The Duncan Corporation, a firm in the $20\%$ marginal tax bracket, with an $18\%$ required rate of return or discount rate, is considering a new project. This project involves the introduction of a new product. This product is expected to last $5$ years and then, because it is somewhat of a fad product, it will be terminated.

Cost of new plant and equipment: $$4,750,000$

Shipping and installation costs: $250,000$

Unit sales:

Year Units Sold

$14,000$

$24,000$

$34,000$

$42,000$

$52,000$

Sales price per unit: $$700/$unit in years $1-3$ and $$500/$unit in years $4$ and $5$

Variable cost per unit: $$300/$unit throughout the five years

Annual fixed costs: $$5,000,000.$

There will be an initial working capital requirement of $$1,500,000$ just to get production started. At the conclusion of the project, the plant and equipment can be sold for $$8,000,000.$ The plant and equipment will be depreciated over five years on a straight$-$line basis to a zero$-$salvage value.

Required:

a$)$ Determine the payback period for the project.

b$)$ Determine the net present value of the project.

c$)$ Determine the internal rate of return of the project.

d$)$ Explain why you would or would not recommend the project.The Duncan Corporation, a firm in the $20\%$ marginal tax bracket, with an $18\%$ required rate of return or discount rate, is considering a new project. This project involves the introduction of a new product. This product is expected to last $5$ years and then, because it is somewhat of a fad product, it will be terminated.

Cost of new plant and equipment: $$4,750,000$

Shipping and installation costs: $250,000$

Unit sales:

Year Units Sold

$14,000$

$24,000$

$34,000$

$42,000$

$52,000$

Sales price per unit: $$700/$unit in years $1-3$ and $$500/$unit in years $4$ and $5$

Variable cost per unit: $$300/$unit throughout the five years

Annual fixed costs: $$5,000,000.$

There will be an initial working capital requirement of $$1,500,000$ just to get production started. At the conclusion of the project, the plant and equipment can be sold for $$8,000,000.$ The plant and equipment will be depreciated over five years on a straight$-$line basis to a zero$-$salvage value.

Required:

a$)$ Determine the payback period for the project.

b$)$ Determine the net present value of the project.

c$)$ Determine the internal rate of return of the project.

d$)$ Explain why you would or would not recommend the project.