Question

your firm is considering an investment that will cost $920,000 today. the investment will produce cash flows of $450,000 in year 1, $270,000 in years 2 through 4, and $200,000 in year 5. the discount rate that your firm uses for projects of this type is 12%. How much would the NPV change if discount rate increases to 14%?

Answer 1

NPV is the net present value of the future cashflows and is calculated as follows:

Where C₀ is the initial investment i.e. $9,20,000

C_n is the cashflow of the nth period

i is the discount rate.

So, if the discount rate is 12%, the following table illustrates the present value of the future cash inflows.

It is important to note that here PVIF means present value interest factor i.e. the rate which is multiplied to the future cashflows to ascertain its present value. It is calculated as follows:

Here i is the discount rate, n is the year

The present value of cashflow is PVIF * Amount of Cashflow

So, NPV = C₀ + Total Present Value since the initial investment is an outflow, it'll be negative.

NPV = -$9,20,000 + $10,94,283.98

NPV when discount rate is 12% = $1,74,283.98

Similarly, we can ascertain the NPV when the discount rate is 14%. The following table illustrates the present value when the discount rate is 14%

So, the total present value when the discount rate is 14% is $10,48,470.792

Therefore, NPV when discount rate is 14% = -$9,20,000 + $10,48,470.792 = $1,28,470.792

Now, the amount by which NPV changed when discount rate increases from 12% to 14% is:

Change in NPV = NPV when discount rate is 14% - NPV when discount rate is 12%

Therefore, Change in NPV = $1,28,470.792 - $1,74,283.98 = - $45,813.19 approx

So, NPV decreased by $45,813.19 when discount rate changed from 12% to 14%