Question

The manufacture of folic acid is a competitive business. A new plant costs $100,000 and lasts for three years. The cash flow from the plant is as follows: year 1: +$43,300, year 2: +$43,300 and year 3 = +$58,300. (Assume no taxes.) If the discount rate is 20%, what is the value of the plant at the end of year 1?

a) +$76,569
b) -$23,400
c) $48,600
d) none of the options

Answer 1

The value of the plant at the end of year 1, after discounting future cash flows at a 20% discount rate, is $76,569. This is achieved by calculating the present values of year 2 and year 3 cash flows and summing them. Option A is correct answer.

Step-by-step explanation:

To determine the value of the plant at the end of year 1, we need to calculate the present value of future cash flows from year 2 and year 3, discounted at the given rate of 20%. Since we are calculating this as of the end of year 1, we do not need to discount the year 1 cash flow.

Here is the step-by-step calculation:

• Year 2 cash flow: We discount the $43,300 cash flow from year 2 back one year at the 20% discount rate, which is $43,300 / (1+0.20) = $36,083.33.
• Year 3 cash flow: We discount the $58,300 cash flow from year 3 back two years at the 20% discount rate, which is $58,300 / (1+0.20)^2 = $40,486.11.

Adding these two amounts gives us the value of the future cash flows at the end of year 1:

$36,083.33 (year 2) + $40,486.11 (year 3) = $76,569.44

Therefore, the correct option is a) $76,569.