# Calculating Payback Period, IRR and NPV fo Investments

Problems:

1). You are a real estate agent thinking of placing a sign advertising your services at a local bus stop. The sign will cost $ 5000 and will be posted for one year. You expect that it will generate additional revenue of $ 500 per month. What is the payback period?

2). Innovation Company is thinking about marketing a new software product. Upfront costs to market and develop the product are $5 million. The product is expected to generate profits of $ 1 million per year for ten years. The company will have to provide product support expected to cost $ 100,000 per year in perpetuity for 10 years. Assume all profits and expenses occur at the end of the year. What is the NPV of this investment if the cost of capital is 6 %? Should the firm under-take the project? Repeat the analysis for discount rates of 2 % and 11 %.

3). You own a coal mining company and are considering opening a new mine. The mine itself will cost $ 120 million to open. If this money is spent immediately, the mine will generate $ 20 million for the next ten years. After that, the coal will run out and the site must be cleaned and maintained at environmental standards. The cleaning and maintenance are expected to cost $ 2 million per year in perpetuity for 10 years. What does the IRR rule say about whether you should accept this opportunity? If the cost of capital is 8 %, what does the NPV rule say?

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#### Solution Preview

Please refer attached Excel file for better clarity of tables and formulas.

Solutions:

1). You are a real estate agent thinking of placing a sign advertising your services at a

local bus stop. The sign will cost $ 5000 and will be posted for one year. You expect that

it will generate additional revenue of $ 500 per month. What is the payback period?

Solution:

Since additional revenue generation is same throughout the teure

Pay back period = Initial cost/ periodic net cash inflow=5000/50=10 months

2). Innovation Company is thinking about marketing a new software product. Upfront

costs to market and develop the product are $5 million. The product is expected to

generate profits of $ 1 million per year for ten years. The company will have to provide

product support expected to cost $ 100,000 per year in perpetuity for 10 years. Assume

all profits and expenses occur at the end of the year.

What is the NPV of this investment if the cost of capital is 6 %? Should the firm

under-take the project? Repeat the analysis for discount rates of 2 % and 11 %.

Initial outlay=-5 million

Net annual cash inflow=1,000,000-100,000= 0.9million

PV factor of ordinary annuity for period = 10 year and discout rate=6%

PV factor =7.3601

PV of inflows = PV factor*net cash inflow=6.62 million

Net Present Value=Initial outlay+PV of net cash flows

NPV=-5+6.62=1.62 ...

#### Solution Summary

There are three problems. Solution to these problems demonstrate the steps to calculate Payback period, Internal rate of retrun and net present value for given investment proposals.