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Chapter 12: Problem 15

You have the chance to participate in a project that produces the following cash flows: $$\begin{array}{ccc} C_{0} & C_{1} & C_{2} \\\\\hline+\$ 5,000 & +\$ 4,000 & -\$ 11,000 \\\\\hline\end{array}$$ The internal rate of return is 13.6 percent. If the opportunity cost of capital is 12 percent, would you accept the offer?

Short Answer

Expert verified
No, the offer should not be accepted based on the Opportunity Cost of Capital of 12 percent since the Net Present Value is negative.

Step by step solution

01

Understanding the Cash Flows

The given set of cash flows indicate that there's an inflow of \$5,000 at time 0 (C_{0}), inflow of \$4,000 at time 1 (C_{1}), and an outflow of \$11,000 at time 2 (C_{2}). The negative sign before the \$11,000 indicates it's an outflow or a cost.
02

Calculating the Net Present Value

The Net Present Value (NPV) can be calculated using the formula \(NPV = \sum \frac{C_{t}}{(1 + r)^{t}}\), where C = Cash flows, r = Discount rate or opportunity cost of capital and t = time period. Substituting values from the cash flows and r=12 percent, we find: \( NPV = \frac{5000}{(1+0.12)^0} + \frac{4000}{(1+0.12)^1} - \frac{11000}{(1+0.12)^2} = \$5,000 + \$3,571.43 - \$8,741.63 = -\$170.2 \)
03

Make a Decision

The negative Net Present Value implies that the project will produce less return than the expected returns at 12% opportunity cost of capital. This means the returns are not adequate for the risks assumed. With respect to usual decision rule for investment - if NPV is positive take the project and if NPV is negative reject the project, this project should be rejected.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Cash Flow Analysis
In the realm of financial decision-making, cash flow analysis is pivotal. It assesses the timing, amount, and predictability of cash inflows and outflows over a specific period.

With our textbook exercise, we scrutinize an offer to join a project which promotes distinct cash flows at various points. Specifically, an inflow of \(5,000 (C0) at the outset, a subsequent \)4,000 (C1) gain after one year, and an outlay of $11,000 (C2) in the second year. The negative figure indicates a cash expenditure or obligation.

When you investigate such cash flows, you are observing the project's liquidity over time, assessing not only how much money is received or spent, but when these transactions occur. This temporal element is crucial, as receiving money today is preferred over receiving the same amount in the future, mainly because of the potential interest it could earn if invested promptly. This is where the calculation of Net Present Value (NPV) becomes essential in our analysis, as it discounts future cash flows back to their value in today's dollars, factoring in the opportunity cost of capital.
Internal Rate of Return
The internal rate of return (IRR) serves as a compass guiding investment decisions. It represents the interest rate at which the Net Present Value (NPV) of all cash flows from a particular project equals zero. In essence, the IRR is the break-even rate of return.

The textbook example cites an IRR of 13.6 percent. This highlights an attractive quality of the project being evaluated鈥攊t suggests that for every dollar invested, the project is expected to generate an annual return of 13.6 percent.

Comparing IRR with the opportunity cost of capital is crucial. If the IRR exceeds the opportunity cost of capital, which is the return one could expect from the next best investment alternative, the project might be deemed profitable. However, if IRR is lower, it poorly positions the project relative to alternative investments. Although the IRR is an indicator of profitability, it should not be the sole factor in accepting a project, as it does not consider the scale of the investment or the overall dollar value added.
Opportunity Cost of Capital
At the core of investment decision-making lies the concept of opportunity cost of capital. It acknowledges that capital has alternative uses and these alternatives are forsaken when an investment is made.

In the context of our textbook exercise example, the opportunity cost of capital is 12 percent. This is essentially the return that could be earned if the money were invested elsewhere. When evaluating a potential investment, if an undertaking offers lower returns than the opportunity cost of capital, it is not exploiting the capital to its fullest potential.

Injecting this concept into the NPV formula forces us to examine our project through the rigorous lens of what we're sacrificing for its undertaking. The opportunity cost of capital helps ensure we're not undervaluing the potential earning power of our capital. It's a stern reminder that we should gravitate towards investments that outperform this minimum acceptable rate鈥攐r at least, meet it鈥攖o justify the choice of one investment over another.

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Most popular questions from this chapter

Book Rate of Return. Consider these data on a proposed project: Original investment = 200 dollar Straight-line depreciation of 50 dollar a year for 4 years Project life \(=4\) years. a. Fill in the blanks in the table. b. Find the book rate of return of this project in each year. c. Find project \(\mathrm{NPV}\) if the discount rate is 20 percent.

Consider this project with an internal rate of return of 13.1 percent. Should you accept or reject the project if the discount rate is 12 percent? $$\begin{array}{cc} \text { Year } & \text { Cash Flow } \\\\\hline 0 & +\$ 100 \\\1 & -60 \\\2 & -60 \\\\\hline\end{array}$$

A machine costs 8,000 dollarand is expected to produce profit before depreciation of 2,500 dollar in each of Years 1 and 2 and 3,500 dollar in each of Years 3 and 4 . Assuming that the machine is depreciated at a constant rate of 2,000 dollar a year and that there are no taxes, what is the average return on book?

Growth Enterprises believes its latest project, which will cost 80,000 dollar to install, will generate a perpetual growing stream of cash flows. Cash flow at the end of this year will be 5,000, dollar and cash flows in future years are expected to grow indefinitely at an annual rate of 5 percent. a. If the discount rate for this project is 10 percent, what is the project NPV? b. What is the project IRR?

If you insulate your office for \(\$ 1,000\), you will save \(\$ 100\) a year in heating expenses. These savings will last forever. a. What is the NPV of the investment when the cost of capital is 8 percent? 10 percent? b. What is the IRR of the investment? c. What is the payback period on this investment?
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