Question

Richman Co. purchased some equipment 3 years ago. The company's required rate of return is 12%, and the net present value of the project was $(900). Annual cost savings were: $10,000 for year 1; $8,000 for year 2; and $6,000 for year 3.

The amount of the initial investment was


a.
$18,316.

b.
$20,116.

c.
$20,478.

d.
$18,678.

Answer 1

The initial investment amount can be calculated by finding the present value of the cash flows and subtracting it from the net present value (NPV).

Step-by-step explanation:

The initial investment amount can be calculated by finding the present value of the cash flows and subtracting it from the net present value (NPV). In this case, the cost savings for each year need to be discounted back to the present value. The formula to calculate the present value of cash flows is:

PV = CF / (1 + r)^n

Where:

• PV is the present value
• CF is the cash flow
• r is the required rate of return
• n is the number of years

Using this formula, the initial investment amount is $20,116 (option b).

Answer 2

The correct answer is option (C) $20,478

Step-by-step explanation:

Solution

Given that:

The Net present value is defined as:

Net present value

= Present value of all flow of cash discounted at the rate required of return - Initial investment

Thus,

$ - 900 = 10000/1.12 + 8000/ (1.12)^2 + 6000/(1.12)^3 - The initial investment

So,

Initial Investment = $ 19,578 + $ 900

= $ 20,478

Therefore the amount of initial investment was $20,478