Delta Widget Corp. $($DWC$)$ is considering whether to purchase immediately a new widget$-$producing machine at a cost of $$1,000,000.$ The machine would produce $100,000$ widgets per year for four years. Delta would sell the machine after four years. Depreciation would be based on a five$-$year life, i$.$e$.,$ $$200,000$ per year. The salvage value on the machine would be $$300,000$ based on current price levels, but management anticipates that the actual salvage value four years from now will increase proportional to accumulated inflation. Currently, widget prices are $$26,$ while the materials and labor required to purchase a widget cost $$22.$ The inflation rate is forecast to be $5\%$ per year, and the prices of both widgets and widget inputs are expected to increase at the inflation rate. The income tax rate is $34\%,$ while the capital gains tax rate is $25\%.$ Other than the cost of purchasing the machine now, all cash flows occur at the end of each year.

$($a$)$ Delta management has selected a nominal discount rate of $7\mathrm{.}10\%$ per year for this project. What real discount rate is implied by this selection?

$($b$)$ Compute the net nominal post$-$tax cash flows resulting from the purchase of a widget machine on a year$-$by$-$year basis, and the NPV$.$

Identify whether each of the following would $($other things equal$)$ increase or decrease the NPV of the widget machine, and briefly explain why $$ no computations are required:

$($c$)$ An increase in the real discount rate.

$($d$)$ An increase in the forecast inflation rate. $($Note$,$ there are two contributors here $$ identify both for full credit$).$