Question

A factory costs $1,090,440. You forecast that it will produce cash inflows of $733,922 in year 1, $175,000 in year 2, and $280,000 in year 3. The discount rate is 16.50%. a. Calculate the PV of cash inflows. (Do not round intermediate calculations. Round your answer to 2 decimal places.) .Please provide with formulas and Calculation

Answer 1

The present value of the cash inflows from the factory, discounted at 16.50%, is calculated using the formula
`PV = Cash flow / (1 + r)^n` for each year and then summing the individual present values to get a total of $941,202.87.

Step-by-step explanation:

To calculate the present value (PV) of cash inflows discounted at a rate of 16.50%, we will apply the formula for PV of a single cash flow, which is
`PV = Cash flow / (1 + r)^n`, where r is the discount rate and n is the number of periods. Here are the step-by-step calculations:

• PV of year 1 cash inflows:
  
  `PV = $733,922 / (1 + 0.165)^1`
  PV = $733,922 / 1.165
  PV = $629,760.52
• PV of year 2 cash inflows:
  
  `PV = $175,000 / (1 + 0.165)^2`
  
  `PV = $175,000 / 1.165^2`
  PV = $129,579.53
• PV of year 3 cash inflows:
  
  `PV = $280,000 / (1 + 0.165)^3`
  
  `PV = $280,000 / 1.165^3`
  PV = $181,862.82

Adding these up, the total present value of cash inflows is:

PV total = PVyear1 + PVyear2 + PVyear3
PV total = $629,760.52 + $129,579.53 + $181,862.82
PV total = $941,202.87