A company is contemplating buying a $300,000 security system. The system is sele

Question

A company is contemplating buying a $300,000 security system. The system is selected after a a group within the company spent $20,000 studying similar security systems last year. The new system will save them $175,000 each year before taxes. Working capital would also be reduced by $75,000 in year 1, and $20,000 in year 2, which are permanent reductions. Three years later, the scrap value of the security system would be $100,000. Regulations require the system be depreciated according to a MACRS 3-year schedule. Assume the firm’s discount rate is 10 percent and the tax rate is 30 percent.

What is the NPV and the IRR of this new project?

Potential Recovery Percentages are listed below:

Year

            3 years            5 years          7 years               10 years

1          16.5%              10%                 7%                   5%

2          22.5%              16%                 12.5%              9%

3          7.5%                9.5%                8.5%                7%

4          3.5%                6%                   6.5%                6%

5                                  5.5%                4.5%                4.5%

6                                  3%                   4.5%                3.5%

7                                                          4.5%                3.5%

8                                                                                  3.5%

9                                                                                  3.5%

10                                                                                3%

11                                                                                1.5%

Explanation / Answer

Calculation of depreciation:

Depreciable value = Cost – Scrap Value

=$300000 - $100000

= $200000

Year

Calculation

Depreciation

1

$200000 * 16.5% * 2

$66000

2

$200000 * 22.5% * 2

$90000

3

$200000 * 7.5% * 2

$30000

4

$200000 * 3.5% * 2

$14000

$200000

Calculation of NPV:

1

2

3

4

Savings

$175000

$175000

$175000

Savings after tax (Savings (1-tax rate))

$122500

$122500

$122500

Working capital reduction

-$75000

-$20000

Tax shelter on depreciation (Depreciation * tax rate)

$19800

$27000

$9000

$4200

Scrap Value

$100000

Total Cash inflows

$67300

$129500

$231500

$4200

PVF (10%)

0.909

0.826

0.751

0.683

PV of cash inflows

$61175.70

$106967

$173856.50

$2868.60

PV of Cash inflows = $61175.70 + $106967 + $173856.50 + $2868.60 = $344867.80

Value of expenditure incurred before installation of security system as at the begging of Year 1

= $20000 * FVF (10%, 1 yr)

= $20000 * 1.1

= $22000

NPV = PV of cash inflows – PV of cash outflows

= $344867.800 - $22000 - $300000

=$22867.80

Calculation of IRR:

IRR is the rate at which NPV is '0' i.e., PV of cash inflows =PV of cash outflows

Applying trial and error method:

At 14%, NPV= {[67300/(1+0.14)]+[129500/(1+0.14)2]+[231500/(1+0.14)3]+[4200/(1+0.14)4]]}-322000

= $317423.78 - $322000

= -$4576.22

At 13%, NPV= {[67300/(1+0.13)]+[129500/(1+0.13)2]+[231500/(1+0.13)3]+[4200/(1+0.13)4]]}-322000

=$323992.07 - $322000

=$1992.07

For 1% decrease in IRR, NPV increased by $6568.29

For how much decrease in IRR, NPV increases by $4576.22?

4576.22 / 6568.29 = 0.6967%

Therefore, IRR= 14 – 0.6967 = 13.30% (approx.)

NPV       = $ 22867.80

IRR         = 13.30%

Year

Calculation

Depreciation

1

$200000 * 16.5% * 2

$66000

2

$200000 * 22.5% * 2

$90000

3

$200000 * 7.5% * 2

$30000

4

$200000 * 3.5% * 2

$14000

$200000

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