Corporate Finance, Module 4: “Net Present Value vs Other Valuation Models”

Homework Assignments

(The attached PDF file has better formatting.)

Answer either one of the following two homework exercises.

Exercise 4.1: Project Duration

A firm has two potential projects, with the following expected cash flows:

    Cash Flows in Year X
    Yr 1    Yr 2    Yr 3    Yr 4
Project #1    (400)    220    310    –
Project #2    (400)    130    190    260


The firm’s opportunity cost of capital is 13% per annum.

A.    What is the net present value of Project #1?
B.    What is the net present value of Project #2?
C.    What project is better from an NPV perspective?
D.    What is the internal rate of return of Project #1? (You may use financial calculator to determine the IRR, or you may solve a quadratic equation)
E.    Is the internal rate of return of Project #2 higher or lower than the IRR for Project #1? (To see if the IRR for Project #2 is higher or lower than the IRR for Project #1, use the Project #1 IRR as the hurdle rate to compute the NPV of Project #2.)
F.    What project is better from an IRR perspective?
G.    Explain why the two performance measures give different answers. (See the practice problems for the explanation.)


Exercise 4.2: Project Size

A firm has two potential projects, with the following expected cash flows:

    Cash Flows in Year X
    Yr 1    Yr 2    Yr 3    Yr 4
Project #1    (800)    360    360    360
Project #2    (400)    130    190    260


The firm’s opportunity cost of capital is 13% per annum. (Project #2 is the same as in the previous homework assignment.)

A.    What is the net present value of Project #1?
B.    What is the net present value of Project #2?
C.    What project is better from an NPV perspective?
D.    What is the internal rate of return of Project #1?
E.    What is the internal rate of return of Project #2?
F.    What project is better from an IRR perspective?
G.    Explain why the two performance measures give different answers. (See the practice problems for the explanation.)

{Comments from a discussion forum thread:}

Question: What is the initial investment?

Answer: The initial investment is the negative cash flow at time 1.

Question: Does a project always have a negative cash flow followed by positive cash flows?

Answer: Not necessarily. A loan is a project. The borrower has a positive cash flow at time 0 and negative cash flows at each coupon payment date and at maturity.

Question: Are there other examples besides loans?

Answer: A state lottery collects money from consumers, and pays the winnings a few weeks later.

Question: Why do the examples generally have a negative initial cash flow followed by positive cash flows?

Answer: That is the most common sequence. Even for the state lottery, the state must spend money (an initial investment) preparing the structure: tickets, sales offices, advertisements, and so forth. This is an initial investment. The sequence of cash flows is a small initial investment at time 0, a large cash inflow at time 1, and a cash outflow at time 2.

Question: If a firm borrows money, is there a similar initial investment?

Answer: No one walks into a bank and says: “I’m setting up a firm which needs to borrow $100,000.” A person first sets up a firm, creates a business plan, creates a prototype of the product, and does all the work to show that the firm might succeed. This may cost $100,000, which is the initial investment. The firm then borrows $200,000 from the bank, to cover its production and operating costs.

Question: Does the initial investment have to be at time zero?

Answer: The time index is arbitrary. We can call it time 0, time 1, or time 2006.


Question: What should we focus on for the final exam?

Answer: The final exam may give a multiple choice question asking which project has the higher IRR and which has the higher NPV. Understand why a larger project or a longer project may have a higher NPV but a lower IRR. Know also two principles:

●    Both profit measures give the same accept/reject decision.
●    A change in the opportunity cost of capital changes the NPV but not the IRR.

Question: These two principles are not consistent. If a change in the opportunity cost of capital changes the NPV but not the IRR, why do the two measure give the same accept vs reject decision?

Answer: The hurdle rate for the IRR measure is the opportunity cost of capital. A higher opportunity cost of capital reduces the NPV (for investment projects, not loans) and increases the hurdle rate.