Question

Below are the estimated cash flows for two projects: S and L. The WACC is 10%.

Time	0	1	2	3
Project L	-100	10	60	80
Project S	-100	70	50	20

1a. What is the payback period? Find the paybacks for Projects L and S.

1b..What is the rationale for the payback method? According to the payback criterion, which project(s) should be accepted if the firm’s maximum acceptable payback is 2 years, if Projects L and S are independent? If Projects L and S are mutually exclusive?

1c. What is the difference between the regular and discounted payback methods? What is Project L’s discounted payback, assuming a 10% cost of capital?

1d.Define the term net present value (NPV). What is each project’s NPV?

1e. What is the rationale behind the NPV method? According to NPV, which project(s) should be accepted if they are independent? Mutually exclusive?

1f. Define the term internal rate of return (IRR). What is each project’s IRR?

1g. What is the logic behind the IRR method? According to IRR, which project(s) should be accepted if they are independent? Mutually exclusive?

1h. If a project with normal cash flows has an IRR greater than the WACC, the project must also have a positive NPV.

Answer 1

1a.Project L

Payback period= full years until recovery + unrecovered cost at the start of the year/cash flow during the year

= 2 years + ($100 - $70)/ $80

= 2 years + $30/ $80

   = 2 years + 0.3750

= 2.38 years.

Project S

Payback period= full years until recovery + unrecovered cost at the start of the year/cash flow during the year

= 1 year + ($100 - $70)/ $50

= 1 year + $30/ $50

= 1 year + 0.60

= 1.60 years.

1b. In the payback period method,  the time period to recover the initial cost of investment is calculated. The lower the payback period, the better.

If projects L and S are independent, only project S is accepted since it's payback period is less than the maximum allowable payback of 2 years.

If projects L and S are mutually exclusive, only project S is accepted since it's payback period is less than the maximum allowable payback of 2 years.

1c. Both methods, payback and discounted payback time period to recover the initial cost of investment. But discounted payback also accounts for the time value of money.

Project L

Discounted payback period= full years until recovery + unrecovered cost at the start of the year/ discounted cash flow during the year

= 2 years + ($100 - $58.68)/ $60.11

= 2 years + $41.32/ $60.11

= 2 years + 0.69

= 2.69 years.

Project S

Discounted payback period= full years until recovery + unrecovered cost at the start of the year/ discounted cash flow during the year

= 1 year + ($100 - $63.64)/ $41.32

= 1 year + $36.36/ $41.32

= 1 year + 0.88

= 1.88 years.

1d. In The net present value, cash flows are determined and they are discounted back to present values. The project with the highest net present value is selected.

Project L

Net present value can be solved using a financial calculator. The steps to solve on the financial calculator:

• Press the CF button.
• CF0= -$100. Indicate the initial cash flow by a negative sign since it is a cash outflow.  
• Cash flow for each year should be entered.
• Press Enter and down arrow after inputting each cash flow.
• After entering the last cash flow cash flow, press the NPV button and enter the cost of capital of 10%.
• Press enter after that. Press the down arrow and CPT buttons to get the net present value.  

Net present value at 10% cost of capital is $18.78.

Project S

Net present value can be solved using a financial calculator. The steps to solve on the financial calculator:

• Press the CF button.
• CF0= -$100. Indicate the initial cash flow by a negative sign since it is a cash outflow.  
• Cash flow for each year should be entered.
• Press Enter and down arrow after inputting each cash flow.
• After entering the last cash flow cash flow, press the NPV button and enter the cost of capital of 10%.
• Press enter after that. Press the down arrow and CPT buttons to get the net present value.  

Net present value at 10% cost of capital is $19.99

1e.The net present value measures the value added by the project accepted.

According to the net present value, both projects can be accepted if the projects are independent since both generated a positive net present value and project S should be accepted if the projects are mutually exclusive since it has the highest net present value.

1f.Internal rate of return is the rate of return that makes the net present value of all cash flows of a certain investment equal to zero. It is helpful in comparing investments and making capital budgeting decisions.

Project L

Internal rate of return can be calculated using a financial calculator by inputting the below:

• Press the CF button.
• CF0= -$100. The initial cash flow is indicated by a negative sign since it is a cash outflow.  
• Cash flow for each of the fifteen years should be entered.
• Press Enter and down arrow after inputting each cash flow.
• After entering the last cash flow cash flow, press the IRR and CPT button to get the IRR of the project.

The IRR of the project is 18.13%.

Project S

Internal rate of return can be calculated using a financial calculator by inputting the below:

• Press the CF button.
• CF0= -$100. The initial cash flow is indicated by a negative sign since it is a cash outflow.  
• Cash flow for each of the fifteen years should be entered.
• Press Enter and down arrow after inputting each cash flow.
• After entering the last cash flow cash flow, press the IRR and CPT button to get the IRR of the project.

The IRR of the project is 23.56%.

1g. If the internal rate of return is higher or equal to the cost of capital, the project should be accepted. If the internal rate of return is lesser than the cost of capital, the project should be rejected.

According to IRR, if the projects are independent, both the project should be accepted since the internal arte of return computed is higher than the cost of capital.

If the projects are mutually exclusive, project S is accepted since it has the highest internal rate of return.

1h.The statement which says that If a project with normal cash flows has an IRR greater than the WACC, the project must also have a positive NPV is true.

In case of any query, kindly comment on the solution.