Question

Tri-Star, Inc., has the following mutually exclusive projects.

a. Calculate the NPV, IRR, MIRR, TPB and DPB for the projects.

b. Suppose the company's traditional payback period cutoff is two years. Which of these two projects should be chosen on that basis? Explain why

c. Suppose the company uses the NPV rule to rank these two projects. Which project should be chosen if the appropriate discount rate is 15 percent? Explain why

d. Suppose the company uses the IRR rule to rank these two projects. Which project should be chosen if the appropriate discount rate is 15 percent? Explain why

e. Suppose the company uses the MIRR rule to rank these two projects. Which project should be chosen if the appropriate discount rate is 15 percent? Explain why

Year	Project A	Project B
0	(15,300)	(10,700)
1	8,700	5,300
2	7,400	4,300
3	3,100	4,800

Answer 1

1). NPV for Project A:

Formula	Year (n)	0	1	2	3
	Cash flow	-15,300.00	8,700.00	7,400.00	3,100.00
1/(1+d)^n	Discount factor @15%	1.000	0.870	0.756	0.658
Cash flow*discount factor	Discounted cash flow	-15,300.00	7,565.22	5,595.46	2,038.30
Sum of all discounted cash flows	NPV	-101.02

2). NPV for Project B:

Formula	Year (n)	0	1	2	3
	Cash flow	-10,700.00	5,300.00	4,300.00	4,800.00
1/(1+d)^n	Discount factor @15%	1.000	0.870	0.756	0.658
Cash flow*discount factor	Discounted cash flow	-10,700.00	4,608.70	3,251.42	3,156.08
Sum of all discounted cash flows	NPV	316.19

3). IRR for Project A = 14.54%

4). IRR for Project B = 16.81%

5). MIRR for Project A (using the required rate of return 15% as the re-investment rate) = 14.75%

6). MIRR for Project B (using the required rate of return 15% as the re-investment rate) = 16.12%

Note: IRR and MIRR has been calculted using excel functions IRR & MIRR.

7). Payback Period (PB) for Project A:

Formula	Year (n)	0	1	2	3
	Cash flow	-15,300.00	8,700.00	7,400.00	3,100.00
	Cumulative cash flow	-15,300	-6,600.00	800.00	3,900.00

Cumulative cash flow turns positive in Year 2, so fraction of the year = last year's cumulative cash flow/this year's cash flow

= 6,600/7,400 = 0.89

Thus, PB = 1 + 0.89 = 1.89 years

8).  Payback Period (PB) for Project B:

Formula	Year (n)	0	1	2	3
	Cash flow	-10,700.00	5,300.00	4,300.00	4,800.00
	Cumulative cash flow	-10,700.00	-5,400.00	-1,100.00	3,700.00

Cumulative cash flow turns positive in Year 3, so fraction of the year = last year's cumulative cash flow/this year's cash flow

= 1,100/4,800 = 0.23

Thus, PB = 2 + 0.23 = 2.23 years

9). Discounted Payback Period (DPB) for Project A:

Formula	Year (n)	0	1	2	3
	Cash flow	-15,300.00	8,700.00	7,400.00	3,100.00
1/(1+d)^n	Discount factor @15%	1.000	0.870	0.756	0.658
Cash flow*discount factor	Discounted cash flow	-15,300.00	7,565.22	5,595.46	2,038.30
	Cumulative discounted cash flow	-15,300.00	-7,734.78	-2,139.32	-101.02

Cumulative discounted cash flow never turns positive within the life of the project so as per DPB, Project A is not viable.

10). Discounted Payback Period (DPB) for Project B:

Formula	Year (n)	0	1	2	3
	Cash flow	-10,700.00	5,300.00	4,300.00	4,800.00
1/(1+d)^n	Discount factor @15%	1.000	0.870	0.756	0.658
Cash flow*discount factor	Discounted cash flow	-10,700.00	4,608.70	3,251.42	3,156.08
	Cumulative discounted cash flow	-10,700.00	-6,091.30	-2,839.89	316.19

Cumulative discounted cash flow turns positive in Year 3, so fraction of the year = last year's cumulative discounted cash flow/this year's discounted cash flow  

= 2,839.89/3,156.08 = 0.90

Thus, DPB = 2 + 0.90 = 2.9 years.

b). If the company's traditional PB period cutoff is 2 years then Project A should be chosen as it has a PB of 1.89 years.

c). Using NPV, Project B should be chosen since Project A has a negative NPV.

d). Using IRR, Project B should be chosen, since it has a higher IRR compared to Project A.

e). Using MIRR, Project B should be chosen, since it has a higher MIRR compared to Project A.