By NEAS - 6/7/2005 2:11:17 PM
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.
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By NEAS - 8/21/2018 7:35:48 PM
+xFor G, do we need further explanations than the following? The NPV and IRR methods give different recommendations because they have different assumptions about unused cash. The NPV rule assumes that unused cash earns the opportunity cost of capital; the IRR rule assumes that unused cash earns the internal rate of return. |
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