I am manufacturing and marketing a mobile phone. Each phone costs me $40 to prod

Question

I am manufacturing and marketing a mobile phone. Each phone costs me $40 to produce, and I am selling them for $100. My fixed costs for the manufacture and marketing are $400,000 per year. Over the next twelve months I expect to sell 10,000 phones, going up by 1,000 phones per year over the following four years; beyond that, the phone will be obsolete and I don’t expect to sell any more. (So I expect to sell 10,000 before the end of 2016, 11,000 between then and the end of 2017, 12,000 between the end of 2017 and 2018, 13,000 between the end of 2018 and 2019, and, finally, 14,000 before the end of 2020.)

There is a bug in the phones’ software that allows eavesdroppers to intercept phone conversations. I estimate that there is only one chance in 100,000, per phone, per year, that anyone will discover this bug. Once anyone does discover it, I don’t expect that anyone will buy any more of my phones in any subsequent year. In that event, I will close down my factory, and will not pay any more fixed or variable costs. However, I don’t expect to recall any phones or to pay any damages.

My software department estimates that they can find and remove the bug before I make the first sale, but it will be expensive. What is the most it would be worth my paying, right now, to have it removed? Assume that all other costs and revenues occur at the end of the year, but that users could discover the bug any time after the beginning of the year.

My MARR is 20%.

Explanation / Answer

I am manufacturing and marketing a mobile phone. Each phone costs me $40 to prod

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