ECHO University (EU) is considering a project to buiild a new student residential building. The project will cost £100 million and would generate a FCF of £10 a year for the 15-year life of the building, after which it will be demolished at a zero net cost. EU does not pay tax. The land that would be used for the new building cannot be sold or rented and has no alternative use. EU estimates that the cost of capital for the FCFs is 10%.

a. What is the NPV of the project?

b. What is the IRR of the project’s FCFs?

c. What is the IRR rule and can it be used reliably in this case to decide whether or not to go ahead with the project?

Thiel, a former EU student, now a financial consultant, tells EU that, because they would be able to fund the building partly with borrowing, the project is more profitable than it might at first appear.

Thiel constructs a spreadsheet in which he assumes that EU borrows £80 million at an interest rate of 5%. Interest is paid annually and the loan is repaid in 15 years’ time. He then works out the “total project cash flows” by adding the loan cash flows to the FCFs from the project and reports that these total project cash flows have an IRR that is much higher than the project’s cost of capital of 10%.

d. Show that Thiel is correct in saying that Thiel’s “total project cash flows” have an IRR that is higher than 10%. What is this IRR?

e. Is the existence of an IRR greater than 10% for Bob’s “total project cash flows” consistent with the project’s NPV that you have calculated in part (a)? Explain your answer.

f. Should EU go ahead with the project?