9) A project costs $3000 immediately. The project yields nominal returns of $100

Question

9) A project costs $3000 immediately. The project yields nominal returns of $100 in year 1, $200 in year 2, $300 in year 3, $400 in year 4, and $500 in year 5. In addition, the project will have capital worth $2500 (in nominal $) left over in year 5. The real discount rate is 7% and the expected inflation rate is 3%. What is the NPV of this project? 10)You have $2000 to invest, and are choosing between two projects, both of which cost $2000 up front and will yield six years of returns. The returns for the first investment will be paid in nominal $, starting at $400 a year from now and increasing at 8% annually. The returns for the second will be paid in real $, starting at $500 and increasing at 2% annually. If your real hurdle rate is 4.5% and the expected inflation rate is 3.1%, which of these investments should you choose (if any)?

Explanation / Answer

9) Since the problem lists nominal cash flows and a real discount rate, one must determine the nominal discount rate before computing the net present value of the project. 1+Real Discount Rate = (1+Nominal Discount Rate)/(1+inflation Rate) 1.07 = (1+Nominal Discount Rate)/(1.03) Nominal Discount Rate = 0.1021 Year NPV 0 -3000             -3,000 1 100*(1+0.1021)^1 =                  110 2 200*(1+0.1021)^2 =                  243 3 300*(1+0.1021)^3 =                  402 4 400*(1+0.1021)^4 =                  590 5 500*(1+0.1021)^5 =                  813 5 2500*(1+0.1021)^5 =              4,065              3,223 10) Year Project 1 Project 2 NPV of Project 1 NPV of Project 2 0 -2000 -2000 -2000*(1+0.077)^0 =       -2,000 -2000*(1+0.045)^0 =       -2,000 1 400 500 400*(1+0.077)^1 =            431 500*(1+0.045)^1 =            523 2 432 510 432*(1+0.077)^2 =            501 510*(1+0.045)^2 =            557 3 467 520 467*(1+0.077)^3 =            583 520*(1+0.045)^3 =            594 4 504 531 504*(1+0.077)^4 =            678 531*(1+0.045)^4 =            633 5 544 541 544*(1+0.077)^5 =            789 541*(1+0.045)^5 =            674 6 588 552 588*(1+0.077)^6 =            917 552*(1+0.045)^6 =            719         1,898         1,699 I will select project 1. becouse NPV of total project showing higher than project 2 1+Real Discount Rate = (1+Nominal Discount Rate)/(1+inflation Rate) 1.045 = (1+Nominal Discount Rate)/(1.031) Nominal Discount Rate = 0.077

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