Chapter 12, Problem 41E

1.

To determine

Calculate the investment’s net after-tax annual cash inflow of company, D & G.

Explanation of Solution

A capital investment is a project involving large fund expenditure and future benefits expected over a number of years. Capital budgeting is the process of identification, assessment, selection and controlling invested capital. A strategic control system relates to the processes and uses organization to monitor organizational progress in terms of the achievement of its strategic objectives. A capital budget for a given time period consists of a listing of approved and anticipated investment projects cash outflows linked to those projects.

The capital structure refers to the means of financing a company; the mix between debt, and capital stock.

Sensitivity analysis is the process of varying a key input variable selectively, for

Example: discount rate, to determine the range within which a capital budget decision is valid.

Calculate depreciation/year:

Depreciation per year, SL basis: ($30,600 – $600) ÷ 6 years = $5,000

Particulars	Amount
Taxable income ($8,000 – $5,000)	$\$3,000$
Multiply: Tax rate	$\times 40\%$
Income tax	$\$1,200$

Pre-tax annual cash flow (cash savings) = $8,000

Calculate net after-tax annual cash inflow of company, D & G:

$\begin{array}{c}\text{Net after}-\text{tax annual cash inflow}=\$8,000-\$1,200\\ =\$6,800\end{array}$

Working notes:

Total cost of machine is $30,600.

Estimated life of machine is 6 years and its estimated salvage value is $600.

Estimated annual cash savings by using new machine is $8,000.

Company’s after tax cost of capital is 8% and its income tax rate is 40%.

2.

To determine

Calculate the payback period assuming that the net after-tax annual cash flow of the investment is $5,000.

Explanation of Solution

A capital investment is a project involving large fund expenditure and future benefits expected over a number of years. Capital budgeting is the process of identification, assessment, selection and controlling invested capital. A strategic control system relates to the processes and uses organization to monitor organizational progress in terms of the achievement of its strategic objectives. A capital budget for a given time period consists of a listing of approved and anticipated investment projects cash outflows linked to those projects.

The capital structure refers to the means of financing a company; the mix between debt, and capital stock.

An investment's payback period is the amount of time required for cumulative after-tax cash inflows from an investment to recover initial outlay of the investment.

Calculate the payback period of company, D & G:

$\begin{array}{c}\text{Payback period}=\text{Total initial capital investment}÷\text{Annual after-tax cash inflows}\\ =\$30,600÷\$5,000\\ =\$6.12\text{ years}\end{array}$

Hence, the payback period of company, D & G will be 7 years.

Working notes:

Total cost of machine is $30,600.

Estimated life of machine is 6 years and its estimated salvage value is $600.

Estimated annual cash savings by using new machine is $8,000.

Company’s after tax cost of capital is 8% and its income tax rate is 40%.

3.

To determine

Calculate the NPV of the investment of company, D & G assuming the net after-tax annual cash inflow of the investment is $5,000.

Explanation of Solution

A capital investment is a project involving large fund expenditure and future benefits expected over a number of years. Capital budgeting is the process of identification, assessment, selection and controlling invested capital. A strategic control system relates to the processes and uses organization to monitor organizational progress in terms of the achievement of its strategic objectives. A capital budget for a given time period consists of a listing of approved and anticipated investment projects cash outflows linked to those projects.

The capital structure refers to the means of financing a company; the mix between debt, and capital stock.

NPV is the difference between present value (PV) of cash inflows and PV of cash outflows.

The actual value of a future cash flow (PV) is its current equivalent value; also known as time-adjusted value.

Calculate the NPV of the investment of company, D & G:

Particulars	Amount
PV of annual after-tax cash savings ($5,000 × 4.623)	$\$23,115$
PV of salvage value ($ 600 × 0.63)	$378$
Total Present Value of Cash Inflows	$\$23,493$
Initial Investment Cash Outlay	$30,600$
Net Present Value	($7,107)

Working notes:

Total cost of machine is $30,600.

Estimated life of machine is 6 years and its estimated salvage value is $600.

Estimated annual cash savings by using new machine is $8,000.

Company’s after tax cost of capital is 8% and its income tax rate is 40%.

4.

To determine

Calculate the minimum net after-tax annual cost savings that make the proposed investment acceptable.

Explanation of Solution

A capital investment is a project involving large fund expenditure and future benefits expected over a number of years. Capital budgeting is the process of identification, assessment, selection and controlling invested capital. A strategic control system relates to the processes and uses organization to monitor organizational progress in terms of the achievement of its strategic objectives. A capital budget for a given time period consists of a listing of approved and anticipated investment projects cash outflows linked to those projects.

The capital structure refers to the means of financing a company; the mix between debt, and capital stock.

NPV is the difference between present value (PV) of cash inflows and PV of cash outflows.

The actual value of a future cash flow (PV) is its current equivalent value; also known as time-adjusted value.

Let X = a minimum yearly cost savings after tax, and let NPV = 0. The Initial Investment Outlay ($30,600) is reduced by an 8 percent discount rate (i.e. $378) on the PV of the asset's salvage value. Thus, we have (by definition): if NPV = $0

Calculate the minimum net after-tax annual cost savings:

$\begin{array}{c}\text{PV of After}-\text{tax Cash Inflows}=\text{PV of Cash Outflows}\\ 4.623\text{X}=\$30,600-\$378\\ X=\$30,222÷4.623\\ X=\$6,537\end{array}$

Hence, the minimum net after-tax annual cost savings required to justify the investment is $6,537.

Working notes:

Total cost of machine is $30,600.

Estimated life of machine is 6 years and its estimated salvage value is $600.

Estimated annual cash savings by using new machine is $8,000.

Company’s after tax cost of capital is 8% and its income tax rate is 40%.