Question

Byer, a plastics processor, is considering the purchase of a high-speed extruder as one option. The new extruder would cost $50,000 and would have a residual value of $3000 at the end of its 6-year life. The annual operating expenses of the new extruder would be $5000. The other option that Byer has is to rebuild its existing extruder. The rebuilding would require an investment of $30,000 and would extend the life of the existing extruder by 6 years. The existing extruder has annual operating costs of $13,000 per year and does not have a residual value. Byer's discount rate is 12%. Using net present value analysis, which option is the better option and by how much? Present Value of $1 Periods 12% 14% 16% 6 0.507 0.456 0.410 8 0.404 0.351 0.305 10 0.322 0.270 0.227 12 0.257 0.208 0.168Present Value of Annuity of $1 Periods 12% 14% 16% 6 4.111 3.889 3.685 8 4.968 4.639 4.344 10 5.650 5.216 4.833 12 6.194 5.660 5.197

Answer 1

To find the better investment option for Byer, NPV calculation is performed for both purchasing a new extruder and rebuilding the existing one, taking into account the initial outlay, operating expenses, residual value and the discount rate of 12%.

Step-by-step explanation:

To determine the better option between purchasing a new extruder and rebuilding the existing one using net present value (NPV) analysis, we need to calculate the present value of costs for both options by discounting them at Byer's rate of 12%.

For the new extruder, the initial outlay is $50,000, and the annual operating expenses are $5,000 over a 6-year life, with a residual value of $3,000 at the end.

Using the provided Present Value of Annuity of $1 table, we find that at 12% for six periods, the multiplier is 4.111. We calculate the present value of the operating expenses as $5,000 x 4.111 = $20,555.

We also need to discount the residual value of $3,000 back six years, which is $3,000 x 0.507 = $1,521. The total NPV for the new extruder is calculated by subtracting the initial cost and the present value of operating expenses from the present value of the residual value.

For rebuilding the existing extruder, the investment is $30,000, and the operating costs are $13,000 yearly, with no residual value. Following the same methods, we find the present value of the operating expenses to be $13,000 x 4.111 = $53,443.

We now compare the NPVs to decide which is the better option. If one option has a higher NPV, it is more financially viable.

Answer 2

Option of the new extruder is better by $14,411.16

Step-by-step explanation:

The present value of each option needs to be determined in order that the cheaper option in present value terms can be recommended.

Present value of new extruder=$50,000/(1+12%)^0+$5000/(1+12%)^1+$5000/(1+12%)^2+$5000/(1+12%)^3+$5000/(1+12%)^4+$5000/(1+12%)^5+$5000/(1+12%)^6-$3000/(1+12%)^6=$ 69,037.14

The discount factor each year=1/(1+r)^n where is 12% discount rate and n is the year

resent value of old extruder=$30,000/(1+12%)^0+$13,000/(1+12%)^1+$13000/(1+12%)^2+$13000/(1+12%)^3+$13000/(1+12%)^4+$13000/(1+12%)^5+$13000/(1+12%)^6=$ 83,448.30

The first option is better since it has a lower preset value of costs of $ 69,037.14

Difference in PVs= 83,448.30-69,037.14=$14,411.16