Question

1. (NPV and IRR​ calculation)East Coast Television is considering a project with an initial outlay of​ $X (you will have to determine this​ amount). It is expected that the project will produce a positive cash flow of $55,000 a year at the end of each year for the next 16 years. The appropriate discount rate for this project is 9 percent. If the project has an internal rate of return of 12 ​percent, what is the​ project's net present​ value?

a. If the project has an internal rate of return of 12​%, then the​ project's initial outlay is $ (Round to the nearest​ cent.)     

b. If the discount rate is 9%, then the​ project's NPV is% (Round to the nearest​ dollar.) 

Answer 1

Part a:

Net present value=-Initial cash outflow + Present value of future cash flows.
Internal rate of return (IRR) is the rate at which the net present value=0.
=>0=-Initial cash outflow + Present value of future cash flows
=>Initial cash outflow=Present value of future cash flows
Given that the project will produce a positive cash flow of $55,000 a year at the end of each year for the next 16 years.
Using internal rate of return of 12%, we need to calculate the present value of the cash flows equal to $55,000 a year for the next 16 years.

Present value of the future cash flows is calculated as the summation of (cash flow in year n)/[(1+IRR)^(Year n)]

Present value=$55000/(1+12%)^1+$55000/(1+12%)^2+$55000/(1+12%)^3+$55000/(1+12%)^4+$55000/(1+12%)^5+$55000/(1+12%)^6+$55000/(1+12%)^7+$55000/(1+12%)^8+$55000/(1+12%)^9+$55000/(1+12%)^10+$55000/(1+12%)^11+$55000/(1+12%)^12+$55000/(1+12%)^13+$55000/(1+12%)^14+$55000/(1+12%)^15+$55000/(1+12%)^16

=$55000/(1.12)^1+$55000/(1.12)^2+$55000/(1.12)^3+$55000/(1.12)^4+$55000/(1.12)^5+$55000/(1.12)^6+$55000/(1.12)^7+$55000/(1.12)^8+$55000/(1.12)^9+$55000/(1.12)^10+$55000/(1.12)^11+$55000/(1.12)^12+$55000/(1.12)^13+$55000/(1.12)^14+$55000/(1.12)^15+$55000/(1.12)^16
=$55000/1.12+$55000/1.2544+$55000/1.404928+$55000/1.57351936+$55000/1.762341683+$55000/1.973822685+$55000/2.210681407+$55000/2.475963176+$55000/2.773078757+$55000/3.105848208+$55000/3.478549993+$55000/3.895975993+$55000/4.363493112+$55000/4.887112285+$55000/5.473565759+$55000/6.13039365

=$49107.14286+$43845.66327+$39147.91363+$34953.49431+$31208.47707+$27864.71167+$24879.20685+$22213.57754+$19833.55138+$17708.52801+$15811.18573+$14117.13011+$12604.58046+$11254.08969+$10048.29437+$8971.691402
=$383569.2384 or $383569 (Round to the nearest​ cent)
Project's initial outlay is $383569.

Part b:
Project's net present value at discount rate of 9%.
We can calculate this using excel. As $383569 is a cash outflow, it is shown as negative in excel.
The value of NPV using a discount rate of 9% is equal to $73,621.70

Note: 9% used in the NPV formula in excel refers to the discount rate.