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FINM 1001: Money Markets and Finance

Making Investment Decisions: Solutions to Practice Questions

Question One

A corporation is considering installing a machine that costs $100,000 plus installation costs of $10,000. It will generate revenues of $200,000 annually and cash expenses annually of $100,000. It will be depreciated to a salvage value of $5,000 over a seven-year life using the straight-line method. Assuming the firm is in a 34% marginal tax bracket, determine the incremental cash flows of this investment project.

The incremental cash flows for the project are as follows:

· Year 0:

• Cost of new machine: $100,000; and,

• Installation cost: $10,000

· Years 1–7 inclusive:

• Yearly revenues less expenses: R – E = 200,000 – 100,000 = $100,000 which yields that

• Yearly depreciation:  giving a tax shield on depreciation

• Salvage value = $5,000 received at the end of year 7.

Tabulating these cash flows:

Question Two

A corporation is considering purchasing one of two machines, A and B. The cash flows of each of the projects are represented below. The project’s required rate of return is 10% p.a.. Since these projects are mutually exclusive, which proposal (if any) should the manufacturer choose?

The NPVs of both projects are calculated as follows:

As Project B has the highest NPV, it is the project that should be selected.

Question Three

A firm is considering two types of machines to produce its output. Machine X is more expensive and lasts longer than Machine Y. The net cash flows (ie, revenues less expenses after tax) generated by each of the two machines are tabulated below.  

Assuming that the required return is 10% p.a. and that the machine that is adopted will be replaced indefinitely, what should the firm do?

The NPV calculations for each machine are as follows:

However, as the lives of the machines are different, these figures are not comparable.  To facilitate comparison, the equivalent annual cash flows as calculated as follows:

As Machine X has the highest equivalent annual cash flow, this is the machine that should be chosen.

Question Four

An office is considering an optimal replacement policy for its copying machines. The cost of running a machine for its three-year life, reflecting acquisition and maintenance costs, after depreciation and tax effects, is:

The salvage value of the copiers is $7,000, $5,500 and $2,000 at the end of the first, second and third years respectively. If the required return is 10% p.a., how frequently should the copiers be replaced?

There are three options open to the office: replace every year, every second year, or every third year. Clearly, the office would like to minimize the annual cost of copying. Hence, we compute the annual equivalent cost of each option and choose the option with the lowest annual equivalent cost.

Option 1: Replace Every Year: The net cash flows, incorporating acquisition and maintenance cost and salvage value are:

The NPV of this series of cash flows is:

Therefore, the annual cost of the copying machines is $5,000 under this alternative.

Option 2: Replace Every Second Year:  The net cash flows, incorporating acquisition and maintenance cost and salvage value are:

The NPV of this series of cash flows is:

.

Expressing this as an annual equivalent yields:

.

Therefore, the annual cost of the copying machines is $4,380.95 under this alternative.

Option 3: Replace Every Third Year:  The net cash flows, incorporating acquisition and maintenance cost and salvage value are:

The NPV of this series of cash flows is:

.

Expressing this as an annual equivalent yields:

.

Therefore, the annual cost of the copying machines is $4,583.08 under this alternative.  Hence, the office should choose to replace the copiers every two years.