Germaine Metals is considering installing a new molding machine which is expected to produce operating cash flows of $57,000 per year for 7 years. At the beginning of the project, inventory will increase by $21,000, accounts receivables will increase by $13,000, and accounts payable will increase by $20,800. At the end of the project, net working capital will return to the level it was prior to undertaking the new project. The initial cost of the molding machine is $268,000. The equipment will be depreciated straight-line to a zero book value over the life of the project. The equipment will be salvaged at the end of the project creating an aftertax cash flow of $40,000. What is the net present value of this project given a required return of 13.9 percent?
Answer (2)
The Net Present Value (NPV) of Germaine Metals' project is approximately -$1,029.96, indicating a potential loss on the investment. This calculation takes into account initial costs, changes in working capital, operating cash flows, and salvage value over 7 years. A negative NPV suggests that the investment may not be worthwhile given the required return of 13.9%.
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Calculate the change in net working capital: $NWC = ($21,000 + $13,000) - $20,800 = 13 , 200. − C a l c u l a t e t h e p rese n t v a l u eo f o p er a t in g c a s h f l o w s : PV_{OCF} = $57,000 * \frac{1 - (1 + 0.139)^{-7}}{0.139} = $245,182.07.
Calculate the present value of the salvage value: $PV_{Salvage} = \frac{$40,000}{(1 + 0.139)^7} = 16 , 083.99. − C a l c u l a t e t h e n e tp rese n t v a l u e : NPV = -$281,200 + $245,182.07 + $16,083.99 = - 19 , 933.94. T h ere f ore , t h e n e tp rese n t v a l u eo f t hi s p ro j ec t i s \boxed{-$19,933.94}$.
Explanation
Problem Analysis Let's analyze the problem. We need to calculate the Net Present Value (NPV) of a project involving the installation of a new molding machine. We have the following information:
Initial cost of the machine: $268,000
Annual operating cash flows: $57,000 for 7 years
Increase in inventory: $21,000
Increase in accounts receivable: $13,000
Increase in accounts payable: $20,800
Net working capital returns to original level at the end of the project
Straight-line depreciation to zero book value over 7 years
After-tax salvage value: $40,000
Required return: 13.9 percent
Calculate Change in Net Working Capital First, we need to calculate the change in net working capital (NWC) at the beginning of the project. This is the sum of the changes in inventory and accounts receivable, minus the change in accounts payable: N W C = ( I n v e n t ory + A cco u n t s R ece i v ab l e ) − A cco u n t s P a y ab l e
NWC Calculation Plugging in the values, we get: N W C = ( $21 , 000 + $13 , 000 ) − $20 , 800 = $13 , 200
Calculate Annual Depreciation Next, we calculate the annual depreciation expense. Since the equipment is depreciated straight-line to a zero book value over 7 years: De p rec ia t i o n = P ro j ec t L i f e I ni t ia l C os t
Depreciation Value Plugging in the values, we get: De p rec ia t i o n = 7 $268 , 000 = $38 , 285.71 (approximately)
Operating Cash Flow The annual after-tax operating cash flow (OCF) is given as $57,000. Since this is already after tax, we don't need to calculate taxes.
Present Value of OCFs Now, we calculate the present value of the annual OCFs using the present value of an annuity formula: P V OCF = OCF ∗ r 1 − ( 1 + r ) − n where r = 0.139 and n = 7 .
PV of OCFs Value Plugging in the values, we get: P V OCF = $57 , 000 ∗ 0.139 1 − ( 1 + 0.139 ) − 7 = $57 , 000 ∗ 0.139 1 − ( 1.139 ) − 7 = $245 , 182.07 (approximately)
Present Value of Salvage Value Next, we calculate the present value of the salvage value: P V S a l v a g e = ( 1 + r ) n S a l v a g e Va l u e where r = 0.139 and n = 7 .
PV of Salvage Value Calculation Plugging in the values, we get: P V S a l v a g e = ( 1 + 0.139 ) 7 $40 , 000 = ( 1.139 ) 7 $40 , 000 = $16 , 083.99 (approximately)
Initial Investment The initial investment includes the cost of the machine and the change in NWC: I ni t ia l I n v es t m e n t = M a c hin e C os t + C han g e in N W C
Initial Investment Value Plugging in the values, we get: I ni t ia l I n v es t m e n t = $268 , 000 + $13 , 200 = $281 , 200
Net Present Value Calculation Finally, we calculate the net present value (NPV): NP V = − I ni t ia l I n v es t m e n t + P V OCF + P V S a l v a g e
NPV Value Plugging in the values, we get: NP V = − $281 , 200 + $245 , 182.07 + $16 , 083.99 = − $19 , 933.94 (approximately)
Final Answer Therefore, the net present value of this project is approximately − $19 , 933.94 .
Examples
Imagine a company is deciding whether to invest in a new coffee machine for its office. The machine costs $5,000 and is expected to increase employee productivity, resulting in cost savings of $1,500 per year for 5 years. At the end of the 5 years, the machine can be sold for $500. By calculating the NPV, the company can determine if the investment is worthwhile, considering the initial cost, annual savings, salvage value, and the company's required rate of return. This helps in making informed decisions about capital investments.
