A firm is considering installing a sprinkler system to minimize damage in the event of a...

A firm is considering installing a sprinkler system to minimize damage in the event of a fire. The sprinkler system will last only 3 years. The initial cost of the system is $30,000. Thus, the firm will take a $10,000 depreciation expense for the equipment each year. Yearly maintenance is expected to be $2,000. If the firm installs the system, its insurance premium can be reduced by $5,000 each year and the losses are expected to decrease by $9,000 each year. The firm’s tax rate is 30% and its opportunity cost of capital (appropriate discount rate) is 7%.

a) What is the net present value (NPV) of the project?

b) What is the most likely decision regarding this project – accept or reject? Explain.

Solutions

Expert Solution

(a) NPV = Present value of cash inflows - Present value of cash outflows

NPV= $33591.04 - $35248.6

= - $1657.56

Working Notes

1. Calculation of Present value of cash outflows

Given Details:-

Cost of capital = 7%,Initial investment = $30000, Yearly maintenance cost = $2000

Year	Cash outflow in $(a)	Present value factor @7% (b)	Present value of outflows in $ (a) * (b)
0	30000	1	30000
1	2000	.9346	1869.2
2	2000	.8734	1746.8
3	2000	.8163	1632.6

Total present value of cash outflow = 30000+ 1869.2+1746.8+1632.6 = $35248.6

2. Calculation of Present value of cash inflows

Given Details:-

Cost of capital = 7%,Tax rate = 30%,Depreciation cost = $10000, Saving in insurance premium per annum= $5000,Decrease in losses per annum = $9000

Cash inflow after tax is calculated = cashflow(1-tax rate)

Cashflow = $9000+ $5000- $10000 = $4000

Cashflow after tax = 4000(1-.30) = $2800

Year	Cash Inflow after tax in $(a)	Depreciation in $ (b)	Total Cash inflow in $ (c) = (a) + (b)	Present value factor @7% (d)	Present value of inflows in $ (c) * (d)
1	2800	10000	12800	.9346	11962.88
2	2800	10000	12800	.8734	11179.52
3	2800	10000	12800	.8163	10448.64

Total present value of cashinflow = $11962.88+$11179.52+$10448.64 = $33591.04

(b) Since from above solution we see that the NPV is negative, which means that the outflow is more tan the inflows. Thus it is advisable to reject the project.

jeff jeffy answered 1 year ago

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