Question

NPVs and IRRs for Mutually Exclusive Projects

Davis Industries must choose between a gas-powered and an electric-powered forklift truck for moving materials in its factory. Because both forklifts perform the same function, the firm will choose only one. (They are mutually exclusive investments.) The electric-powered truck will cost more, but it will be less expensive to operate; it will cost $22,000, whereas the gas-powered truck will cost $17,500. The cost of capital that applies to both investments is 12%. The life for both types of truck is estimated to be 6 years, during which time the net cash flows for the electric-powered truck will be $6,290 per year and those for the gas-powered truck will be $5,000 per year. Annual net cash flows include depreciation expenses.

1. Calculate the NPV for each type of truck. Do not round intermediate calculations. Round your answers to the nearest dollar.

   Electric-powered forklift truck: $ ???

   Gas-powered forklift truck: $ ???

2. Calculate the IRR for each type of truck. Do not round intermediate calculations. Round your answers to two decimal places.

   Electric-powered forklift truck: ??? %

   Gas-powered forklift truck: ???  %

   Which type of the truck should the firm purchase?
   The firm should purchase [(A)Electric powered, (B) Gas powered] forklift truck.

Answer 1

a. Calculating NPV of Electric powered forklift truck

NPV of the electric powered truck = -Cost of truck + Sum of present value of cash flow for year 1 to 6 discounted at 12%

= -22000 + 6290/(1+12%)¹ + 6290/(1+12%)² + 6290/(1+12%)³ + 6290/(1+12%)⁴ + + 6290/(1+12%)⁵ + 6290/(1+12%)⁶

Since the cash flow for year 1 to year 6 form an ordinary annuity, We can find sum of present value of cash flows using PV function in excel

Formula to be used in excel: =PV(rate,nper,-pmt)

Using PV function in excel, we get sum of present value of cash flows for year 1 to year 6 = $25860.7520

NPV of electric powered truck = -22000 + 25860.7520 = 3860.7520 = 3861 (rounded to nearest dollar)

Hence NPV of electric powered forklift truck = 3861

Calculating NPV of Gas powered truck

NPV of gas powered truck = - Cost of gas powered truck + Sum of present value of cash flows for year 1 to 6 discounted at 12% = -17500 + 5000/(1+12%)¹ + 5000/(1+12%)² + 5000/(1+12%)³ + 5000/(1+12%)⁴ + 5000/(1+12%)⁵ + 5000/(1+12%)⁶

Since the cash flow for year 1 to year 6 form ordinary annuity, We can find sum of present value of cash flows using PV function in excel

Formula to be used in excel: =PV(rate,nper,-pmt)

Using PV function in excel, we get sum of present value of cash flows for year 1 to year 6 = $20557.0366

NPV of gas powered truck = -17500 + 20557.0366 = 3057.0366 = 3057 (rounded to nearest dollar)

NPV of gas powered truck = 3057

b. Calculating IRR of Electric powered truck

IRR is the rate of return earned by the project such that sum of present value of cash inflows is equal sum of present value of cash outflows. We have

0 = = -22000 + 6290/(1+IRR%)¹ + 6290/(1+IRR%)² + 6290/(1+IRR%)³ + 6290/(1+IRR%)⁴ + + 6290/(1+IRR%)⁵ + 6290/(1+IRR%)⁶

We can find the IRR of cash flows using IRR function in excel

Formula to be used in excel: =IRR(values)

where values are cash flows for year 0 to year 6

Using IRR function in excel, we get IRR of electric powered truck = 17.9998% = 18.00% (rounded to two decimal places)

Hence IRR of electric powered truck = 18.00%

Calculating IRR of Gas powered truck

IRR is the rate of return earned by the project such that sum of present value of cash inflows is equal sum of present value of cash outflows. We have

0 = = -17500 + 5000/(1+IRR%)¹ + 5000/(1+IRR%)² + 5000/(1+IRR%)³ + 5000/(1+IRR%)⁴ + 5000/(1+IRR%)⁵ + 5000/(1+IRR%)⁶

We can find the IRR of cash flows using IRR function in excel

Formula to be used in excel: =IRR(values)

where values are cash flows for year 0 to year 6

Using IRR function in excel, we get IRR of gas powered truck = 17.9732% = 17.97% (rounded to two decimal places)

Hence IRR of gas powered forklift truck = 17.97%

In case of mutually exclusive projects, we always choose the project or truck with higher NPV because it results in higher increase in shareholder value and higher increment in value of company. Since the electric powered forklift truck has higher NPV as compared to gas powered forklift truck, hence electric powered forklift truck should be purchased.

Answer: a) Electric powered forklift truck