Question

You are considering the following two projects and can take only one. Your cost of capital is 11.2%. The cash flows for the two projects are as follows ($ million): Project Year 0 - $101 - $101 Year 1 $22 $52 Year 2 $29 $40 Year 3 $40 $29 Year 4 $52 $18 a. What is the IRR of each project? b. What is the NPV of each project at your cost of capital? c. At what cost of capital are you indifferent between the two projects? d. What should you do? a. What is the IRR of each project? The IRR for project Ais %. (Round to one decimal place.) The IRR for project Bisl%. (Round to one decimal place.) b. What is the NPV of each project at your cost of capital? The NPV for project A is $ million. (Round to two decimal places.) The NPV for project B is $ million. (Round to two decimal places.) c. At what cost of capital are you indifferent between the two projects? You will be indifferent if the cost of capital is %. (Round to one decimal place.) d. What should you do?

Answer 1

Solution

(a) Determination of Internal Rate of Return:

For Project A: Making a trial-and-error test with 13% and 14% as follows,

Year	Cash Flow	DF @ 13%	DCF	DF @ 14%	DCF
1	22.00	0.8850	19.47	0.8772	19.30
2	29.00	0.7831	22.71	0.7695	22.31
3	40.00	0.6931	27.72	0.6750	27.00
4	52.00	0.6133	31.89	0.5921	30.79
			101.79		99.40

As at IRR, Total DCF = Initial Outlay, Initial outlay of this project is $101, and Total DCF is $101.79 at 13%, and $99.40 at 14%, IRR should be in between these two rates. Assuming IRR = x%, using interpolation method we get,

(x - 13) / (14 - 13) = (101 - 101.79) / (99.40 - 101.79)
or, (x - 13) = 0.79 / 2.39
or, (x - 13) = 0.3305 (Approx.)
or, x = 13.3305

Therefore, IRR for Project A = 13.3%

For Project B: Making a trial-and-error test with 17% and 18% as follows,

Year	Cash Flow	DF @ 17%	DCF	DF @ 18%	DCF
1	52.00	0.8547	44.44	0.8475	44.07
2	40.00	0.7305	29.22	0.7182	28.73
3	29.00	0.6244	18.11	0.6086	17.65
4	18.00	0.5337	9.61	0.5158	9.28
			101.38		99.73

As at IRR, Total DCF = Initial Outlay, Initial outlay of this project is $101, and Total DCF is $101.38 at 17%, and $99.73 at 18%, IRR should be in between these two rates. Assuming IRR = x%, using interpolation method we get,

(x - 17) / (18 - 17) = (101 - 101.38) / (99.73 - 101.38)
or, (x - 17) = 0.38 / 1.65
or, (x - 17) = 0.2303 (Approx.)
or, x = 17.2303

Therefore, IRR for Project B = 17.2%

(b) Determination of Net Present Value:

Year	DF @ 11.2%	Project A		Project B
		Cash Flow	DCF	Cash Flow	DCF
1	0.8993	22.00	19.78	52.00	46.76
2	0.8087	29.00	23.45	40.00	32.35
3	0.7273	40.00	29.09	29.00	21.09
4	0.6540	52.00	34.01	18.00	11.77
			106.34		111.97
Less: Initial Outflow			-101.00		-101.00
Net Present Value			5.34		10.97

(c) For determining the cost of capital at which both the projects will be indifferent shall be calculated as follows,

Year	Project A	Project B	Incremental Flow
0	-101.00	-101.00	0.00
1	22.00	52.00	-30.00
2	29.00	40.00	-11.00
3	40.00	29.00	11.00
4	52.00	18.00	34.00

Again, for the indifferent rate, we have to calculate incremental IRR using the information above.

For calculating IRR, we will run a trial-and-error test using 3% and 4% as follows,

Year	Incremental Flow	DF @ 3%	DCF	DF @ 4%	DCF
1	-30.00	0.9709	-29.13	0.9615	-28.85
2	-11.00	0.9426	-10.37	0.9246	-10.17
3	11.00	0.9151	10.07	0.8890	9.78
4	34.00	0.8885	30.21	0.8548	29.06
			0.78		-0.17

For determining the indifferent IRR, Total DCF should be equal to 0. Here, DCF at 3% is 0.78 and at 4% it is -0.17. Therefore, assuming the IRR = x%, using interpolation,

(x - 3) / (4 - 3) = (0 - 0.78) / (- 0.17 - 0.78)
or, (x - 3) = 0.78 / 0.95
or, (x - 3) = 0.8211 (Approx.)
or, x = 3.8211

Therefore, if the cost the capital is 3.8211%, both the projects will be indifferent.

(d) As we know that if a project has NPV > 0 and IRR > Cost of capital, the project should be worth accepting. Here, both the project has a positive NPV and an IRR more than its actual cost of capital. But as project B is at an edge than project A as both its NPV and IRR is higher than A, it is suggested to go for Project B.

Answer:
(a)
IRR of Project A = 13.3%
IRR of Project B = 17.2%

(b)
NPV of Project A = 5.34
NPV of Project B = 10.97

(c)
If the Cost of Capital is 3.8%, both the projects will be indifferent.

(d)
It is suggested to prefer Project B.