Question

A factory costs $400,000. you forecast that it will produce cash inflows of $120,000 in year 1, $180,000 in year 2, and $300,000 in year 3. the discount rate is 12%.

a. what is the value of the factory?a factory costs $400,000. you forecast that it will produce cash inflows of $120,000 in year 1, $180,000 in year 2, and $300,000 in year 3. the discount rate is 12%.
a. what is the value of the factory?

Answer 1

The value of the factory is determined by calculating the present value of the forecasted cash inflows, discounted at a 12% rate. The present value totals $464,426.84 for cash inflows over three years.

Step-by-step explanation:

To determine the present value of the factory, we need to discount the forecasted cash inflows at the given discount rate of 12%. The formula for calculating the present value (PV) is:

PV = Cash Flow / (1 + r)^t

where 'r' is the discount rate and 't' is the number of years into the future the cash flow will occur. Now, let's calculate the present value for each year and add them up to get the total present value of the factory:

• Year 1: PV = $120,000 / (1 + 0.12)^1 = $107,142.86
• Year 2: PV = $180,000 / (1 + 0.12)^2 = $143,487.05
• Year 3: PV = $300,000 / (1 + 0.12)^3 = $213,796.93

Adding these amounts gives us the total present value of the factory:

Total PV = $107,142.86 + $143,487.05 + $213,796.93

Total PV = $464,426.84

Thus, the value of the factory, when considering the forecast cash inflows and the discount rate, is $464,426.84.

Answer 2

$464,171.83 The discount rate is used to calculate the present value of an asset you expect to get in the future. The formula is PV = FV/(1+R)^n where PV = Present Value FV = Future Value R = Rate n = Number of periods So let's look at the return for the first 3 years Year 1 PV = $120,000/1.12 = $107,142.86 Year 2 PV = $180,000/1.12^2 = $180,000/1.2544 = $143,494.90 Year 3 PV = $300,000/1.12^3 = $300,000/1.404928 = $213,534.07 So the current value is PV = $107,142.86 + $143,494.90 + $213,534.07 = $464,171.83