Chapter 9. Capital Budgeting. Introduction. Capital budgeting involves planning and justifying large expenditures on longterm projects Projects can be classified as: Replacement New business ventures. Characteristics of Business Projects. Project Types and Risk
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Payback period occurs at 3.33 years.
Q: Use the payback period technique to choose between mutually exclusive projects A and B.
Project A
Project B
C0
($1,200)
($1,200)
C1
400
400
C2
400
400
Example
C3
400
350
C4
200
800
C5
200
800
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 4th year. Thus, according to the payback method, Project A is better than B.
Capital Budgeting Techniques—Payback—ExampleQ: Project Alpha has the following cash flows. If the firm considering Alpha has a cost of capital of 12%, should the project be undertaken?
C0
($5,000)
C1
$1,000
C2
$2,000
C3
$3,000
Example
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.
Capital Budgeting Techniques—Net Present Value (NPV) ExampleThe “price” of receiving
the inflows
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%?
C0
C1
C2
C3
($5,000)
$1,000
$2,000
$3,000
A: We’ll start by guessing an IRR of 12%. We’ll calculate the project’s NPV at this interest rate.
Example
Since NPV<0, the project’s IRR must be < 12%.
Techniques—Internal Rate of Return (IRR)—ExampleWe’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.
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.
Interest Rate Guess
Calculated NPV
12%
($377)
10
($184)
Example
9
($83)
8
$22
7
$130
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.
Techniques—Internal Rate of Return (IRR)—ExampleAt a cost of capital of k1, Project A is better than Project B, while at k2 the opposite is true.
Figure 9.2: Projects for Which IRR and NPV Can Give Different SolutionsQ: Find the NPV and IRR for the following series of cash flows:
C0
C1
C2
C3
($5,000)
$2,000
$2,000
$2,000
A: Substituting the cash flows into the NPV equation with annuity inflows we have:
NPV = $5,000 + $2,000[PVFA12, 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[PVFAIRR, 3]
Solving for the factor gives us:
$5,000 $2,000 = [PVFAIRR, 3]
The interest factor is 2.5 which equates to an interest rate between 9% and 10%.
Example
Projects with a Single Outflow and Regular Inflows—ExampleQ: Which of the two following mutually exclusive projects should a firm purchase?
C0
C1
C2
C3
C4
C5
C6
ShortLived Project (NPV = $432.82 at an 8% discount rate; IRR = 23.4%)
($1,500)
$750
$750
$750



LongLived Project (NPV = $867.16 at an 8% discount rate; IRR = 18.3%)
Example
($2,600)
$750
$750
$750
$750
$750
$750
A: The IRR method argues for undertaking the ShortLived Project while the NPV method argues for the LongLived 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.
Comparing Projects with Unequal Lives—ExampleThe Replacement Chain Method involves replicating all projects (if needed) until each project being evaluated has a common time horizon. If the ShortLived Project is replicated for a total of two times, it will have the same life (6 years) as the LongLived Project. This involves buying the ShortLived 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.
C0
C1
C2
C3
C4
C5
C6
ShortLived Project replicated for a total of two times
Example
($1,500)
$750
$750
$750



($1,500)
$750
$750
$750
($750)
Thus, buying the LongLived Project is a better decision than buying the ShortLived Project twice.
The NPV of this stream of cash flows is $776.41.
Comparing Projects with Unequal Lives—ExampleThe EAA Method equates each project’s original NPV to an equivalent annual annuity. For the ShortLived Project the EAA is $167.95 (the equivalent of receiving $432.82 spread out over 3 years at 8%); while the LongLived Project has an EAA of $187.58 (the equivalent of receiving $867.16 spread out over 6 years at 8%). Since the LongLived Project has the higher EAA, it should be chosen. This is the same decision reached by the Replacement Chain Method.
Example
Comparing Projects with Unequal Lives—Example