Question

Jordan and Taylor want to purchase a new 60 quart floor mixer for $12,000. This machine would have a 5 year life with a salvage value of $2,000. The new machine would decrease operating costs by $1,000 each year of its economic life. The straight-line depreciation method would be used for the new machine. The cost of capital is 6%. Before they spend the money, they asked Mary to calculate outcomes with capital investment models. 1. What is the payback period? (Round to two decimal places and make sure your answer is in the correct format.) 2. What is the annual rate of return? (Round to two decimal places and make sure your answer is in the correct format.) 3. What is the internal rate of return? (Round to nearest whole percent and make sure your answer is in the correct format.) 4. What is the net present value? (Round to whole dollars and make sure your answer is in the correct format.) 5. What is the profitability index? (Round to two decimal places.)

Answer 1

Annual Depreciation (straight line method) = (12000 - 2000)/5 = $2000

Annual Operating cash flow = Benefits + Annual depreciation = 1000+2000 = $3000

1. Payback Period = Net Investment / Annual cash inflow

   = (12000 - 2000) /3000 = 10000 / 3000 = 3.33 years

2. Annual rate of return = Average Accounting profit / Average Investment

= 1000/12000 = 8.34%

3.

Investment =	12000
Year	1	2	3	4	5
Cash inflows	3000	3000	3000	3000	3000
Salvage Value					2000

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 = $11949.18

At 11% Discount rate:

Present value of cash inflows = $12274.59

So, as per the method of interpolation:

IRR = 11% + (12% - 11%)*(P.V. at 11% - 12000) / (P.V. at 11% - P.V. at 12%)

IRR = 11% + 1% * (12274.59 - 12000) / (12274.59 - 11949.18) = 11.84% or 12% approx

4. Cost of capital = 6%

NPV = Present value of cash inflows   - Present value of investments

       = 3000*(1-1/1.06^5)/.06 + 2000/1.06^5   - 12000 =14131.61 - 12000

= $2131.61 = $ 2132 approx

5.

Profitability index = Present value of cash inflows/ Present value of investments

                         = 14131.61 / 12000 = 1.18 approx