The owner of Cape Cod Confectionary is considering the purchase of a new semiaut

Question

The owner of Cape Cod Confectionary is considering the purchase of a new semiautomatic candy machine. The machine will cost $30,000 and last 10 years. The machine is expected to have no salvage value at the end of its useful life. The owner projects that the new candy machine will generate $4,800 in after-tax savings each year during its life (including the depreciation tax shield).

Required:   Compute the profitability index on the proposed candy machine, assuming an after-tax hurdle rate of: (a) 8 percent, (b) 10 percent, and (c) 12 percent.

Explanation / Answer

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PROFITABILITY INDEX = PV OF FUTURE CASH FLOWS / INITIAL INVESTMENT REQUIRED

8% 10% 12%

AFTER TAX SAVINGS 4800.00 4800.00 4800.00 .............(a)

PV FACTOR 6.71 6.14 5.65 ..............(b) (refer WN 1)

PV of Future Cash Flows(a*b) 32204.64 29491.20 27120.00 ............(c)

Initial Investment 30000.00 30000.00 30000.00 ............(d)

Profitability Index(c/d) 1.07 0.98 0.90

(as per above formula)

WN 1

Calculation of PVF 8% 10% 12%

Future Cash Flows

Year 1 (1/1.08) 0.926

(1/1.10) 0.909

(1/1.12) 0.893

Year 2 (1/1.082) 0.857

(1/1.102) 0.826

(1/1.122) 0.797

Year 3 (1/1.083) 0.793

(1/1.103) 0.751

(1/1.123) 0.712

and so on...till year 10...

Year 10 (1/1.0810) 0.463

(1/1.1010) 0.386

(1/1.1210) 0.322

Add all the Future Cash Flows as under;-

For 8% = 0.926+0.857+0.793+.................+0.463 = 6.71

For 10% = 0.909+0.826+0.751+................+0.386 = 6.14

For 12% = 0.893+0.797+0.712+.................=0.322 = 5.65

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