Question

The management of Wyoming Corporation is considering the purchase of a new machine costing $375,000. The company's desired rate of return is 6%. The present value factor for an annuity of $1 at interest of 6% for 5 years is 4.212. In addition to the foregoing information, use the following data in determining the acceptability in this situation: YearIncome fromOperationsNet Cash    Flow1$18,750$93,750218,75093,750318,75093,750418,75093,750518,75093,750 The cash payback period for this investment is: A) 4 years B) 5 years C) 3 years D) 20 years 2. The management of Wyoming Corporation is considering the purchase of a new machine costing $375,000. The company's desired rate of return is 6%. The present value factor for an annuity of $1 at interest of 6% for 5 years is 4.212. In addition to the foregoing information, use the following data in determining the acceptability in this situation: YearIncome fromOperationsNet Cash    Flow1$18,750$93,750218,75093,750318,75093,750418,75093,750518,75093,750 The average rate of return for this investment is: A) 15% B) 10% C) 5% D) 25% 3. The management of Wyoming Corporation is considering the purchase of a new machine costing $375,000. The company's desired rate of return is 6%. The present value factor for an annuity of $1 at interest of 6% for 5 years is 4.212. In addition to the foregoing information, use the following data in determining the acceptability in this situation: YearIncome fromOperationsNet Cash    Flow1$18,750$93,750218,75093,750318,75093,750418,75093,750518,75093,750 The net present value for this investment is: A) Negative $19,875 B) Positive $118,145 C) Positive $19,875 D) Negative $118,145 4. The management of Wyoming Corporation is considering the purchase of a new machine costing $375,000. The company's desired rate of return is 6%. The present value factor for an annuity of $1 at interest of 6% for 5 years is 4.212. In addition to the foregoing information, use the following data in determining the acceptability in this situation: YearIncome fromOperationsNet Cash    Flow1$18,750$93,750218,75093,750318,75093,750418,75093,750518,75093,750 The present value index for this investment is: A) .95 B) 1.00 C) 1.05 D) 1.25

Answer 1

Concepts and reason

Capital budgeting:

Capital budgeting refers to a process in which the future investments and the expenses are evaluated in order to determine which investment will be best for the company. This process helps to know which investment project will provide higher returns to the company.

The process of capital budgeting includes the decisions regarding the investment and the capital expenditure is planned and evaluated. It helps to know which investment will be more profitable to the company when compared with the other investment options.

Fundamentals

Cash Payback Period:

Payback period of an investment provides the information about the time which is required to recover the entire initial investment. It helps to know much time will be required by the company to recover its cost of the investment in a project.

The payback period means the period in which the cash inflows generated from a project and the cost of investment that is initial investment in the project will be same.

It is considered that a project should have lower payback period. This is because it indicates that cost of investment in project is recovered by the company in less period of time. A higher payback period is not considered good for the company because it indicates that the cost of investment in a project is recovered in a long period of time.

Payback Period is computed using the following formula:

Payback Period is calculated as follows:

${\rm{PaybackPeriod = }}\frac{{{\rm{Initial investment}}}}{{{\rm{Annual operating cash inflows}}}}$

Average rate of return:

Average rate of return is calculated by dividing the increase in expected average net income by the average investment. It is also calculated by dividing the difference between the average annual incremental net cash inflow from operations and incremental average annual depreciation by the initial investment required.

In the accounting rate of return the cash flows of the project is not considered because the accounting profit is taken into consideration.

Accounting rate of return is calculated as:

${\rm{Average rate of return = }}\frac{{{\rm{Average annual increase in net income}}}}{{{\rm{Average investment}}}}$

The average amount invested is calculated by dividing the sum of amount invested and residual value by 2. The average amount invested is calculated as follows:

${\rm{Average amount of invested = }}\frac{{{\rm{Amount invested + Residual Value}}}}{2}$

Straight line method of Depreciation:

In straight line method of Depreciation the amount of depreciation charged in each year of the useful life of the asset is equal. The amount of depreciation is calculated by reducing the estimated salvage value from the cost of the asset and then dividing it by the number of accounting periods in estimated useful life.

The amount of depreciation in straight line method is calculated as:

${\rm{Depreciation per period = }}\frac{{{\rm{Cost - Residual value}}}}{{{\rm{Service life}}}}$

Net present value:

Net Present Value is a technique which helps to take decision whether a project should be accepted or not. The Net present value refers to the value which is computed by deducting the initial investment or present value of outflows from the present value of inflows. It considers time value of money in evaluating capital investments.

Net Present Value is calculated as:

${\rm{NPV = Present Value of Future Cash Flows }} - {\rm{Initial Outlay}}$

$NPV = \frac{{C{F_1}}}{{{{\left( {1 + k} \right)}^1}}} + \frac{{C{F_2}}}{{{{\left( {1 + k} \right)}^2}}} + ... + \frac{{C{F_n}}}{{{{\left( {1 + k} \right)}^n}}} - IO$

Here:

CF – Future Cash Flows

k- The firm’s required rate of return or cost of capital

IO – Initial Investment

n- Expected life of the project

Present value of cash flows:

Present value of cash flows is to be calculated by multiplying the annual cash inflows by the given discounting factor. Present value of cash flows is calculated by discounting the annual cash flows. In this the value of cash flows is computed backward to a present date by discounting the cash flows. It helps to know what will be the value of tomorrow’s money at a present date.

Present Value Index:

Present Value Index is a technique which is used to compare different investment proposals each having different initial investments or cash outflows and cash inflows. It is calculated by dividing the present value of net cash inflows by the investment required.

Present Value Index is calculated as:

${\rm{Present Value Index = }}\frac{{{\rm{Total Present Value of net cash inflows}}}}{{{\rm{Amount to be invested}}}}$

1.

Calculate the cash payback period.

Calculation of cash payback period:

$\begin{array}{c}\\{\rm{PaybackPeriod = }}\frac{{{\rm{Initial investment}}}}{{{\rm{Annual operating cash inflows}}}}\\\\ = \frac{{\$ 375,000}}{{\$ 93,750}}\\\\ = 4{\rm{ years}}\\\end{array}$

The cash payback period for the investment is 4 years.

2.

Calculate the average rate of return.

Calculation of average rate of return:

$\begin{array}{c}\\{\rm{Average rate of return = }}\frac{{{\rm{Average annual increase in net income}}}}{{{\rm{Average investment}}}}\\\\ = \frac{{\$ 18,750}}{{\$ 187,500}}\\\\ = 10\% \\\end{array}$

The average rate of return for the investment is 10%.

Working Note:

Calculate the amount of depreciation expense.

Calculation of the amount of depreciation expense:

$\begin{array}{c}\\{\rm{Depreciation per period = }}\frac{{{\rm{Cost - Residual value}}}}{{{\rm{Service life}}}}\\\\ = \frac{{\$ 375,000 - \$ 0}}{5}\\\\ = \$ 75,000\\\end{array}$

The amount of depreciation expense per period is $75,000.

Working Note:

Calculate the amount of average annual increase in net income.

Calculation of the amount of average annual increase in net income:

$\begin{array}{c}\\{\rm{Annual increase in net income = Net cash flows}} - {\rm{Depreciation expense}}\\\\ = \$ 93,750 - \$ 75,000\\\\ = \$ 18,750\\\end{array}$

The average annual increase in net income is $18,750.

Working Note:

Calculate the average amount of investment:

$\begin{array}{c}\\{\rm{Average amount of investement = }}\frac{{{\rm{Amount invested + Residual Value}}}}{2}\\\\ = \frac{{\$ 375,000 + \$ 0}}{2}\\\\ = \$ 187,500\\\end{array}$

The average amount of investment is $187,500.

3.

Calculate the net present value of the investment.

Calculation of net present value of investment:

$\begin{array}{c}\\{\rm{NPV = Present Value of Future Cash Flows }} - {\rm{Initial Outlay}}\\\\ = \$ 394,875 - \$ 375,000\\\\ = \$ 19,875\\\end{array}$

The net present value of the investment is positive $19,875.

Working Note:

Calculate the present value of net cash flows.

Calculation of present value of net cash flows:

$\begin{array}{c}\\{\rm{Present value of cash flows = Net cash flows}} \times {\rm{Present value factor for annuity}}\\\\ = \$ 93,750 \times 4.212\\\\ = \$ 394,875\\\end{array}$

The present value of net cash flows is $394,875.

4.

Calculate the present value index for the investment.

Calculation of present value index of investment:

$\begin{array}{c}\\{\rm{Present Value Index = }}\frac{{{\rm{Total Present Value of net cash inflows}}}}{{{\rm{Amount to be invested}}}}\\\\ = \frac{{\$ 394,875}}{{\$ 375,000}}\\\\ = 1.05\\\end{array}$

The present value index for the investment is 1.05.

Ans: Part 1

The cash payback period for the investment is 4 years.

Part 2

The average rate of return for the investment is 10%.

Part 3

The net present value of the investment is positive $19,875.

Part 4

The present value index for the investment is 1.05.