Question

Q1.) A project has the following cash flows for years 0 through 2, respectively: -13,568, 9,415, 9,983. What is the internal rate of return on this project?

Q2.) GDebi Enterprises is thinking of building a chemical processing plant to produce 4-hydroxy-3-methoxybenzaldehyde. The firm estimates that the initial cost of the project will be $11.7 million, and the plant will produce cash inflows of $7.2 million for the next 5 years, after which time the project will terminate. In the 6th year however, the firm will need to clean up the site, which it estimates will cost it $3.2 million. The discount rate the firm wants to use for the project is 10 percent. What is the NPV of this project? (Enter answer in millions.)

Q3.) The Blueberry Company is considering a project which will cost $372 initially. The project will not produce any cash flows for the first 3 years. Starting in year 4, the project will produce cash inflows of $405 a year for 4 years. This project is risky, so the firm has assigned it a discount rate of 18.3 percent. What is the net present value?

Answer 1

1)

IRR is the discount rate that makes NPV = 0

-13,658 + 9415 / ( 1 + r)¹ + 9983 / ( 1 + r)² = 0

Using trial and error method, lets use 26.6475% as the rate:

-13,658 + 9415 / ( 1 + 0.266475)¹ + 9983 / ( 1 + 0.266475)² = 0

-13,658 + 7,434.019621 + 6,223.974842 = 0

0 = 0

Therefore, 26.6475% is the IRR

2)

NPV = Present value of cash inflows - present value of cash outflows

Present value of cash inflow = PMT x ((1 - (1 / (1 + r) ^ n)) / r)

Present value of cash inflow = 7,200,000 x ((1 - (1 / (1 + 0.1) ^ 5)) / 0.1)

Present value of cash inflow = 7,200,000 x 3.790787

Present value of cash inflow = 27,293,664.74

Present value of cash outflow at year 6 = 3,200,000 / ( 1 + 0.1)⁶

Present value of cash outflow at year 6 = 1,806,316.576

Total cash outflow = 1,806,316.576 + 11,700,000 = 13,506,316.58

NPV = 27,293,664.74 - 13,506,316.58 = 13,787,348.16

3)

NPV = Present value of cash inflows - present value of cash outflows

Present value of cash flows at year 3 = PMT x ((1 - (1 / (1 + r) ^ n)) / r)

Present value of cash flows at year 3 = 405 * ((1 - (1 / (1 + 0.183) ^ 4)) / 0.183)

Present value of cash flows at year 3 = 405 * 2.674444

Present value of cash flows at year 3 = 1,083.14985

Present value today = 1,083.14985 / ( 1 + 0.183)³

Present value today = 654.23581

NPV = 654.23581 - 372

NPV = $282.2359