A small sporting goods company is considering investing $$3000$ in a project that will produce volleyballs

over the next five years. The company plans to produce and sell $200$ volleyballs in the first year, and

expects that volume to grow by $10\%$ each year thereafter. The unit selling price forecast the company has

developed is $$20$ in year $1,$ $$22$ in year $2,$ $$25$ in year $3,$ $$28$ in year $4,$ and $$31\mathrm{.}50$ in year $5.$ Variable

costs are forecast to be $$15$ per unit produced, and there will be a fixed overhead cost in each year of

$$500.$

a$)$ Use the above information to develop a simple cash flow sheet, and then apply Excel's NPV function

to calculate the project value assuming a $10\%$ discount rate. What is your answer?

b$)$ Suppose the company thinks it may be able to produce and sell more than currently planned. What

growth rate of production would produce an NPV of $$10,000?$

c$)$ Suppose instead that the company thinks it can reduce its variable cost rate. What rate would produce

an NPV of $$10,000?$