## (solution) Question 1: A firm is considering bidding on a project to produce

Question 1:

A firm is considering bidding on a project to produce eight widgets per year for the next four years. In order to complete the project, the firm must lease facilities for \$30,000 per year, purchase equipment that costs \$100,000, as well as pay labour and material costs of \$19,000 per unit produced. The equipment can be depreciated at the Class 8 CCA rate of 20%. At the end of the fourth year, it can be sold for \$10,000, and the asset class will remain open after the disposal of the equipment. In addition, net working capital will increase by \$50,000 if the project is undertaken, but these can be recovered at the end of the project. The company?s tax rate is 40%.

What is the minimum bid per widget if the firm requires 18% return on its investment?

Question 2.

• 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.

a.Write the expression for NPV using the unknown r as discount rate.

b.Write this expression as a function of [1/(1+r)].

c.Show that the expression in (b) as a quadratic equation. Look this up if necessary.

d.Solve the quadratic equation for its two roots.

e.Prepare a table of NPV vs. r for r= 0,10,20,40,100%.

f.Draw the graph of NVP vs. r.

g. Under what range of r values is this an acceptable investment?

h.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).

What is the maximum value of NPV? (There is one bonus point for the correct answer using calculus).
Calculation of minimum bid price per widget Year PVF

(18%) Cash flows PV Cash flows * PVF

Purchase Cost of equipment 0 1 \$ 100,000.00 \$ 100,000.00 Cost of lease facilities (Net of tax) =...

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Sep 13, 2020

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