Question

Elliot is thinking about buying a mixer for $12,000. It would have a 5 year life with a salvage value of $2,000. It would decrease operating costs by $1,000 each year of its economic life. The straight-line depreciation method would be used for it with the cost of capital being 6%.

1. What is the payback period? (use 2 decimal places)

2. What is the annual rate of return? (use 2 decimal places)

3. What is the internal rate of return? (round to nearest whole %)

4. What is the net present value? (Round to whole dollars)

5. What is the profitability index? (use 2 decimal places)

Answer 1

Annual cash inflow = Reduction in operation cost + Depreciation per year

= $1000 + ((12000 - 2000)/5)

= $1000 + $2000

= $3000

1) Payback Period ;-

= Net Investment / Annual Cash Inflow

= ($12000 - $2000) / $3000

= $10000 / $3000

= 3.33 years or 3 years and 4 months

2) ARR = Average Accounting Profit / Average Investment

= $1000 / $12000

= 8.33 %

3) IRR :-

P.V. of Cash inflow = $3000*(1-(1/(1+R)^5) / R) + $2000/(1+R)^5

At 12% Discount Rate

Present Value of Cash Inflows = $11949

At 11% Dis. Rate

Present Value of Cash Inflow = $12275

IRR = 11% + (12% - 11%) * ($12275-$12000) / ($12275 - $11949)

= 11% + 1% * ($275 / 326)

= 11% + 0.84%

= 11.84%

4) Calculation of NPV :-

Cost of Capital = 6%

NPV = Present Value of Cash inflows - Present Value of Investments

= (($3000*((1-1/1.06^5)/0.06)) + ($2000/1.06^5)) - $12000

= $14131.61 - $12000

= $2131.61 or 2132

5) Profitability Index :-

= Present Value of Cash Inflows / Present Value of Investments

= $14131.61 / $12000

= 1.18