NPVs and IRRs for Mutually Exclusive Projects Davis Industries must choose betwe

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. Since 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 $23,000, whereas the gas-powered truck will cost $17,100. The cost of capital that applies to both investments is 11%. 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 $6,500 per year and those for the gas-powered truck will be $4,950 per year. Annual net cash flows include depreciation expenses.

Calculate the NPV for each type of truck. Round your answers to the nearest dollar.

Calculate the IRR for each type of truck. Round your answers to two decimal places.

Which type of the truck should the firm purchase?
-Select-Electric-poweredGas-powered

Shao Airlines is considering two alternative planes. Plane A has an expected life of 5 years, will cost $100 million and will produce net cash flows of $30 million per year. Plane B has a life of 10 years, will cost $132 million and will produce net cash flows of $27 million per year. Shao plans to serve the route for only 10 years. Inflation in operating costs, airplane costs, and fares is expected to be zero, and the company's cost of capital is 11%.

By how much would the value of the company increase if it accepted the better project (plane)? Enter your answer in millions. For example, an answer of $1.2 million should be entered as 1.2, not 1,200,000. Round your answer to two decimal places.
$    million

What is the equivalent annual annuity for each plane? Enter your answer in millions. For example, an answer of $1.2 million should be entered as 1.2, not 1,200,000. Round your answers to two decimal places.

Explanation / Answer

NPV for Electric power fork lift NPV for gas powered fork lift Year cash flows Discount rate@11% Present value of cash flows Year cash flows Discount rate@11% Present value of cash flows 0 ($23,000) 0 ($17,100) 1 $6,500.00 0.901 $5,856.50 1 $4,950.00 0.901 $4,459.95 2 $6,500.00 0.812 $5,278.00 2 $4,950.00 0.812 $4,019.40 3 $6,500.00 0.731 $4,751.50 3 $4,950.00 0.731 $3,618.45 4 $6,500.00 0.659 $4,283.50 4 $4,950.00 0.659 $3,262.05 5 $6,500.00 0.593 $3,854.50 5 $4,950.00 0.593 $2,935.35 6 $6,500.00 0.535 $3,477.50 6 $4,950.00 0.535 $2,648.25 $39,000.00 $27,501.50 $29,700.00 $20,943.45 NPV for Electric power fork lift = -23,000+27501.50 = $ 4,501.50 NPV for gas powered fork lift = -17,100+ 20,943.45 = $ 3,843.45 To calculate the Internal rate of return Annuity for Electric power fork lift = 39,000/5 = $ 7800 Annuity for gas powered fork lift = 29,700/5 = $ 5940 Pay back period for electric power fork lift = 23,000/7800 = 2.94 years Pay back period for gas powered fork lift = 17,000/5940 = 2.86 years discount factor for electic powered fork lift = 25% discount factor for gas powered fork lift = 26% IRR for Electric power fork lift Year cash flows Discount rate@25% Present value of cash flows Discount rate@17% Present value of cash flows Discount rate@18% Present value of cash flows 0 ($23,000) 1 $6,500.00 0.8 $5,200.00 0.855 $5,557.50 0.847 $5,505.50 2 $6,500.00 0.64 $4,160.00 0.731 $4,751.50 0.718 $4,667.00 3 $6,500.00 0.512 $3,328.00 0.624 $4,056.00 0.609 $3,958.50 4 $6,500.00 0.41 $2,665.00 0.534 $3,471.00 0.516 $3,354.00 5 $6,500.00 0.328 $2,132.00 0.456 $2,964.00 0.437 $2,840.50 6 $6,500.00 0.262 $1,703.00 0.39 $2,535.00 0.37 $2,405.00 $39,000.00 $19,188.00 $23,335.00 $22,730.50 IRR for electric power fork lift = 17% + 23335 - 23,000/ 23335 - 22730 = 17.55% IRR for gas power fork lift Year cash flows Discount rate@17% Present value of cash flows Discount rate@18% Present value of cash flows Discount rate@19% Present value of cash flows 0 ($17,100) 1 $4,950.00 0.855 $4,232.25 0.847 $4,192.65 0.84 $4,158.00 2 $4,950.00 0.731 $3,618.45 0.718 $3,554.10 0.706 $3,494.70 3 $4,950.00 0.624 $3,088.80 0.609 $3,014.55 0.593 $2,935.35 4 $4,950.00 0.534 $2,643.30 0.516 $2,554.20 0.499 $2,470.05 5 $4,950.00 0.456 $2,257.20 0.437 $2,163.15 0.419 $2,074.05 6 $4,950.00 0.39 $1,930.50 0.37 $1,831.50 0.352 $1,742.40 $17,770.50 $17,310.15 $16,874.55 IRR for gas power fork lift = 18% + 17310 - 17100 / 17310 - 16874.55 = 18.48 % The firm should purchase gas powered fork lift because the IRR is high when compared to gas powered fork lift. Q 2) PLANE A PLANE B year cash flows( Million) discount rate @ 11% Present value of cash flows year cash flows( Million) discount rate @ 11% Present value of cash flows 0 - $100 million 0 -132 1 $30 0.901 $27.03 1 27 0.901 24.327 2 $30 0.812 $24.36 2 27 0.812 21.924 3 $30 0.731 $21.93 3 27 0.731 19.737 4 $30 0.659 $19.77 4 27 0.659 17.793 5 $30 0.593 $17.79 5 27 0.593 16.011 $110.88 6 27 0.535 14.445 7 27 0.482 13.014 8 27 0.434 11.718 9 27 0.391 10.557 10 27 0.352 9.504 159.03 NPV for Plane A = 100+110.80 = $ 10.80 million NPV for Plane B = -132+159.03 = $ 27.03 million The value of the company increase by 27.03 million if it accepted the better project plane i.e Plane B. Equivalent annual annuity c = r X npv / 1 - (1+r)e-n Equivalent annual annuity for plane A = 0.11X10.80 / 1 - (1+.11)e-5 = $ 2.92 million Equivalent annual annuity for plane B = .11X27.03 / 1 - (1+.11)e-10 = $ 4.58 million

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