Question

Two investment alternatives are under consideration. Alternative A requires an initial investment of $10,000 and will generate net annual returns of $6000 per year for 3 years; it will have a $900 salvage value at the end of its useful life of 3 years. Alternative B also requires an initial investment of $25,000; and will generate net annual returns of $12,000 per year for 6 years and it will have a $5000 salvage value at the end of its useful life of 6 years. If the two alternatives are considered, using an Annual Worth comparison with a MARR of 10% per year, which would be preferred?

Question 3. ( 5 Marks) The installation costs of a battery system in a home were $5,000 in 2017. Assume that the life of the system is 3 years. The real internal rate of return on this investment is 10% and the average inflation is 3%. Find its equivalent future worth at 2020 (in terms of actual and real dollars).

Answer 1

Question 1:

To determine the preferred alternative using an Annual Worth comparison, we need to calculate the Annual Worth (AW) for each alternative and compare them.

For Alternative A:

Initial investment: -$10,000

Annual returns: $6,000 for 3 years

Salvage value: $900

Using the Annual Worth formula: AW = (Annual returns - Annual costs) * (P/A, MARR, n) + (Salvage value * (P/F, MARR, n))

AW_A = ($6,000 - $10,000) * (P/A, 10%, 3) + ($900 * (P/F, 10%, 3))

For Alternative B:

Initial investment: -$25,000

Annual returns: $12,000 for 6 years

Salvage value: $5,000

AW_B = ($12,000 - $25,000) * (P/A, 10%, 6) + ($5,000 * (P/F, 10%, 6))

Calculate the values using the appropriate interest factor tables or financial calculator.

Compare the Annual Worth values (AW_A and AW_B) and choose the alternative with the higher value. The alternative with the higher Annual Worth is the preferred option.

Question 2:

To find the equivalent future worth of the battery system at 2020 in actual and real dollars, we need to consider the effects of inflation.

Given:

Installation costs in 2017: $5,000

System life: 3 years

Real internal rate of return: 10%

Average inflation rate: 3%

To find the equivalent future worth in actual dollars, we can use the Future Worth (FW) formula:

FW_actual = Installation costs * (F/P, inflation, n)

FW_actual = $5,000 * (F/P, 3%, 3)

To find the equivalent future worth in real dollars, we can use the Future Worth (FW) formula but adjust the inflation rate:

FW_real = FW_actual * (P/F, inflation, n)

FW_real = FW_actual * (P/F, 3%, 3)

Calculate the values using the appropriate interest factor tables or financial calculator to obtain the equivalent future worth in actual and real dollars.