Question

1. Jack Engineering is considering two projects, Project Alpha and Project Beta system, in this year's capital budget. The projects are independent. The cash outlay for the Project Alpha is $44,860 and that for the Project Beta is $34,200. The firm's cost of capital is 14%. After-tax cash flows, including depreciation, are as follows:

Year	Project Alpha	Project Beta
1	15,000	10,200
2	15,000	10,200
3	15,000	10,200
4	15,000	10,200
5	15,000	10,200

Required:

1. Calculate the IRR for each project.

2. Calculate the NPV, for each project

3. Calculate the MIRR for each project

4. Indicate the correct accept-reject decision for each.

Answer 1

Project Alpha

IRR = 20% (IRR is the rate at which NPV = 0)

NPV = $6,636

MIRR = 17.19 %

Present Value = Cash Flow / (1+ Discount Rate) ^ T, where T is the year of cash flow

For example PV of Cash flow for 4th year = 15000 / (1+14%)^4 = 15000/ 1.689 = $8881.20

Similarly other PV are calculated

Future Value is calculated using with the re-investment rate of 14% or the cost of capital = Cash Flow X (1+ Reinvestment Rate) ^(T- t), where T-t is the time for reinvestment

Thus FV of 2nd year cash flow can be calculated as 15000 x (1+14%) ^(5-2) = 15000 x (1.140)^3

= 15000 X 1.481 = 22,223.16

Similarly FV is calculated for other periods as well.

NPV = Sum of present value of all cash flows including investment ( which is taken as -ive sign)

IRR is calculated using excel function IRR and putting all values of cash flows

MIRR = Modified Internal Rate of Return

= (Sum of FV of positive cash flows / Sum of PV of all negative cash flows) ^ (1/n) -1

= (99152 / 44860)^(1/5) -1 = (2.21^0.5) - 1 = 17.14%

Year	Project Alpha Cash Flows	Project Alpha - PV of Cash Flows (Disc rate =14%)	Project Alpha - FV of Positive Cash Flows (Rate =14%)
0	(44,860)	(44,860.00)
1	15,000	13,157.89	$25,334.40
2	15,000	11,542.01	$22,223.16
3	15,000	10,124.57	$19,494.00
4	15,000	8,881.20	$17,100.00
5	15,000	7,790.53	$15,000.00
IRR	20.00%
NPV		6,636
Future Value of Positive Cash flows			99,152
MIRR = (FVCF/ PVCF) ^(1/n) -1	17%

Project Beta

IRR = 15% (IRR is the rate at which NPV = 0)

NPV = $ 817

MIRR = 14.54 %

Project Alpha which has higher IRR, NPV and MIRR should be selected

For IRR, accept reject rule is - Projects with IRR higher than minimum required rate are accepted

For NPV, accept reject rule is, Projects with positive NPV are selected