Question

1. Your division is considering two projects. The required rate of return for both projects is 10%. Below are the cash flows of both the projects:

Projects	Initial investment	Year 1	Year 2	Year 3	Year 4
A	-$30	$5	$10	$15	$20
B	-$30	$20	$10	$8	$6

1. Calculate the Payback period and discounted payback period. Why are they different? .
2. Calculate the NPV for both the projects
3. Which projects should be accepted?

1. if both the projects are independent.
2. if both projects are mutually exclusive.

Answer 1

a.Project A

Cumulative cash flow in year 1= $5

Cumulative cash flow in year 2= $15

Cumulative cash flow in year 3= $30

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

= 3 years + $0

Payback period= 3 years

Project B

Cumulative cash flow in year 1= $20

Cumulative cash flow in year 2= $30

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

= 2 years + $0

Payback period= 2 years

b.Project A

Discounted cash flow in year 1= $4.55

Discounted cash flow in year 2= $8.26

Discounted cash flow in year 3= $11.27

Discounted cash flow in year 4= $13.66

Cumulative discounted cash flow in year 3= $24.08

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

= 3 years + ($30 - $24.08)/ $13.66

= 3 years + $5.92/ $13.66

= 3 years + 0.43

= 3.43 years.

Project B

Discounted cash flow in year 1= $18.18

Discounted cash flow in year 2= $8.26

Discounted cash flow in year 3= $6.01

Cumulative discounted cash flow in year 2= $26.44

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

= 2 years + ($30 - $26.44)/ $6.01

= 2 years + $3.56/ $6.01

= 2 years + 0.59

= 2.59 years.

The payback period and discounted payback period are different because the discounted payback period takes into the time value of money.

b.Project A

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

• Press the CF button.
• CF0= -$30. 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 required rate of return of 10%.
• Press enter after that. Press the down arrow and CPT buttons to get the net present value.  

Net present value at 10% required rate of return is $7.74.

Project B

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

• Press the CF button.
• CF0= -$30. 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 required rate of return of 10%.
• Press enter after that. Press the down arrow and CPT buttons to get the net present value.  

Net present value at 10% required rate of return is $6.55.

c.i.If the projects are independent, both the projects should be accepted since they generate a positive net present value.

ii.If the projects are mutually exclusive, project A should be accepted since it generates the largest net present value.