Question

Your division is considering two investment projects, each of which requires an up-front expenditure of $24 million. You estimate that the cost of capital is 11% and that the investments will produce the following after-tax cash flows (in millions of dollars):

Year Project A Project B

1 5 20

2 10 10

3 15 8

4 20 6

What is the regular payback period for each of the projects? Round your answers to two decimal places.

Project A

Project B

What is the discounted payback period for each of the projects? Round your answers to two decimal places.

Project A

Project B

If the two projects are independent and the cost of capital is 11%, which project or projects should the firm undertake?

If the two projects are mutually exclusive and the cost of capital is 5%, which project should the firm undertake?

If the two projects are mutually exclusive and the cost of capital is 15%, which project should the firm undertake?

What is the crossover rate? Round your answer to two decimal places.

If the cost of capital is 11%, what is the modified IRR (MIRR) of each project? Round your answers to two decimal places.

Project A

Project B

Answer 1

Regular Payback period for project A

Year	Project A	Cumualtive cash flow
0	-24	-24
1	5	-19
2	10	-9
3	15	6
4	20	26

Regular paynack period = Last year of negative cumulative cash flow + absolute value of cumulative cash flow that year / Cash flow next year

Regular Payback period for project A = 2 +9/15 = 2.60 Years

Regular Payback period for Project B

Year	Project B	Cumualtive cash flow
0	-24	-24
1	20	-4
2	10	6
3	8	14
4	6	20

Regular payback period for project B = 1 + 4/10 = 1.4 Years

Discounted payback for project A

Year	Project A	Duiscounted Cash flow	Cumualtive cash flow
0	-24	-24.00	-24.00
1	5	4.50	-19.50
2	10	8.12	-11.38
3	15	10.97	-0.41
4	20	13.17	12.76

Discounted payback for Project A = 3 + 0.41/13.17 = 3.03 Years

Discounted payabck for Project B

Year	Project B	Duiscounted Cash flow	Cumualtive cash flow
0	-24	-24.00	-24.00
1	20	18.02	-5.98
2	10	8.12	2.13
3	8	5.85	7.98
4	6	3.95	11.94

Discounted payback for Project B = 1 + 5.98/8.12 = 1.74 Years

If the two projects are independent at 11% cost of capital, we calculate the NPV of both projects

Year	Project A
0	-24
1	5
2	10
3	15
4	20
NPV	$    12.76
Year	Project B
0	-24
1	20
2	10
3	8
4	6
NPV	$    11.94

Since both Projects A and B have positive NPV, both of them can be selected since they are independent

If the two projects are mutually exclusive at 5% cost of capital, we calculate the NPV of both projects

Year	Project A
0	-24
1	5
2	10
3	15
4	20
NPV	$    19.24
Year	Project B
0	-24
1	20
2	10
3	8
4	6
NPV	$    15.96

Since at 5%, project A has a higher NPV, Project A should be selected

If the two projects are mutually exclusive at 15% cost of capital, we calculate the NPV of both projects

Year	Project A
0	-24
1	5
2	10
3	15
4	20
NPV	$       9.21
Year	Project B
0	-24
1	20
2	10
3	8
4	6
NPV	$       9.64

Since at 15%, project B  has a higher NPV, Project B should be selected

Cross over rate is the internal rate of return (IRR) of the differential cash flow between the two projects

Year	Project A	Project B	Difference
0	-24	-24	0
1	5	20	-15
2	10	10	0
3	15	8	7
4	20	6	14
CROSS OVER RATE			13.53%

MIRR of the two projects at 11%

Year	Project A
0	-24
1	5
2	10
3	15
4	20
MIRR of Project A	23.49%
Year	Project B
0	-24
1	20
2	10
3	8
4	6
MIRR of Project B	22.79%