$()$The management of Unter Corporation, an architectural design firm, is considering an investment with the following cash flows:

Year Investment Cash Inflow

$1$ $ $52,000$ $ $4,000$

$2$ $ $6,000$ $ $8,000$

$3$ $ $16,000$

$4$ $ $17,000$

$5$ $ $20,000$

$6$ $ $18,000$

$7$ $ $16,000$

$8$ $ $14,000$

$9$ $ $13,000$

$10$ $ $13,000$

Required:

$1.$ Determine the payback period of the investment.

$2.$ Would the payback period be affected if the cash inflow in the last year were several times as large?

$()$Labeau Products, Limited, of Perth, Australia, has $$16,000$ to invest. The company is trying to decide between two alternative uses for the funds as follows:

Invest in Project X Invest in Project Y

Investment required $ $16,000$ $ $16,000$

Annual cash inflows $ $5,000$

Single cash inflow at the end of $6$ years $ $35,000$

Life of the project $6$ years $6$ years

The company$$s discount rate is $15\%.$

Click here to view Exhibit $12$B$-1$ and Exhibit $12$B$-2,$ to determine the appropriate discount factor$($s$)$ using tables.

Required:

$1.$ Compute the net present value of Project X$.$

$2.$ Compute the net present value of Project Y$.$

$3.$ Which project would you recommend the company accept?

$()$The Riteway Ad Agency provides cars for its sales staff. In the past, the company has always purchased its cars from a dealer and then sold the cars after three years of use. The company$$s present fleet of cars is three years old and will be sold very shortly. To provide a replacement fleet, the company is considering two alternatives:

Purchase alternative: The company can purchase the cars, as in the past, and sell the cars after three years of use. Ten cars will be needed, which can be purchased at a discounted price of $$19,000$ each. If this alternative is accepted, the following costs will be incurred on the fleet as a whole:

Annual cost of servicing, taxes, and licensing $ $5,200$

Repairs, first year $ $3,100$

Repairs, second year $ $5,600$

Repairs, third year $ $7,600$

At the end of three years, the fleet could be sold for one$-$half of the original purchase price.

Lease alternative: The company can lease the cars under a three$-$year lease contract. The lease cost would be $$71,000$ per year $($the first payment due at the end of Year $1).$ As part of this lease cost, the owner would provide all servicing and repairs, license the cars, and pay all the taxes. Riteway would be required to make a $$15,500$ security deposit at the beginning of the lease period, which would be refunded when the cars were returned to the owner at the end of the lease contract.

Riteway Ad Agency$$s required rate of return is $15\%.$

Click here to view Exhibit $12$B$-1$ and Exhibit $12$B$-2,$ to determine the appropriate discount factor$($s$)$ using tables.

Required:

$1.$ What is the net present value of the cash flows associated with the purchase alternative?

$2.$ What is the net present value of the cash flows associated with the lease alternative?

$3.$ Which alternative should the company accept?

$()$The management of Ballard MicroBrew is considering the purchase of an automated bottling machine for $$57,000.$ The machine would replace an old piece of equipment that costs $$15,000$ per year to operate. The new machine would cost $$7,000$ per year to operate. The old machine currently in use is fully depreciated and could be sold now for a salvage value of $$24,000.$ The new machine would have a useful life of $10$ years with no salvage value.

Required:

$1.$ What is the annual depreciation expense associated with the new bottling machine?

$2.$ What is the annual incremental net operating income provided by the new bottling machine?

$3.$ What is the amount of the initial investment associated with this project that should be used for calculating the simple rate of return?

$4.$ What is the simple rate of return on the new bottling machine? $($Round your answer to $1$ decimal place i$.$e$.0\mathrm{.}123$ should be considered as $12\mathrm{.}3\%.)$

$()$Lukow Products is investigating the purchase of a piece of automated equipment that will save $$110,000$ each year in direct labor and inventory carrying costs. This equipment costs $$700,000$ and is expected to have a $6-$year useful life with no salvage value. The company$$s required rate of return is $8\%$ on all equipment purchases. Management anticipates that this equipment will provide intangible benefits such as greater flexibility and higher$-$quality output that will result in additional future cash inflows.

Click here to view Exhibit $12$B$-1$ and Exhibit $12$B$-2,$ to determine the appropriate discount factor$($s$)$ using table.

Required:

$1.$ What is the net present value of the piece of equipment before considering its intangible benefits? $($Enter negative amount with a minus sign. Round your final answer to the nearest whole dollar amount.$)$

$2.$ What minimum dollar value per year must be provided by the equipment$$s intangible benefits to justify the $$700,$