If a project has a cost of $10,000, expected net cash flows of $1500 a year for 12 years and you use a discount rate of 6%, 1. What is the following:
a. Payback period (no application of discount rate)
b. Payback period (using discount rate)
c. NPV
d. IRR
2. Should the project be accepted?
3. If another project has a cost of $10,000 and has expected life of 8 years and it will generate $3000 a year should you accept the project if your boss says the cost of capital is 5%?

1a, 6.67 years

b. 8.9 years

c. NPV = $2,575.77

d. IRR = 10.45%

2. it should be accepted

3. it should be accepted.

Explanation:

Payback calculates the amount of time it takes to recover the amount invested in a project from it cumulative cash flows

Payback period = $10,000 / $1500 = 6.67 years

Discounted payback calculates the amount of time it takes to recover the amount invested in a project from it cumulative discounted cash flows

discounted cash flow in year 1 = $1500 / 1.06 = $1415.09

discounted cash flow in year 2 = $1500 / 1.06^2 = $1,334.99

discounted cash flow in year 3 = $1500 / 1.06^3 = $1,259.43

discounted cash flow in year 4 = $1500 / 1.06^4  = $1,188.14

discounted cash flow in year 5 = $1500 / 1.06 ^5 = $1,120.89

discounted cash flow in year 6 = $1500 / 1.06^6 = $1,057.44

discounted cash flow in year 7 = $1500 / 1.06^7 = $997.59

discounted cash flow in year 8 = $941.12

please check the attached image on how the discounted payback period was calculated

Net present value is the present value of after tax cash flows from an investment less the amount invested.  

Internal rate of return is the discount rate that equates the after tax cash flows from an investment to the amount invested

NPV and IRR can be calculated using a financial calculator  

Cash flow in year 0 = $-10,000

Cash flow each year from year 1 to 12 = $1,500

I = 6%

NPV = $2,575.77

IRR = 10.45%

The project should be accepted because the NPV is positive, this indicates that the project is profitable. Also, the IRR is greater than the discount rate, so the project should be accepted.

to determine if the project should be accepted, the NPV  of the project should be determined.

Cash flow in year 0 = $-10,000

Cash flow each year from year 1 to 8 = $3,000

I = 5%

NPV = $13,165.20

the project should be accepted because the NPV is positive

To find the NPV using a financial calculator:

1. Input the cash flow values by pressing the CF button. After inputting the value, press enter and the arrow facing a downward direction.

2. after inputting all the cash flows, press the NPV button, input the value for I, press enter and the arrow facing a downward direction.  

3. Press compute  

To find the IRR using a financial calculator:

1. Input the cash flow values by pressing the CF button. After inputting the value, press enter and the arrow facing a downward direction.

2. After inputting all the cash flows, press the IRR button and then press the compute button.  

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