Corporate Finance, Module 4: “Net Present Value vs Other Valuation Models”
Homework Assignments
(The attached PDF file has better formatting.)
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; you can also use trial and error to get an approximate figure.)
E. What is the internal rate of return of Project #2? (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 measurement yardsticks give different answers. (See the corresponding practice problem 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 measurement yardsticks give different answers. (See the corresponding practice problem 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.