) -1

=17.34%

Working shown in Excel

	Cash Flows		Discounted cash flows
Year	Truck	Pulley	PV @ 11%	Truck	Pulley
0	-15000	-21000	1.000	-15000	-21000
1	5100	7500	0.901	4595	6757
2	5100	7500	0.812	4139	6087
3	5100	7500	0.731	3729	5484
4	5100	7500	0.659	3360	4940
5	5100	7500	0.593	3027	4451
IRR	20.76%	23.06%	NPV	$3,849.1	$6,719.2
MIRR	16.19%	17.34%

1) As NPV of both Truck and Pulley is positive, we can accept both projects.

2) As the IRR of both Truck and Pulley is greater than the cost of capital(11%), we can accept both projects.

3) Similarly for MIRR, as the MIRR of both Truck and Pulley is greater than the cost of capital(11%), we can accept both projects.