Question

Project	C0	C1	C2	C3	C4
A	-5000	+1000	+1000	+3000	0
B	-1000	0	+1000	+2000	+3000
C	-5000	+1000	+1000	+3000	+5000

1. If the opportunity cost of capital is 11%, and you have unlimited access to the capital, which one(s) would you accept? What would be your action if the cost of capital is 16%?
2. Suppose that you have limited access to the capital and you need to choose only one project. Which one would you choose? The discount rate is still 11%.
3. What is the payback period of each project? Please analyse if in general decision based on payback is consistent with decision based on NPV.
4. What are the internal rates of return (IRR) on the three projects? Does the IRR rule in this case give the same decision as NPV?
5. If the opportunity cost of capital is 11%, what is the profitability index for each project? Please analyse if in general decisions based on profitability index is consistent with decisions based on NPV.
6. What is the most generally accepted measure to choose between the projects? Please justify your answer.

Answer 1

A) Using financial calculator to calculate the NPV at 11%

Project A

Inputs: C0= -5,000

C1= 1,000. Frequency= 2

C2= 3,000. Frequency= 1

I= 11%

Npv= compute

We get, NPV of the project A as -$1,093.90

Project B

Using financial calculator to calculate the Npv at 11%

Inputs: C0= -1,000

C1= 0 frequency=1

C2= 1,000. Frequency= 1

C3= 2,000. Frequency= 1

C4= 3,000. Frequency=1

I= 11%

Npv= compute

We get, Npv of the project B as $3,250.20

Project C

Using financial calculator to calculate the NPV at 11%

Inputs: C0= -5,000

C1= 1,000. Frequency= 2

C2= 3,000. Frequency= 1

C3= 5,000 Frequency= 1

I= 11%

Npv= compute

We get, NPV of the project C as $2,199.75

On the basis of the NPV calculated above, we should choose Project B and C , because they have a positive NPV.

B)

Using financial calculator to calculate the NPV at 16%

Project A

Inputs: C0= -5,000

C1= 1,000. Frequency= 2

C2= 3,000. Frequency= 1

I= 16%

Npv= compute

We get, NPV of the project A as -$1,472.80

Project B

Using financial calculator to calculate the Npv at 16%

Inputs: C0= -1,000

C1= 0 frequency=1

C2= 1,000. Frequency= 1

C3= 2,000. Frequency= 1

C4= 3,000. Frequency=1

I= 16%

Npv= compute

We get, Npv of the project B as $2,681.35

Project C

Using financial calculator to calculate the NPV at 16%

Inputs: C0= -5,000

C1= 1,000. Frequency= 2

C2= 3,000. Frequency= 1

C3= 5,000. Frequency= 1

I= 16%

Npv= compute

We get, NPV of the project C as $1,288.66

On the basis of the NPV calculated above, we should choose Project B and C , because they have a positive NPV.

C) We should choose Project B because it has the highest NPV .

D) Payback period refers to the time period required to recover initial investment.

Project A = Payback period is 3 years

Project B= payback period is 2 years

Project C= payback period is 3 years.

In this case, the payback period is consistent with the Npv decision. But, in general the payback period doesn't take into consideration the time value of money. So, the decision might differ.

E) IRR of Project A

Using financial calculator to calculate the IRR

Inputs: C0= -5,000

C1= 1,000. Frequency= 2

C2= 3,000. Frequency= 1

IRR= compute

We get, IRR of the project A as 0%

IRR of project B

Using financial calculator to calculate the IRR

Inputs: C0= -1,000

C1= 0 Frequency= 1

C2= 1,000. Frequency= 1

C3= 2,000. Frequency= 1

C4= 3,000. Frequency= 1

IRR= compute

We get, IRR of the project B as 76.138%

IRR of project C

Using financial calculator to calculate the IRR

Inputs: C0= -5,000

C1= 1,000. Frequency= 2

C2= 3,000. Frequency= 1

C3= 5,000. Frequency= 1

IRR= compute

We get, IRR of the project C as 25.20%

Yes, the IRR decision is aligned with the NPV decision.

F) Profitability Index of Project A = Initial investment + NPV / Initial Investment

= 5,000 - 1,093.90 / 5,000

= 3,906.10 / 5,000

= 0.78

Profitability Index of Project B = Initial investment + NPV / Initial Investment

= 1,000 + 3,250.20 / 1,000

= 4,250.20 / 1,000

= 4.25

Profitability Index of Project C = Initial investment + NPV / Initial Investment

= 5,000 + 2,199.75 / 5,000

= 7,199.75 / 5,000

= 1.44

Yes, the decisions are aligned with the Npv. This is because a project based on Profitability index can only be selected if the index is more than 1, and it is only possible if Npv is positive.

G) The most general way to choose is by calculating the Net present value, because it take into consideration the time value of money and overcomes the problem of all other neasures.