Final answer:
To choose between Alternative A and B, calculate their net present values using the provided initial cost, annual benefits, salvage value, useful life, and a discount rate of 20%. The present value of these cash flows is computed by discounting them at the given interest rate. The alternative with the higher NPV is the better choice.
Step-by-step explanation:
The student has asked to use Present Worth Analysis to determine whether Alternative A or B should be chosen. Given the interest rate of 20%, the student must calculate the net present value (NPV) of both options. To calculate NPV for Alternative A and Alternative B, we have to discount their cash flows to the present value and take into account the initial cost, annual benefits, salvage value, and the useful life.
To find the present value of the annual benefits and salvage value, the student can use the formula for the present value of an annuity and the present value of a lump sum respectively. For example, the present value of an annual benefit (AB) over 'n' years at an interest rate 'i' can be calculated using:
PV = AB * [(1 - (1 + i)^(-n)) / i]
The salvage value (SV) at the end of the useful life can be converted to present value using the formula:
PV = SV / (1 + i)^n
By summing these present values and subtracting the initial cost, the student will arrive at the NPV for each alternative. The alternative with the higher NPV is the more economically favorable option.
It's important to reiterate that the concept of opportunity cost and present discounted value is essential for understanding these calculations, as it allows comparison of costs and benefits occurring at different times on a like-for-like basis.