# NPV, IRR and payback calculations

Question 1

You are considering an investment in a project with a life of eight years, an initial outlay of $120,000 and annual after-tax cash flows of $52,000. The project also requires an increase in inventories of $22,000. This $22,000 investment in inventories is required at the outset of the project and will be released when the project is completed. The appropriate discount rate for this project is 10%.

a) Compute the payback period of this project.

b) Compute the discounted payback period of this project.

c) The firm has a required payback period of 3 years. Would you accept this project?

d) Compute the NPV of this project.

e) According to your results in a), b) and c) should the project be accepted. Motivate your answer.

Question 2

Your old machine has finally lost its productive usefulness. You are considering two potential new machines for replacement. Machine I will last for 6 years and will require annual operating costs of $250,000 per year. Machine II will last for 9 years and will require annual operating costs of $100,000. The initial costs of Machines I and II are $1,200,000 and $1,400,000, respectively. Assume that the risk-adjusted discount rate of 10%.

a) Compute the cost of each machine in terms of NPV.

b) Which machine will be cheaper for the company to use? Explain.

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#### Solution Preview

The calculations are in the attached file

1a. Payback period is when the initial investment is recovered. We cumulate the cash flows starting from the initial investment, till it becomes zero. In year 2 it is -38,000 and in year 3 it is +14,000. For zero, we need to find out when do we get 38,000. In the year 3, the cash flow is 52,000. In 12 months we get 52,000 so in how many months we get 38,000. These months are added to 2 ...

#### Solution Summary

The solution explains how to calculate the cash flows and NPV, IRR, payback and discounted payback and the acceptance or rejection of the project