1. What is NPV? The net present value (NPV) of a project is the sum of the present values of all the cash flows – positive and negative – that are expected to occur over the life of a project. 2. What are the implications of the additivity property of NPV? Several implications of the additivity property of NPV are: # The value of a firm can be expressed as the sum of the present value of projects in place as well as the net present value of prospective projectsValue of a firm = ∑Present value of projects + ∑NPV of expected future projects The first term on the right hand side of this equation captures the value of assets in place and the second term the value of growth opportunities. # When a firm terminates an existing project which has a negative NPV based on its expected future cash flows, the value of the firm increases by that amount. Likewise, when a firm undertakes a new project that has a negative NPV, the value of the firm decreases by that amount. # When a firm divests itself of an existing project, the price at which the project is divested affects the value of the firm. If the price is greater/lesser than the present value of the anticipated cash flows of the project the value of the firm will increase/decrease with the divestiture. # When a firm takes on a new project with a positive NPV, its effect on the value of the firm depends on whether its NPV is in line with expectation. # When a firm makes an acquisition and pays a price in excess of the present value of the expected cash flows from the acquisition it is like taking on a negative NPV project and hence will diminish the value of the firm. 3. Discuss the general formula of NPV when discount rates vary over time. So far we assumed that the discount rate remains constant over time. This need not be always the case. The NPV can be calculated using time-varying discount rates. The general formula of NPV is as follows:
∑ Where
is the cash flow at the end of the year t, and
In even more general terms NPV is expressed as follows:
∑
∏
(
)
is the discount rate for year t.
Where is the cash flow at the end of the year t, and of the project.
is the one period discount rate, and n is the life
4. What is the rationale for the NPV rule? The NPV measures the opportunity costs between two or more projects. It is important to know what we are giving up in order to make our decision. A higher NPV indicates a greater rate of return, but is not always the best choice as at some times the financial risks associated with the project may be unacceptable. Likewise a low NPV project may not be worthwhile because it would simply be better to put our money into a savings account since the return is so low. When the net present value is maximized we reach the highest consumption frontier. This constitutes the rationale for the net present value criterion. 5. How is modified NPV calculated? Calculation of modified NPV has two steps: Step 1: Calculate the terminal value of the project’s cash inflows using the explicitly defined reinvestment rate(s) which are supposed to reflect the probability of investment opportunities ahead of the firm.
∑
́
where TV is the terminal value of the project’s cash inflows, is the cash inflow at the end of the year t, and ́ is the reinvestment rate applicable to the cash inflows of the project. Step 2: Determine the modified net present value
where is the modified net present value, TV is the terminal value, r is the cost of the capital and I is the investment outlay. 6. Show why the NPV of a simple project decreased as the discount rate increased. A simple project involves as initial cash outflow, or a series of initial cash outflows, followed by cash inflows. The NPV of a simple project steadily decreases as the discount rate increases. The decrease in NPV, however, is at a decreasing rate. To demonstrate this point, consider a simple project which has the following cash flow stream.
The net present value as a function of the discount rate, r, may be expressed as :
Assuming that r is a continuous variable and NPV(r) is a continuous and differentiable function, we get:
This is a negative for all values of -1 < r < ∞. Hence the net present value of a simple project is steadily decreasing. The second derivative of the net present value function with respect to (1+r) is:
This is a positive for all values of -1 < r < ∞. Hence the net present value function decreases at a decreasing rate. 7. What are the limitations of NPV? Limitations of NPV are# The NPV is expressed in absolute terms rather than relative terms and hence does not factor in the scale of investment. Advocates of NPV, however, argue that what matters is the surplus value, over and above the hurdle rate, irrespective of what the investment is. # The NPV rule does not consider the life of the project. Hence, when mutually exclusive projects with different lives are being considered, the NPV is biased in favor of the longer term project. 8. What are the two ways of defining the benefit-cost ratio? Two ways of defining the relationship between benefits and costs: Benefit-cost ratio : BCR Net benefit-cost ratio : NBCR where PVB is the present value of benefits, and I is the initial investment. 9. Evaluate the benefit-cost ratio as an investment criteria. The proponents of benefit-cost ratio argue that since this criterion measures net present value per taka of outlay, it can discriminate better between large and small investments and hence is preferable to the net present value criterion. Weingartner, who examined this criterion theoretically finds that: (i) Under unconstrained conditions, the benefit-cost ratio criterion will accept and reject the same projects as the net present value criterion. (ii) When the capital budget is limited in the current period, the benefit-cost ratio criterion may rank projects correctly in the order of decreasingly efficient use of capital. However, its use is not
recommended because it provides no means for aggregating several smaller projects into a package that can be compared with a large project. (iii) When cash outflows occur beyond the current period, the benefit-cost ratio criterion is unsuitable as a selection criterion. 10. What is IRR and how is it calculated? The internal rate of return (IRR) of a project is the discount rate which makes its NPV equal to zero. It is the value of r in the following equation:
∑ where is the cash flow at the end of the year t, r is the internal rate of return (IRR), and n is the life of the project. In the NPV calculation we assume that the discount rate (cost of capital) is known and determine the NPV. In the IRR calculation, we set the NPV equal to zero and determine the discount rate that satisfies this condition. 11. Discuss the problems associated with IRR. There are problems in using IRR when the cash flows of the project are not conventional or when two or more projects are being compared to determine which one is the best. In the first case it is difficult to define ‘what is IRR’ and in the second case IRR can be misleading. Further IRR cannot distinguish between lending and borrowing. Finally, IRR is difficult to apply when short-term interest rates differ from long term interest rates. 12. What are the redeeming qualities of IRR? Despite its deficiencies, IRR is immensely popular is practice, even more than NPV. It perhaps fill a need that NPV does not. Managers as well as financial analysts usually think in terms of rates of return rather than absolute taka values. Although IRR can be misleading, the result can be readily interpreted by all parties. No wonder surveys suggest that the IRR is the most popular investment evaluation technique. Further, in certain situations, the IRR offers a practical advantage over NPV. We can’t estimate the NPV unless we know the discount rate, but we can still calculate the IRR. 13. What does IRR mean? There are two possible economic interpretations of internal rate of return: (i) The internal rate of return represents the rate of return on the unrecovered investment balance in the project. (ii) The internal rate of return is the rate of return earned on the initial investment made in the project. 14. How is MIRR calculated? The procedure for calculating MIRR is as follows: Step 1: Calculate the present value of costs (PVC) associated with the project, using the cost of capital (r) as the discount rate:
∑ Step 2: Calculate the terminal value (TV) of the cash inflows expected from the project:
∑ Step 3: Obtain MIRR by solving the following equation:
15. Why is MIRR superior to the regular IRR? MIRR is superior to the regular IRR in two ways. First, MIRR assumes that project cash flows are reinvested at the cost of the capital whereas the regular IRR assumes that project cash flows are reinvested at the project’s own IRR. Since, re-investment at cost of capital is more realistic than reinvestment at IRR, MIRR reflects better the true profitability of a project. Second, the problem of multiple rates does not exist with MIRR. 16. What is Payback Period? The payback period is the length of time required to recover the initial cash outlay on the project. According to the payback criterion, the shorter the payback period, the more desirable the project. 17. Evaluate payback as an investment criterion. A widely used investment criterion, the payback period seems to offer the following advantages: # It is simple, both in concept and application. It does not use involved concepts and tedious calculations and has few hidden assumptions. # It is a rough and ready method for dealing with risk. It favours projects which generate substantial cash inflows in early years and discriminates against projects which bring substantial cash inflows in later years. Now, if risk tends to increase with futurity – in general, this may be true – the payback criterion may be helpful in weeding out risky projects. # Since it emphasizes earlier cash inflows, it may be a sensible criterion when the firm is pressed with problems of liquidity. The limitations of the payback criterion, however, are very serious:
# It fails to consider the time value of money. # It ignores cash flows beyond the payback period. # It is a measure of project’s capital recovery, not profitability. # Though it measures a project’s liquidity, it does not indicate the liquidity position of the firm as a whole, which is more important. 18. Why is payback is popular, despite its shortcomings? Despite its serious shortcomings the payback period is widely used in appraising investments. It appears that the payback measure serves, as a proxy for certain types of information which are useful in investment decision making. # The payback period may be regarded roughly as the reciprocal of the internal rate of return when the annual cash inflow is constant and the life of the project fairly long. # The payback period is somewhat akin to the break-even point. A rule of thumb. It serves as a useful shortcut in the process of information generation and evaluation. # The payback period conveys information about the rate at which the uncertainty associated with a project resolved. The shorter the payback period, the faster the uncertainty associated with the project is resolved. The longer the payback period, the slower the uncertainty associated with the project is resolved. 19. What is discounted payback? In the discounted payback period method, cash flows are first converted into their present values (by applying suitable discounting factors) and then added to ascertain the period of time required to recover the initial outlay of the project. 20. How is accounting rate of return calculated? The accounting rate of return, also called the average rate of return, is defined as:
21. What are the pros and cons of accounting rate of return? Pros # It is simple to calculate. # It is based on accounting information which is readily available and familiar to businessmen. # It considers benefits over the entire life of the project.
Cons # It is based upon accounting profit, not cash flow. # It does not take into account the time value of money. # It is internally inconsistent.
