Consider the cash flows from two mutually exclusive projects: Cash Flow Year Pro
ID: 2727577 • Letter: C
Question
Consider the cash flows from two mutually exclusive projects: Cash Flow Year Project A Project B 0 -$470,000 -$460,000 1 $120,000 $392,000 2 $210,000 $110,000 3 $375,000 $120,000 The appropriate discount rate is 11.7%.
Calculate the net present value (NPV) for both projects, and determine which project should be accepted based on NPV. Round both NPVs to the nearest dollar.
Calculate the internal rate of return (IRR) for both projects, and determine which project should be accepted based on IRR.
Calculate the net present value (NPV) for both projects using the crossover rate as your discount rate. Round both NPVs to the nearest dollar.
Explanation / Answer
The assumptions taken as per details given
The initial investment of project A is $470,000
The cash inflow year 1 is $120,000 , year 2 $210,000 and year 3$375,000
The cost of capital is 11.7%
Calculation of NPV of project A
year
investment
cashinflow
present value factor @11.7%
present value of cash inflow
0
(470,000.00)
1
(470,000)
1
120000
0.8953
107431
2
210000
0.8015
168311
3
375000
0.7175
269074
Net present value
74,816
The initial investment of project B is $460,000
The cash inflow year 1 is $392,000 , year 2 $110,000 and year 3$120,000
The cost of capital is 11.7%
Calculation of NPV of project B
year
investment
cashinflow
present value factor @11.7%
present value of cash inflow
0
(460,000.00)
1
(460,000)
1
392000
0.895255
350940
2
110000
0.801482
88163
3
120000
0.717531
86104
Net present value
65,207
Based on NPV project A has more positive NPV than Project B hence project A is recommended
2) the IRR is internal rate of return (IRR) is the interest rate at which the net present value of all the cash flows (both positive and negative) from a project or investment equal zero.
The formula for IRR is:
0 = P0 + P1/(1+IRR) + P2/(1+IRR)2 + P3/(1+IRR)3 + . . . +Pn/(1+IRR)n
where P0, P1, . . . Pn equals the cash flows in periods 1, 2, . . . n, respectively; and
IRR equals the project's internal rate of return.
IRR of project A = 19.19%
IRR of project B = 22.24%
Based on IRR project B is accepted as it has higher IRR
3) calculation of crossover rate we subtract the cashflows and cash outflow from one project from the cash flows of the other project, and find the IRR of the differential cash flows.
•We will subtract the cash flows from Project Y from the cash flows from Project X.
•It is irrelevant which cash flows we subtract from the other
.•Subtracting the cash flows, the equation to calculate the IRR for the these differential cash inflows
Calculation of crossover rate
Investment
Cash inflow
Difference
year
project A
Project B
project A
Project B
0
(470,000.00)
(460,000.00)
(10,000.00)
1
120000
392000
-272000
2
210000
110000
100000
3
375000
120000
255000
The IRR is which is crossover rate is 14.12%
This will be cost of capital instead of 11.7% the NPV calculation of project A and B are given
Calculation of NPV of project A
year
investment
cashinflow
present value factor @14.12%
present value of cash inflow
0
(470,000.00)
1
(470,000)
1
120000
0.8763
105152
2
210000
0.7679
161249
3
375000
0.6728
252317
Net present value
48,718
Calculation of NPV of project B
year
investment
cashinflow
present value factor @14.12%
present value of cash inflow
0
(460,000.00)
1
(460,000)
1
392000
0.8763
343498
2
110000
0.7679
84464
3
120000
0.6728
80741
Net present value
48,703
Calculation of NPV of project A
year
investment
cashinflow
present value factor @11.7%
present value of cash inflow
0
(470,000.00)
1
(470,000)
1
120000
0.8953
107431
2
210000
0.8015
168311
3
375000
0.7175
269074
Net present value
74,816