Question

Your division is considering two investment projects, each of which requires an up-front expenditure of $28 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	6	18
2	10	12
3	15	8
4	22	5

1. What is the regular payback period for each of the projects? Round your answers to two decimal places.
2. What is the NPV and IRR for each of the projects? Round your answers to two decimal places.
3. If the two projects are independent and the cost of capital is 11%, which project or projects should the firm undertake?
4. What is the crossover rate? Round your answer to two decimal places.
5. If the two projects are mutually exclusive and the cost of capital is 5%, which project should the firm undertake?
6. If the cost of capital is 11%, what is the MIRR of each project? Round your answers to two decimal places.

Answer 1

(a): Payback for the two projects are:

Year	A	cumulative cash flows of A		B	cumulative cash flows of B
0	-          28.00	-                       28.00		-      28.00	-                       28.00
1	6.00	-                       22.00		18.00	-                       10.00
2	10.00	-                       12.00		12.00	2.00
3	15.00	3.00		8.00
4	22.00			5.00

Thus payback of A = 2 + (12/15) = 2.80 years

Payback of B = 1 + (10/12) = 1.83 years

(b): NPV:

Year	A	1+r	PVIF	PV of A's cash flow		B	PV of B's cash flow
0	-          28.00	1.11	1.00000	-              28.00		-      28.00	-      28.00
1	6.00		0.90090	5.41		18.00	16.22
2	10.00		0.81162	8.12		12.00	9.74
3	15.00		0.73119	10.97		8.00	5.85
4	22.00		0.65873	14.49		5.00	3.29
			Total	10.98			7.10

NPV of A = $10.98 million and NPV of B = $7.10 million

IRR: This is the rate at which NPV is nil.

Year	A	1+r	PVIF	PV of A's cash flow		B	1+r	PVIF	PV of B's cash flow
0	-          28.00	1.2482	1.00	-              28.00		-      28.00	1.2556	1.00	-      28.00
1	6.00		0.80	4.81		18.00		0.80	14.34
2	10.00		0.64	6.42		12.00		0.63	7.61
3	15.00		0.51	7.71		8.00		0.51	4.04
4	22.00		0.41	9.06		5.00		0.40	2.01
			Total	0.00					0.00

IRR of A = 24.82% and IRR of B = 25.56%

(c):  In this case the firm will undertake both the projects as their NPV>0 and IRR>cost of capital.

(d): Crossover rate is the rate at which NPV of both the projects are same. The rate is:

Year	A	1+r	PVIF	PV of A's cash flow		B	PV of B's cash flow
0	-          28.00	1.2348	1.00000	-              28.00		-      28.00	-          28.00
1	6.00		0.80984	4.86		18.00	14.58
2	10.00		0.65584	6.56		12.00	7.87
3	15.00		0.53112	7.97		8.00	4.25
4	22.00		0.43012	9.46		5.00	2.15
			Total	0.85			0.85

Hence the crossover rate is 23.48%

(e): Here compute the NPV at 5% rate:

Year	A	1+r	PVIF	PV of A's cash flow		B	PV of B's cash flow
0	-          28.00	1.0500	1.00000	-              28.00		-      28.00	-          28.00
1	6.00		0.95238	5.71		18.00	17.14
2	10.00		0.90703	9.07		12.00	10.88
3	15.00		0.86384	12.96		8.00	6.91
4	22.00		0.82270	18.10		5.00	4.11
			Total	17.84			11.05

Project A will be selected as at 5% its NPV is higher.

(f): For A terminal value of cash inflows = 6*(1.11)^3 + 10*(1.11)^2 + 15*(1.11)^1 + 22

= 59.18. Thus 28 = 59.18/(1+mirr)^4

Or MIRR of A = 20.58%

For B terminal value of cash inflows = 18*(1.11)^3 + 12*(1.11)^2 + 8*(1.11)^1 + 5 = 53.28

Thus 28 = 53.28/(1+mirr)^4

Or Mirr of B = 17.45%

Thus MIRR of A = 20.58% and of B = 17.45%