Question

Payback, NPV, and MIRR

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 9% 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 years

Project B years

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

Project A years

Project B years

If the two projects are independent and the cost of capital is 9%, 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 9%, what is the modified IRR (MIRR) of each project? Round your answers to two decimal places.

Project A %

Project B %

Answer 1

For project A

Calculation showing Payback period

Year	Cash flow	Cummulative cash flow
1	5	5
2	10	15
3	15	30
4	20	50

Using interpolation we can find payback period

Year	Cummulative cash flow
2	15
3	30
1	15
?	9

=9/15 = 0.6

Thus payback period = 2+0.6 = 2.6 years

For Project B

Calculation showing Payback period

Year	Cash flow	Cummulative cash flow
1	20	20
2	10	30
3	8	38
4	6	44

Using interpolation we can find payback period

Year	Cummulative cash flow
1	20
2	30
1	10
?	4

=4/10 = 0.4

Thus payback period = 1+0.4 = 1.4 years

For project A

calculation showing discounted payback period

Year	Cash flow	PVIF @ 9%	Present value	Cumulative dicounted cash flow
1	5	0.917	4.59	4.59
2	10	0.842	8.42	13.00
3	15	0.772	11.58	24.59
4	20	0.708	14.17	38.76

Using interpolation we can find discounted payback period

Year	Cumulative dicounted cash flow
2	13
3	24.59
1	11.59
?	11

11/11.59 = 0.949

Thus discounted payback period = 2+0.949 = 2.949 years

For project B

calculation showing discounted payback period

Year	Cash flow	PVIF @ 9%	Present value	Cumulative dicounted cash flow
1	20	0.917	18.35	18.35
2	10	0.842	8.42	26.77
3	8	0.772	6.18	32.94
4	6	0.708	4.25	37.19

Using interpolation we can find discounted payback period

Year	Cumulative dicounted cash flow
1	18.35
2	26.77
1	8.42
?	5.65

=5.65/8.42 = 0.67

Thus discounted payback period = 1+0.67 = 1.67 years

Statement showing NPV

For Project A

Year	Cash flow	PVIF @ 9%	Present value
1	5	0.917	4.59
2	10	0.842	8.42
3	15	0.772	11.58
4	20	0.708	14.17
Total			38.76
Less PV of cashoutflow			24
NPV			14.76

For project B

Year	Cash flow	PVIF @ 9%	Present value
1	20	0.917	18.35
2	10	0.842	8.42
3	8	0.772	6.18
4	6	0.708	4.25
Total			37.19
Less PV of cashoutflow			24
NPV			13.19

Thus project A should be selected

If cost of capital is 5%, then

Statement showing NPV

For project A

Year	Cash flow	PVIF @ 5%	Present value
1	5	0.952	4.76
2	10	0.907	9.07
3	15	0.864	12.96
4	20	0.823	16.45
Total			43.24
Less PV of cashoutflow			24
NPV			19.24

For project B

Year	Cash flow	PVIF @ 9%	Present value
1	20	0.952	19.05
2	10	0.907	9.07
3	8	0.864	6.91
4	6	0.823	4.94
Total			39.96
Less PV of cashoutflow			24
NPV			15.96

Project A should be selected

If cost of capital is 15%, then

Statement showing NPV

For Project A

Year	Cash flow	PVIF @ 5%	Present value
1	5	0.870	4.35
2	10	0.756	7.56
3	15	0.658	9.86
4	20	0.572	11.44
Total			33.21
Less PV of cashoutflow			24
NPV			9.21

For project B

Year	Cash flow	PVIF @ 9%	Present value
1	20	0.870	17.39
2	10	0.756	7.56
3	8	0.658	5.26
4	6	0.572	3.43
Total			33.64
Less PV of cashoutflow			24
NPV			9.64

Thus project B should be selected