You recall from a few weeks ago that Lyons Limited sells expertly$-$crafted stained glass pieces. You helped them analyze their free cash flows. Now they need your help deciding whether or not they should produce some of their new materials in$-$house starting next year or whether they should continue outsourcing production of certain raw materials. You previously made calculations based on only the next five years of data. But you$$ve remembered that Lyons Limited is a corporation and we should make forecasts beyond simply five years. You must help them decide which course of action to take given your newfound knowledge.

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In both scenarios, Lyons Limited forecasts that they will sell $100,000$ units of stained glass for a price of $$50$ each for the next five years and face a tax rate of $20\%.$ If they produce the materials in$-$house then their cost$-$of$-$goods sold $($COGS$)$ is projected to be $10\%$ of revenues and their SG&A expenses are projected to be $20\%$ of revenues. But if they outsource their production, their COGS is projected to be $30\%$ of revenues and their SG&A expenses are projected to be $5\%$ of revenues. After year $5,$ revenues are expected to grow at a rate of $2\%$ per year. If Lyons Limited switches to in$-$house production, this will require an initial capital expenditure of $$1,000,000$ occurring immediately, and will be depreciated using a straight$-$line schedule down to $$0$ starting next year for the next five years $($i$.$e$.$ after five years, the asset has been depreciated to $$0).$

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As the finance manager, you$$ve asked your intern to estimate any changes in net working capital over the next five years. Your intern has informed you that in year $1,$ receivables are expected to increase by $$50,000$; cash requirements are expected to increase by $$10,000$; payables are expected to increase by $$25,000.$ These changes are expected to be permanent.

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Question $29$: At what discount rate would Lyons Limited be indifferent between the two options $($i$.$e$.$ at what discount rate would the two NPVs be equal$)?$