Question

What is the NPV of a project that costs $120,000 today and is expected to generate annual cash inflows of $10,000 for the next 12 years, followed by a final inflow of $21,000 in the year after. Use discount rate of 14%. Round to the nearest cent.  

Answer 1

Given,
Initial Cost = $120000
Annual Cash Inflow = $10000
Final Inflow = $21000
Discount Rate = r = 14% = 0.14
No of Years = 12+1 = 13
NPV of Project
= (-Initial Cost) + Present Value of Cash Inflows
= (-Initial Cost) + Annual Cash Inflow * Present Value Annuity Factor @14%
for 12 years + Final Inflow * Discount Factor @ 14% at 13th year
= (-Initial Cost) + Annual Cash Inflow*[(1+r)12-1 / r(1+r)12] + Final Inflow*[1/(1+r)13]
= (-120000) + 10000*[(1+0.14)12-1 / 0.14(1+0.14)12] + 21000*[1/(1+0.14)13]
= (-120000) + 10000*[(1.14)12-1 / 0.14(1.14)12] + 21000*[1/(1.14)13]
= (-120000) + 10000*[4.8179-1 / 0.14*4.8179] + 21000*[0.182069]
= (-120000) + 10000*[3.8179 / 0.674506] + 3823.45
= (-120000) + 10000*5.660291 + 3823.45
= (-120000) + 56602.91 + 3824.10
= (-59572.99)