8. Capital Budgeting Techniques—Payback—Example Q: Use the payback period technique to choose between mutually exclusive projects A and B. Example 800 200 C 5 800 200 C 4 350 400 C 3 400 400 C 2 400 400 C 1 ($1,200) ($1,200) C 0 Project B Project A A: Project A’s payback is 3 years as its initial outlay is fully recovered in that time. Project B doesn’t fully recover until sometime in the 4 th year. Thus, according to the payback method, Project A is better than B.
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13. Capital Budgeting Techniques—Net Present Value (NPV) Example Q: Project Alpha has the following cash flows. If the firm considering Alpha has a cost of capital of 12%, should the project be undertaken? Example $3,000 C 3 $2,000 C 2 $1,000 C 1 ($5,000) C 0 A: The NPV is found by summing the present value of the cash flows when discounted at the firm’s cost of capital. Since Alpha’s NPV<0, it should not be undertaken.
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18. Techniques—Internal Rate of Return (IRR)—Example Q: Find the IRR for the following series of cash flows: If the firm’s cost of capital is 8%, is the project a good idea? What if the cost of capital is 10%? Example $1,000 C 1 ($5,000) C 0 $2,000 C 2 $3,000 C 3 A: We’ll start by guessing an IRR of 12%. We’ll calculate the project’s NPV at this interest rate. Since NPV<0, the project’s IRR must be < 12%.
19. Techniques—Internal Rate of Return (IRR)—Example We’ll try a different, lower interest rate, say 10%. At 10%, the project’s NPV is ($184). Since the NPV is still less than zero, we need to try a still lower interest rate, say 9%. The following table lists the project’s NPV at different interest rates. Example Since NPV becomes positive somewhere between 8% and 9%, the project’s IRR must be between 8% and 9%. If the firm’s cost of capital is 8%, the project is marginal. If the firm’s cost of capital is 10%, the project is not a good idea. $130 7 $22 8 ($83) 9 ($184) 10 ($377) 12% Calculated NPV Interest Rate Guess The exact IRR can be calculated using a financial calculator. The financial calculator uses the iterative process just demonstrated; however it is capable of guessing and recalculating much more quickly.
24. Figure 9.2: Projects for Which IRR and NPV Can Give Different Solutions At a cost of capital of k 1 , Project A is better than Project B, while at k 2 the opposite is true.
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28. Projects with a Single Outflow and Regular Inflows—Example Q: Find the NPV and IRR for the following series of cash flows: Example A: Substituting the cash flows into the NPV equation with annuity inflows we have: NPV = -$5,000 + $2,000[PVFA 12, 3 ] NPV = -$5,000 + $2,000[2.4018] = -$196.40 Substituting the cash flows into the IRR equation with annuity inflows we have: 0 = -$5,000 + $2,000[PVFA IRR, 3 ] Solving for the factor gives us: $5,000 $2,000 = [PVFA IRR, 3 ] The interest factor is 2.5 which equates to an interest rate between 9% and 10%. $2,000 C 1 ($5,000) C 0 $2,000 C 2 $2,000 C 3
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34. Comparing Projects with Unequal Lives—Example Q: Which of the two following mutually exclusive projects should a firm purchase? Example Short-Lived Project (NPV = $432.82 at an 8% discount rate; IRR = 23.4%) $750 $750 $750 $750 $750 $750 ($2,600) - C 5 - C 4 $750 C 3 Long-Lived Project (NPV = $867.16 at an 8% discount rate; IRR = 18.3%) $750 C 1 ($1,500) C 0 $750 C 2 - C 6 A: The IRR method argues for undertaking the Short-Lived Project while the NPV method argues for the Long-Lived Project. We’ll correct for the unequal life problem by using both the Replacement Chain Method and the EAA Method. Both methods will lead to the same decision.
35. Comparing Projects with Unequal Lives—Example The Replacement Chain Method involves replicating all projects (if needed) until each project being evaluated has a common time horizon. If the Short-Lived Project is replicated for a total of two times, it will have the same life (6 years) as the Long-Lived Project. This involves buying the Short-Lived Project again in year 3 and receiving the same stream of cash flows as originally expected for the following three years. This stream of cash flows is represented in the table below. Example ($750) Short-Lived Project replicated for a total of two times $750 $750 $750 ($1,500) - C 5 - C 4 $750 C 3 $750 C 1 ($1,500) C 0 $750 C 2 - C 6 Thus, buying the Long-Lived Project is a better decision than buying the Short-Lived Project twice. The NPV of this stream of cash flows is $776.41.
36. Comparing Projects with Unequal Lives—Example The EAA Method equates each project’s original NPV to an equivalent annual annuity. For the Short-Lived Project the EAA is $167.95 (the equivalent of receiving $432.82 spread out over 3 years at 8%); while the Long-Lived Project has an EAA of $187.58 (the equivalent of receiving $867.16 spread out over 6 years at 8%). Since the Long-Lived Project has the higher EAA, it should be chosen. This is the same decision reached by the Replacement Chain Method. Example
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