Question

Firm is evaluating the following project to install a new production facility. The production facility requires an investment in a machine costing 25,000 USD.

The machine will be fully depreciated according to the straight-line method. The life of the project is estimated to be 4 years. When the project is over, although the

book value of the machine is 0, you expect to sell the machine at a market value of 1,000 USD. The project also requires working capital in the amount of 10% of the following

year's sales revenue. (since the projected sales revenue stays the same, there is additional working capital only at t=0 and this will be recouped after the project is over at t=4.

From the project, you expect to sell 3,000 products each year during the project's life at the price of 80 per product. Production variable costs are estimated to be 70 USD per product

This project requires you to use the facility which is rented out with an after-tax rent cash inflow of 10,000 USD per year. if you proceed with the project, you can not receive the rent from t=1. among your staff, your firm currently employs workers. The annual salaries of the workers are 30,000 USD and you plan to continue to hire them, regardless of whether you do this project or not.

The company's cost of debt is 5%, cost of equity is 10%, the current capital structure is 20% debt. Tax rate is 30%.

1. What are the NPV and IRR for this project?

2. As a sensitivity analysis with respect to the production variable costs, what are the NPVs and IRRs when production variable costs (1) drops to 68 USD, and (2) increases to 72 USD?

3. Wheat is the break-even point of NPV=0 for the production variable cost?

Answer 1

Sales

(-) Fixed Cost (Salaries) - Working Capital - Variable Cost - Depreciation - Interest - Opportunity Cost of Rent (Pre-tax) = Operating Profit

Operating Profit - Tax = Profit after Tax

Profit after Tax + Depreciation = Cash Inflow

Cash Inflow * Discounting Factor = P.V. of Cash Inflow

N.P.V. = P.V. of Cash Inflow - Cash Outflow

Investment	25000
No. of Product	3000
Sales price per porduct	80
Variable cost per product	70
Annual Sales	240000
Rate of tax	30%

Calculation of WACC
			Capital Structure
Cost of Debt	5%	4%	20%	0.01
Cost of Equity		10%	80%	0.08
WACC				0.09

Contribution of Investment
	Amount	Interest
Debt	5000	250
Equity	20000

	year 0	Year 1	year 2	year 3	year 4	year 4
Sales		240000	240000	240000	240000
Variable Cost		210000	210000	210000	210000
Working Capital	24000	24000	24000	24000		24000
Depreciation		6000	6000	6000	6000
Salary	30000	30000	30000	30000	30000
Interest		250	250	250	250
Opportunity Cost of rent		14286	14286	14286	14286
Operating Profit	-54000	-44536	-44536	-44536	-20536
Tax	-16200	-13360.8	-13360.8	-13360.8	-6160.8
Profit after Tax	-37800	-31175.2	-31175.2	-31175.2	-14375.2
Depreciation		6000	6000	6000	6000
Cash Inflow		-25175.2	-25175.2	-25175.2	-8375.2
Discounting Factor		0.917431193	0.84168	0.77218348	0.708425211	0.708425
P.V. of Cash Inflow	-37800	-23096.5138	-21189.5	-19439.87355	-5933.20283	17498.1
Terminal Value of Machinery (post-tax)						700

NPV	-114961
IRR	-44%

b)

Investment	25000
No. of Product	3000
Sales price per porduct	80
Variable cost per product	68
Annual Sales	240000
Rate of tax	30%

Calculation of WACC
			Capital Structure
Cost of Debt	5%	4%	20%	0.01
Cost of Equity		10%	80%	0.08
WACC				0.09

Contribution of Investment
	Amount	Interest
Debt	5000	250
Equity	20000

	year 0	Year 1	year 2	year 3	year 4	year 4
Sales		240000	240000	240000	240000
Variable Cost		204000	204000	204000	204000
Working Capital	24000	24000	24000	24000		24000
Depreciation		6000	6000	6000	6000
Salary	30000	30000	30000	30000	30000
Interest		250	250	250	250
Opportunity Cost of rent		14286	14286	14286	14286
Operating Profit	-54000	-38536	-38536	-38536	-14536
Tax	-16200	-11560.8	-11560.8	-11560.8	-4360.8
Profit after Tax	-37800	-26975.2	-26975.2	-26975.2	-10175.2
Depreciation		6000	6000	6000	6000
Cash Inflow		-20975.2	-20975.2	-20975.2	-4175.2
Discounting Factor		0.917431193	0.84168	0.77218348	0.708425211	0.708425
P.V. of Cash Inflow	-37800	-19243.3028	-17654.4	-16196.70293	-2957.81694	17498.1
Terminal Value of Machinery (post-tax)						700

NPV	-101354
IRR	-39%

Investment	25000
No. of Product	3000
Sales price per porduct	80
Variable cost per product	72
Annual Sales	240000
Rate of tax	30%

Calculation of WACC
			Capital Structure
Cost of Debt	5%	4%	20%	0.01
Cost of Equity		10%	80%	0.08
WACC				0.09

Contribution of Investment
	Amount	Interest
Debt	5000	250
Equity	20000

	year 0	Year 1	year 2	year 3	year 4	year 4
Sales		240000	240000	240000	240000
Variable Cost		216000	216000	216000	216000
Working Capital	24000	24000	24000	24000		24000
Depreciation		6000	6000	6000	6000
Salary	30000	30000	30000	30000	30000
Interest		250	250	250	250
Opportunity Cost of rent		14286	14286	14286	14286
Operating Profit	-54000	-50536	-50536	-50536	-26536
Tax	-16200	-15160.8	-15160.8	-15160.8	-7960.8
Profit after Tax	-37800	-35375.2	-35375.2	-35375.2	-18575.2
Depreciation		6000	6000	6000	6000
Cash Inflow		-29375.2	-29375.2	-29375.2	-12575.2
Discounting Factor		0.917431193	0.84168	0.77218348	0.708425211	0.708425
P.V. of Cash Inflow	-37800	-26949.7248	-24724.5	-22683.04416	-8908.58871	17498.1
Terminal Value of Machinery (post-tax)						700

NPV	-128568
IRR	-48%

This project cannot be taken up as the NPV is negative with varisble cost of 70, 68 or 72.

Hence, it is a loss making project.