Question

pls help Asap! show calculations in writting

10 points Save Answe We believe we can sell 75,000 home security devices per year at $200 per piece. They cost $120 to manufacture (variable cost yFixed production costs run $215,000 per year. The necessary equipment costs $785,000 to buy and would be depreciated at a 25% CCA rate. The equipment would have a zero salvage value after the five-year life of the project. We need to invest $140,000 in net working capital up front; no additional net working capital investment is necessary. The discount rate is 19%, and the tax rate is 35%. What is the NPV of the project? (Do not round your intermediate calculations. Round the final answer to 2 decimal places. Omit $ sign in your response.)

Answer 1

Lets note down the data provided in the question.

Annual Units Sold (a)	75,000
Price per unit (b)	$200
Variable cost per unit (c)	$120
Annual Sales (a x b)	$15,000,000
Annual Variable Costs (a x c)	$9,000,000
Annual Fixed Costs	$215,000
Tenure of the project	5 years
Tax rate applicable	35%
Discount rate applicable for discounting annual cashflows	19%
Equipment Cost	$785,000
Salvage value at the end of 5 years	$0
CCA Depreciation Rate (Assuming Declining Balance Depreciation)	25%
Upfront Net Working Capital Investment	$140,000
Release of Net Working Capital at the end of 5 years (assumption)	$140,000

While the '$' sign was used just to represent the data provided, I will not use the same in further calculations as asked in the question.

The initial investment in the project in the equipment cost and the initial net working capital investment.

For the next 5 years we will compute the profits by subtracting the annual variable and fixed costs from the annual sales and then subtract depreciation (25% depreciation on a reducing balance basis; so equipment value at the end of 1st year after subtracting depreciation, becomes the opening value for next year on which the 25% depreciation will be calculated) from the same to arrive at the Profit before tax. The 35% tax rate will be applied to this Profit before tax to arrive at the tax value and thereafter the Profit After Tax.

Now, since we need cashflows to calculate NPV and depreciation is a non-cash expense, we add back the annual depreciation to the annual Profit After Tax to get the annual cash inflows. These cashflows will then be discounted at 19% discount rate using the following formula:

Present Value of nth year cash inflow = (nth year Cash inflow) / (1 + Discount rate)^n

NPV will then be calculated by subtracting the initial cash outflow from the discounted values of future cash inflows.

In this problem, since it is not specified whether the net working capital is released at the end of the project, I have computed the NPV for both the scenarios. Scenario 1 is when net working capital of $140,000 is released at the end of year 5 (which is typically the case as net working capital will eventually be converted into cashflow at the end of the project). Scenario 2 is when there is no release of net working capital at the end of year 5.

All the above description is now presented in a tabular format below:

Scenario 1: Net working capital is released (as a cash inflow of 140,000) at the end of year 5.

	Year 0	Year 1	Year 2	Year 3	Year 4	Year 5
Equipment (a)	-785,000.00	785,000.00	588,750.00	441,562.50	331,171.88	248,378.91
Sales		15,000,000.00	15,000,000.00	15,000,000.00	15,000,000.00	15,000,000.00
Variable Costs		9,000,000.00	9,000,000.00	9,000,000.00	9,000,000.00	9,000,000.00
Fixed Costs		215,000.00	215,000.00	215,000.00	215,000.00	215,000.00
Depreciation (b)		196,250.00	147,187.50	110,390.63	82,792.97	62,094.73
NWC investment (c)	-140,000.00
Profit Before tax		5,588,750.00	5,637,812.50	5,674,609.38	5,702,207.03	5,722,905.27
Tax at 35% rate		1,956,062.50	1,973,234.38	1,986,113.28	1,995,772.46	2,003,016.85
Profit After tax (d)		3,632,687.50	3,664,578.13	3,688,496.09	3,706,434.57	3,719,888.43
Initial Cash Outflow (a+c)	-925,000.00
Cash Inflow (b+d)		3,828,937.50	3,811,765.63	3,798,886.72	3,789,227.54	3,921,983.15
Discounted cashflows at 19% discount rate	-925,000.00	3,217,594.54	2,691,734.78	2,254,319.46	1,889,569.37	1,643,504.57
NPV	10,771,722.71

Scenario 2: No release of Net working capital (so 0 cash inflow from it) at the end of year 5.

	Year 0	Year 1	Year 2	Year 3	Year 4	Year 5
Equipment (a)	-785,000.00	785,000.00	588,750.00	441,562.50	331,171.88	248,378.91
Sales		15,000,000.00	15,000,000.00	15,000,000.00	15,000,000.00	15,000,000.00
Variable Costs		9,000,000.00	9,000,000.00	9,000,000.00	9,000,000.00	9,000,000.00
Fixed Costs		215,000.00	215,000.00	215,000.00	215,000.00	215,000.00
Depreciation (b)		196,250.00	147,187.50	110,390.63	82,792.97	62,094.73
NWC investment (c)	-140,000.00
Profit Before tax		5,588,750.00	5,637,812.50	5,674,609.38	5,702,207.03	5,722,905.27
Tax at 35% rate		1,956,062.50	1,973,234.38	1,986,113.28	1,995,772.46	2,003,016.85
Profit After tax (d)		3,632,687.50	3,664,578.13	3,688,496.09	3,706,434.57	3,719,888.43
Initial Cash Outflow (a+c)	-925,000.00
Cash Inflow (b+d)		3,828,937.50	3,811,765.63	3,798,886.72	3,789,227.54	3,781,983.15
Discounted cashflows at 19% discount rate	-925,000.00	3,217,594.54	2,691,734.78	2,254,319.46	1,889,569.37	1,584,837.66
NPV	10,713,055.80

Note: If you are not able to get clarification from your instructor regarding the treatment of Net working capital at the end of the project, I would recommend using the NPV as per Scenario 1 (10,771,722.71) as that is how it works in the real world.