Question

Rump Industries is considering the purchase of a new production machine for $100,000. The introduction of the machine will result in an increase in earnings before interest and tax of $25,000 per year. Set-up of the machine will involve installation costs of $5,000 after-tax. Additionally, the machine will require workers to undergo training that will cost the company $5,000 after-tax. An initial increase in raw materials and inventory of $25,000 will also be required. The machine has an expected life of 10 years and is expected to have no salvage value at the end of its life. To purchase the new machine the company will have to borrow $80,000 at 10 per cent interest from the bank, which will require interest payments of $8,000 per year. The company will depreciate the machine straight-line over its life. The tax rate is 30 per cent and tax is paid in the year of income. Rump Industries’ required rate of return (WACC) is 12 per cent.

Required: 1. Calculate the initial outlay associated with the project

2. Calculate the annual after-tax cash flows for years 1-9

3. Calculate the after-tax cash flow in year 10

4. Calculate the Net Present Value.

Answer 1

Answer to 1

Initial Outlay = Purchase price of new machine + Installation Cost (After Tax) + Training Cost (After Tax) + Increase in Working Capital (Increase in Raw Material)

Initial Outlay = $ 100000 + $ 5000 + $ 5000 + $ 25000

Initial Outlay = $ 135000

Answer to 2

Let us first Calculate the depriciation of the Machine

Derpiciation = Purchase Price / Life of Machine (As there is 0 salvage Value)

Derpiciation = $ 100000 / 10 Years

Derpiciation = $ 10000

Now, Annual After Tax Cash Flows for year 1 to 9 = (Earnings Before Interest and Tax) x (1- Tax Rate) + Depriciation

Annual After Tax Cash Flows for year 1 to 9= ($ 25000) * (1-0.30) + $ 10000

Annual After Tax Cash Flows for year 1 to 9= $ 27500

Note that interest cost are not deducted, as they are already accounted for in the Weighted Average Cost of Capital.

Answer to 3

Now After Tax Cash Flow in Year 10 = Annual After Tax Cash Flow as computed above + Releaze of Working Capital

Now After Tax Cash Flow in Year 10 = $ 27500 + +$ 25000 = $ 52500

Answer to 4

Net Present Values = Present Values of Cash Flows - Initial Outlay where the cash flows are discounted using the WACC = 12%

Therefore we have the following Cash Flows

	Year 0	Year 1	Year 2	Year 3	Year 4	Year 5	Year 6	Year 7	Year 8	Year 9	Year 10
Initial Outlay (A)	-135000
Annual After Tax Cash Flows (B)		27500	27500	27500	27500	27500	27500	27500	27500	27500	52500
Net Cash Flows (C = A + B)	-135000	27500	27500	27500	27500	27500	27500	27500	27500	27500	52500
Disocount Factor @12% (D)	1.0000	0.8929	0.7972	0.7118	0.6355	0.5674	0.5066	0.4523	0.4039	0.3606	0.3220
Disocount Factor @12%	''=1/1.12^0	'=1/1.12^1	'=1/1.12^2	'=1/1.12^3	'=1/1.12^4	'=1/1.12^5	'=1/1.12^6	'=1/1.12^7	'=1/1.12^8	'=1/1.12^9	'=1/1.12^10
Present Values (E= D x C)	-135000	24,553.57	21,922.83	19,573.96	17,476.75	15,604.24	13,932.36	12,439.60	11,106.79	9,916.78	16,903.59

Therefore NPV = Sum total of All the Present Values of Cash Flows = $ 28430.46