Question

What is the NPV of a project that costs $100,000, provides $21,000 in cash flows annually for six years, requires a $5,000 increase in net working capital which will be recovered later? The discount rate is 14%.

-$13,283

-$21,060

- $18,142

$15,561

Answer 1

Answer:-$21,060

The initial investment=$100,000

Add the working capital increase=$5,000

So total Initial outlay=$105,000

The Annual Cash flows are $21,000 per year , during the final year the working capital will be recovered so final year inflow =$21,000+$5000=$26,000

Excel has been used to compute the NPV

The formula used to compute NPV =NPV(14%,B3:B8)+B2 we get NPV as -$21,060

Manual Calculations

NPV=PV of Cash Flows-Initial Outlay

The Annual Cash Flow from Years 1 to 5 are 21,000 each the year 6 cash flow would be =$21,000+$5000=$26,000.

To find the NPV multiply these cash flows with their Present value interest factor.

The Present value interest factor can be obtained by using the formula (1/(1+r)^n here the r(discount rate)=14% and n stands for years,it will be 1 for year 1 and 6 for year 6.

We get the following values .877193,.769468,.674972,.59208,.519369 and .455587.

Now multipying each years cash flow with the aforementioned values we get the PV of Cash Flows as for years 1 to 6 18421.05,16158.82,14174.4,12,433.69,10906.74,11845.25

Adding them we get the sum of PV of Cash Flows as 18421.05+16158.82+14174.4+12,433.69+10906.74+11845.25 =$83,939.95

Now the Initial Outlay is 105,000($100,000+$5,000)

So the NPV would be 83939.95-105,000=-$21,060.05 which when rounded gives -$21,060