Consider the following cash flow [-100, + 230, -132]. We want to decide under what range of discount rate this is an advantageous investment. But noting the change in sign, we conclude IRR is not a suitable instrument. Write the expression for NPV using the unknown r as discount rate. Write this expression as a function of [1/(1+r)].Â Show that the expression in (b) as a quadratic equation. Look this up if necessary. Solve the quadratic equation for its two roots. Prepare a table of NPV vs. r for r= 0,10,20,40,100%. Draw the graph of NVP vs. r. Under what range of r values is this an acceptable investment? Noting that NPV increases then declines as r grows from 0 to 40%, determine at what level of r NPV is a maximum (recall that d(NPV)/ds = 0, where NPV is a maximum). If you have sufficient background, solve this using calculus. If not, graphically find the top of the NPV hill (where slope = 0). â€¨What is the maximum value of NPV? (There is one bonus point for the correct answer using calculus).

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## You are evaluating a project for Ultimate Inc. The project

You are evaluating a project for Ultimate Inc. The project produces chew-resistant doghouses. You estimate the sales price of these doghouses to be $500 and sales volume to be 2,500 units per year over the projectâ€™s three-year life. Variable costs amount to $300 per unit and fixed costs (not including depreciation) are $150,000 per year. The project requires an initial investment of $250,000 and this will be depreciated on a straight-line basis to zero over the three-year project life. There will be an initial net working capital investment of $90,000 (t0) and two further investments of $90,000 at the beginning of each year thereafter. The full amount of working capital will be recovered at the end of the projectâ€™s life (i.e., $270,000 at t3). The tax rate is 35% and the required return on the project is 15%. a.Â What is the EBIT for the project in the first year? b.Â What is the operating cash flow for the project in year 2? c.Â Suppose the actual market value of the initial investment at the end of year 3 is $50,000. What is the effect of the $50,000 salvage value on year 2 cash flows? d.Â What is the NPV of this project?

## A firm is considering the purchase of equipment which will cost

A firm is considering the purchase of equipment which will cost $3 million. This equipment will last for 10 years, at the end of which it can be sold for $800,000. The CCA rate for this asset class is 30%, and the firm expects to have other assets in this asset class at the end of year 10. This equipment is expected to increase before-tax operating cash flows by $750,000 per year. However, in order to put the equipment to use, an additional $150,000 will need to be invested in net working capital initially (i.e., at ). The required rate of return is 16% and the firmâ€™s marginal tax rate is 35%.â€¨ a.Â Should the firm purchase this equipment? b.Â Suppose that to arrive at the before-tax operating cash flows in part (a), we have used the following estimates:Fixed costs = $120,000Variable costs = 60% of sales What is the Net Present Value of the new equipment if, in the best-case scenario, we estimate that fixed costs could be lower by 20% and sales revenues could be higher by 25%? c.Â Given the information in (a), and assuming that fixed costs are $120,000 and variables costs are 60% of sales, what is the sales level at which Net Present Value equals zero? (In other words, what is the financial break-even sales level?)