Question

In: Finance

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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