Your firm is considering investing in a project, the details of which are given below: A new machine costing K10,000 is required. The project also requires an initial net working capital of K1,000, which will be recovered at the end of the project life (year 3) The new machine is being depreciated using the straight-line method to a zero salvage value. The new machine can be sold at the end of the project (end of year 3) for K5,000. The project will generate earnings before depreciation, interest, and taxes (EBDIT) of K4,000 in year 1, K5,000 in year 2 and K6,000 in year 3. The firm's tax rate is 40% (a) What will be the initial investment in year 0? (3 marks) (b) What are the post-tax operating cash flows in years 1 to 3? (9 marks) (c) What is the non-operating cash flow in year 3? (3 marks) (d) Use the AAR, NPV and Pl methods to decide if the project should be undertaken or not. Use 10% as the discount rate where needed. (12
(a) The initial investment in year 0 will include the cost of the new machine and the initial net working capital. Therefore, the initial investment will be K10,000 + K1,000 = K11,000.
(b) To calculate the post-tax operating cash flows in years 1 to 3, we need to first calculate the earnings before taxes (EBT) and then subtract taxes.
Year 1:
EBT = EBDIT - Depreciation
= K4,000 - (K10,000/3)
= K4,000 - K3,333.33
= K666.67
Taxes = EBT * Tax Rate
= K666.67 * 40%
= K266.67
Post-tax Operating Cash Flow = EBT - Taxes
= K666.67 - K266.67
= K400
Year 2:
EBT = EBDIT - Depreciation
= K5,000 - (K10,000/3)
= K5,000 - K3,333.33
= K1,666.67
Taxes = EBT * Tax Rate
= K1,666.67 * 40%
= K666.67
Post-tax Operating Cash Flow = EBT - Taxes
= K1,666.67 - K666.67
= K1,000
Year 3:
EBT = EBDIT - Depreciation
= K6,000 - (K10,000/3)
= K6,000 - K3,333.33
= K2,666.67
Taxes = EBT * Tax Rate
= K2,666.67 * 40%
= K1,066.67
Post-tax Operating Cash Flow = EBT - Taxes
= K2,666.67 - K1,066.67
= K1,600
(c) The non-operating cash flow in year 3 will be the sale of the machine at K5,000.
(d) To decide if the project should be undertaken or not, we will use the Average Accounting Return (AAR), Net Present Value (NPV), and Payback Period (PP) methods.
Average Accounting Return (AAR):
AAR = Average Annual Earnings / Initial Investment
= (EBIT1 + EBIT2 + EBIT3) / 3 / K11,000
= (K666.67 + K1,666.67 + K2,666.67) / 3 / K11,000
= K4,000 / K11,000
= 0.3636 or 36.36%
Net Present Value (NPV):
Discount rate = 10%
NPV = (Post-tax Operating Cash Flow1 / (1+Discount rate)^1) + (Post-tax Operating Cash Flow2 / (1+Discount rate)^2) + (Post-tax Operating Cash Flow3 + Non-operating Cash Flow3) / (1+Discount rate)^3 - Initial Investment
= (K400 / 1.1^1) + (K1,000 / 1.1^2) + (K1,600 + K5,000) / 1.1^3 - K11,000
= (K400 / 1.1) + (K1,000 / 1.21) + (K6,600) / 1.331 - K11,000
= K363.64 + K826.45 + K4,956.24 - K11,000
= K5,146.33 - K11,000
= -K5,853.67
Profitability Index (Pl):
PI = NPV / Initial Investment
= -K5,853.67 / K11,000
= -0.5322 or -53.22%
Based on the AAR, NPV, and Pl methods, the project should not be undertaken as the AAR is 36.36%, NPV is negative at -K5,853.67, and Pl is negative at -53.22%.
(a) The initial investment in year 0 consists of the cost of the new machine and the initial net working capital.
New machine cost: K10,000
Initial net working capital: K1,000
So, the initial investment in year 0 will be K10,000 + K1,000 = K11,000.
(b) To calculate post-tax operating cash flows in years 1 to 3, we need to consider earnings before depreciation, interest, and taxes (EBDIT) and the tax rate.
Year 1:
EBDIT: K4,000
Tax payable (40%): 40% * K4,000 = K1,600
Post-tax operating cash flow: EBDIT - Tax payable = K4,000 - K1,600 = K2,400
Year 2:
EBDIT: K5,000
Tax payable (40%): 40% * K5,000 = K2,000
Post-tax operating cash flow: EBDIT - Tax payable = K5,000 - K2,000 = K3,000
Year 3:
EBDIT: K6,000
Tax payable (40%): 40% * K6,000 = K2,400
Post-tax operating cash flow: EBDIT - Tax payable = K6,000 - K2,400 = K3,600
So, the post-tax operating cash flows in years 1 to 3 are as follows:
Year 1: K2,400
Year 2: K3,000
Year 3: K3,600
(c) The non-operating cash flow in year 3 is the cash flow generated by selling the machine at the end of the project (end of year 3).
Sales proceeds from machine: K5,000
So, the non-operating cash flow in year 3 is K5,000.
(d) To decide whether the project should be undertaken or not, we can use three methods: the Accounting Average Rate of Return (AAR), Net Present Value (NPV), and Profitability Index (PI). Let's calculate each of them:
AAR (Accounting Average Rate of Return):
Annual average earnings after tax = (Year 1 cash flow + Year 2 cash flow + Year 3 cash flow) / number of years
Annual average earnings after tax = (K2,400 + K3,000 + K3,600) / 3 = K3,000
Initial investment = K11,000
AAR = (Annual average earnings after tax / Initial investment) * 100
AAR = (K3,000 / K11,000) * 100
AAR ≈ 27.3%
NPV (Net Present Value):
Discount rate = 10%
NPV = Present value of cash inflows - Present value of cash outflows
Cash inflows:
Year 1: K2,400 / (1 + 0.10)^1 ≈ K2,182
Year 2: K3,000 / (1 + 0.10)^2 ≈ K2,479
Year 3: K3,600 / (1 + 0.10)^3 ≈ K2,901
Cash outflows:
Initial investment (year 0): K11,000
NPV = Sum of present value cash inflows - Present value of cash outflows
NPV = K2,182 + K2,479 + K2,901 - K11,000
NPV ≈ -K3,438
PI (Profitability Index):
PI = (Present value of cash inflows / Present value of cash outflows) + 1
Present value of cash inflows = K2,182 + K2,479 + K2,901 = K7,562
Present value of cash outflows = K11,000
PI = (K7,562 / K11,000) + 1
PI ≈ 1.687
Based on these calculations:
- AAR: 27.3%
- NPV: -K3,438
- PI: 1.687
The project should be undertaken if the AAR is greater than the required rate of return, NPV is positive, or PI is greater than 1. In this case, the AAR is higher than the discount rate (10%) but the NPV is negative, indicating that the project may not be financially viable. The PI is greater than 1, but considering the low NPV, it is still not a strong indication of profitability. Therefore, based on the NPV, it is recommended not to undertake the project.