Chapter 13, Problem 32C

To determine

Introduction:

Investment Project

• Investment Projects refer to projects that require a lot of capital expenditure in the form of investments in assets. These projects aim at being profitable and earning the investor a minimum desired return of return.

• Investment Projects can be in shares of companies, plant and machinery that is manufactured or purchased, research and development projects that aim to create new marketable and sellable goods or services.

Incremental Cash Flows

• Incremental Cash Flows refer to cash inflows in the form of cost savings, incomes such as dividends, profits etc. less cash outflows in the form of investments or periodic payments that take effect when an investment project is implemented.

• An investment project seeks to achieve positive Incremental Cash Flows. In the event that the investment project’s Incremental Cash Flows are negative, the investment project will be rejected.

Contribution Margin:

• Contribution Margin refers to the excess of Sales revenues over variable and fixed costs. Since it contributes to the overall profitability of the business it is referred to as contribution margin.

• Variable costs refer to the costs of manufacture that have a direct co-relation with the volume of the goods manufactured, i.e. the costs increase with an increase in the goods produced. Examples are costs of direct material and direct labor.

• Fixed costs refer to the costs of manufacture that have an inverse co-relation with the volume of the goods manufactured, i.e. the costs decrease with an increase in the goods produced. Examples are costs of factory rent, depreciation on plant and equipment

Net Present Value

• Net present value is the discounted value of the difference between the incremental cash inflows and cash outflows. A discounting factor is used to compute the present value of net incremental cash flows and usually the Internal Rate of Return is used as the discounting factor to arrive at the net present value.

• Internal Rate of Return is the minimum desired rate of return which an investment project should achieve. In the event that the investment project’s net present value is lesser than the Internal Rate of Return, the investment project will be rejected.

Net present value of the project

Answer to Problem 32C

Solution:

Net present value of the project is $192,099.

Explanation of Solution

Particulars	Year 1	Year 2	Year 3	Year 4	Year 5	Year 6
Sales (Units)	9,000.00	15,000.00	18,000.00	22,000.00	22,000.00	22,000.00
Sales Revenue @ $35 per unit (A)	$ 315,000.00	$ 525,000.00	$ 630,000.00	$ 770,000.00	$ 770,000.00	$ 770,000.00
Variable Costs @ $15 per unit (B)	$ 135,000.00	$ 225,000.00	$ 270,000.00	$ 330,000.00	$ 330,000.00	$ 330,000.00
Contribution Margin (Sales - Variable Costs) (A - B)	$ 180,000.00	$ 300,000.00	$ 360,000.00	$ 440,000.00	$ 440,000.00	$ 440,000.00
Fixed costs:
Administrative Costs including depreciation costs	$ 135,000.00	$ 135,000.00	$ 135,000.00	$ 135,000.00	$ 135,000.00	$ 135,000.00
Advertising Costs per year	$ 180,000.00	$ 180,000.00	$ 150,000.00	$ 120,000.00	$ 120,000.00	$ 120,000.00
Total Fixed Costs per annum	$ 315,000.00	$ 315,000.00	$ 285,000.00	$ 255,000.00	$ 255,000.00	$ 255,000.00
Incremental Cash Inflows:
Contribution Margin	$ 180,000.00	$ 300,000.00	$ 360,000.00	$ 440,000.00	$ 440,000.00	$ 440,000.00
Working Capital Released	$ -	$ -	$ -	$ -	$ -	$ 60,000.00
Salvage Value of New Asset	$ -	$ -	$ -	$ -	$ -	$ 15,000.00
Total Incremental Cash Inflows	$ 180,000.00	$ 300,000.00	$ 360,000.00	$ 440,000.00	$ 440,000.00	$ 515,000.00
Incremental Cash Outflows:
Total Fixed Costs per annum	$ 315,000.00	$ 315,000.00	$ 285,000.00	$ 255,000.00	$ 255,000.00	$ 255,000.00
Incremental Cash Flows per annum (Cash inflows - Cash Outflows)	$ (135,000.00)	$ (15,000.00)	$ 75,000.00	$ 185,000.00	$ 185,000.00	$ 260,000.00
Discounting Factor @14%	0.88	0.77	0.67	0.59	0.52	0.46
Present value of Net cash Flows	$ (118,421.05)	$ (11,542.01)	$ 50,622.86	$ 109,534.85	$ 96,083.20	$ 118,452.50

Year	Incremental Cash Flow	Discounting Factor	Present value of Cash Inflows
1	$ (195,000.00)	0.88	$ (171,052.63)
2	$ (15,000.00)	0.77	$ (11,542.01)
3	$ 75,000.00	0.67	$ 50,622.86
4	$ 185,000.00	0.59	$ 109,534.85
5	$ 185,000.00	0.52	$ 96,083.20
6	$ 260,000.00	0.46	$ 118,452.50
Total			$ 192,098.78

• Sales in Units are given for each year and the sales revenue per annum is calculated at $35 per unit

• Variable Costs of $15 per unit will be incurred and total Variable costs are calculated as a product of the Sales in Units and Variable Costs of $15 per unit

• Contribution Margin for each year is calculated as Sales less Total Variable Costs. There is a direct correlation between the contribution margin and sales volume.

• Fixed costs in the form of Administrative Costs including depreciation costs of $135,000 will be incurred and Advertising Costs per year for each year will be also be incurred and are calculated accordingly.

• Total Fixed Costs per annum are the sum of Administrative Costs including depreciation costs of $135,000 and Advertising Costs per year

• Incremental Cash Inflows are the Contribution Margin per annum, Working Capital Released in year 6 and the Salvage Value of New Asset that will be realizable in year 6.

• Total Incremental Cash Inflows will be the sum of Contribution Margin per annum, Working Capital Released in year 6 and the Salvage Value of New Asset that will be realizable in year 6.

• Incremental Cash Outflows comprise of Total Fixed Costs per annum in the form of Administrative Costs including depreciation costs of $135,000 and Advertising Costs per year

• Incremental Cash Flows per annum are calculated as the difference between the Incremental Cash inflows and Incremental Cash Outflows.

• Present value of Incremental Cash Flows is calculated as the product of the Discounting factor and the Incremental Cash Flow for the year. Discounting factor is taken as 14% since that is the desired rate of return.

• Discounting factor is computed as

  $\begin{array}{l}\text{I = 1/ (1+0}\text{.14) ^ n}\\ \\ \text{where,}\\ \\ \text{n = the year such as 1, 2, }\mathrm{....}\text{6}\end{array}$

• Net Present value of Incremental Cash Flows is calculated as the sum of Present value of Incremental Cash Flows for years 1 to 6.

• Since the Net present value is positive, the project may be accepted.

Conclusion

Hence the net present value is calculated.