Question

Project S has a cost of $10,000 and is expected to produce benefits (cash flows) of $3,000 per year for 5 years. Project L costs $25,000 and is expected to produce cash flows of $7,400 per year for 5 years.

Calculate the two projects' NPVs, assuming a cost of capital of 12%. Do not round intermediate calculations. Round your answers to the nearest cent.

Project S: $  

Project L: $  

Which project would be selected, assuming they are mutually exclusive?

Based on the NPV values, -Select-Project SProject L would be selected.

Calculate the two projects' IRRs. Do not round intermediate calculations. Round your answers to two decimal places.

Project S: %

Project L: %

Which project would be selected, assuming they are mutually exclusive?

Based on the IRR values, -Select-Project SProject L would be selected.

Calculate the two projects' MIRRs, assuming a cost of capital of 12%. Do not round intermediate calculations. Round your answers to two decimal places.

Project S: %

Project L: %

Which project would be selected, assuming they are mutually exclusive?

Based on the MIRR values, -Select-Project SProject L would be selected.

Calculate the two projects' PIs, assuming a cost of capital of 12%. Do not round intermediate calculations. Round your answers to three decimal places.

Project S:

Project L:

Which project would be selected, assuming they are mutually exclusive?

Based on the PI values, -Select-Project SProject L would be selected.

Which project should actually be selected?

-Select-Project SProject L should actually be selected.

Answer 1

As we know NPV is the sum of present value of cash inflow(Positive) and out flow (Negative).

r = Cost of Capital = 12%

n = no years

	Project S	Present Value of Project S Present Value = Cash Flow/(1+r)^n	Project L	Present Value of Project L
Year 0 n=0	-10,000	-10000	-25000	-25000
Year 1 n=1	3000	3000/(1+0.12)^1 = 2,678.57	7400	7400/(1+0.12)^1 = 6,607.14
Year 2 n=2	3000	3000/(1+0.12)^2 = 2,391.58	7400	7400/(1+0.12)^2 = 5,899.23
Year 3 n=3	3000	3000/(1+0.12)^3 = 2,135.34	7400	7400/(1+0.12)^3 = 5,267.17
Year 4 n=4	3000	3000/(1+0.12)^4 = 1,906.55	7400	7400/(1+0.12)^4 = 4,702.83
Year 5 n = 5	3000	3000/(1+0.12)^5 = 1,702.28	7400	7400/(1+0.12)^5= 4,198.96
NPV	Sum of all the Present Values	814.32		1,675.33

As NPV of Project L is higher we will choose Project L

2. IRR As we know IRR is found by keeping NPV zero and finding the rate at which the NPV is zero.

IRR cannot be found directly but we need to estimate it by trail and error.

The best way is to consider the Cash flows occuring in future are constant thus formula for present value of annuity can be applied and initial cost is available to us thus we try to put i such that we get the NPV zero.(You can also use annuity table to estimate it)

For Project s

C = 3000 (Net cash flow every year)

n = 5

i(IRR) = x(unknown)

PV annuity =

NPV = - initial cash flow

0 = C* X - 10000 (Here X = )

10000 = 3000 * X

X = 3.3333

Now from table we know that the value of i at which the PV of annuity is 3.333 lies between 15% and 16%

Now with trail and error in X we get value of i = 15.238% So our IRR = 15.238%

Similarly for Project L

C = 7400 (Net cash flow every year)

n = 5

i(IRR) = x(unknown)

NPV = - initial cash flow

0 = C* X - 25000 (Here X = )

X = 25000/7400

X = 3.3783

From table we get a value between 14-15%

After trail and error we get i = 14.672%

Thus by IRR method we choose Project S over Project L