Valor Presente Y Otras Reglas De Inveriosn

CHAPTER 5: NET PRESENT VALUE AND OTHER INVESTMENT RULES

Concepts Review/ Questions

2. Conventional cash flows: if a project has a positive NPV for a certain discount rate, then it will also have a positive NPV for a zero discount rate; thus, the payback period must be less than the project life. If NPV is positive, then the present value of future cash inflows is greater than the initial investment cost; thus, PI must be greater than 1. The IRR must be greater than the required return.

3. a. Payback period is simply the accounting break-even point of a series of cash flows.

b. The IRR is the discount rate that causes the NPV of a series of cash flows to be identically zero. IRR can thus be interpreted as a financial break-even rate of return; at the IRR discount rate, the net value of the project is zero. The acceptance and rejection criteria are:

c. The profitability index is the present value of cash inflows relative to the project cost. The profitability index can be expressed as: PI = (NPV + cost)/cost = 1 + (NPV/cost). If a firm has a basket of positive NPV projects and is subject to capital rationing, PI may provide a good ranking measure of the projects, indicating the ―bang for the buck‖ of each particular project.

d. NPV is simply the present value of a project’s cash flows, including the initial outlay.

5. Two of the most important reasons have to do with transportation costs and exchange rates. Manufacturing in the U.S. means that a much higher proportion of the costs are paid in dollars. Since sales are in dollars, the net effect is to immunize profits to a large extent against fluctuations in exchange rates. This issue is discussed in greater detail in the chapter on international finance.

8. False . If the cash flows of Project B occur early and the cash flows of Project A occur late, then for a low discount rate the NPV of A can exceed the NPV of B. Observe the following example.

C0 C1 C2 IRR NPV @ 0%

Project A –$1,000,000 $0 $1,440,000 20% $440,000

Project B –$2,000,000 $2,400,000 $0 20% 400,000

However, in one particular case, the statement is true for equally risky projects. If the lives of the two projects are equal and the cash flows of Project B are twice the cash flows of Project A in every time period, the NPV of Project B will be twice the NPV of Project A.

11. Project B’s NPV would be more sensitive to changes in the discount rate. The reason is the time value of money. Cash flows that occur further out in the future are always more sensitive to changes in the interest rate. This sensitivity is similar to the interest rate risk of a bond.

12. The MIRR is calculated by finding the present value of all cash outflows, the future value of all cash inflows to the end of the project, and then calculating the IRR of the two cash flows. As a result, the cash flows have been discounted or compounded by one interest rate (the required return), and then the interest rate between the two remaining cash flows is calculated. As such, the MIRR is not a true interest rate. In contrast, consider the IRR. If you take the initial investment, and calculate the future value at the IRR, you can replicate the future cash flows of the project exactly.

Solutions:

1. Cumulative cash flows Year 1 = $6,500 = $6,500

Cumulative cash flows Year 2 = $6,500 + 4,000 = $10,500

Payback period = 1 + ($10,000 – $6,500) / $4,000 = 1.875 years

Project B:

Payback period = 2.20 years

Project A: NPV = –$10,000 + $6,500 / 1.15 + $4,000 / 1.152 + $1,800 / 1.153 = –$139.72

Project B: NPV = –$12,000 + $7,000 / 1.15 + $4,000 / 1.152 + $5,000 / 1.153 = $399.11

2. Payback = 4 + ($220 / $970) = 4.23 years

For an initial cost of $6,200, the payback period is: $6,200 / $970 = 6.39 years

The payback period for an initial cost of $8,000 is a little trickier. Notice that the total cash inflows after eight years will be:

Total cash inflows = 8($70) = $7,760

Initial cost is $8,000, the project never pays back.

If you use the shortcut for annuity cash flows, you get: Payback = $8,000 / $970 = 8.25 years This answer does not make sense—cash flows stop after eight years: there is no payback period.

3. Value today of Year 1 cash flow = $6,000/1.14 = $5,263.16

Value today of Year 2 cash flow = $6,500/1.142 = $5,001.54

Value today of Year 3 cash flow = $7,000/1.143 = $4,724.80

Value today of Year 4 cash flow = $8,000/1.144 = $4,736.64

Discounted payback = 1 + ($8,000 – 5,263.16)/$5,001.54 = 1.55 years

For an initial cost of $13,000:

Discounted payback = 2 + ($13,000 – 5,263.16 – 5,001.54)/$4,724.80 = 2.58 years

If the initial cost is $18,000: 3 + ($18,000 – 5,263.16 – 5,001.54 – 4,724.80) / $4,736.64 = 3.64 years

4. R = 15%: $2,600/1.15 + $2,600/1.152 + $2,600/1.153 + $2,600/1.154 + $2,600/1.155 + $2,600/1.156

= $9,839.66; The project never pays back.

5. 0 = C0 + C1 / (1 + IRR) + C2 / (1 + IRR)2 + C3 / (1 + IRR)3

0 = –$11,000 + $5,500/(1 + IRR) + $4,000/(1 + IRR)2 + $3,000/(1 + IRR)3 Reject.

6. IRR = 33.37% IRR = 29.32%

7. PI = C(PVIFAR,t) / C0 = $65,000(PVIFA15%,7) / $190,000 = 1.423

8. PIAlpha = [$800 / 1.10 + $900 / 1.102 + $700 / 1.103] / $1,500 = 1.331 PIBeta = [$500 / 1.10 + $1,900 / 1.102 + $2,100 / 1.103] / $2,500 = 1.441

11. a. Deepwater Fishing IRR:

0 = –$750,000 + $310,000 / (1 + IRR) + $430,000 / (1 + IRR)2 + $330,000 / (1 + IRR)3 IRR = 19.83%

Submarine Ride IRR:

0 = –$2,100,000 + $1,200,000 / (1 + IRR) + $760,000 / (1 + IRR)2 + $850,000 / (1 + IRR)3

IRR = 17.36%

b. To calculate the incremental IRR,

Year 0 Year 1 Year 2 Year 3

Submarine Ride –$2,100,000 $1,200,000 $760,000 $850,000

Deepwater Fishing –750,000 310,000 430,000 330,000

Submarine – Fishing –$1,350,000 $890,000 $330,000 $520,000

0 = –$1,350,000 + $890,000 / (1 + IRR) + $330,000 / (1 + IRR)2 + $520,000 / (1 + IRR)3 Incremental IRR = 15.78%

c. Deepwater fishing:

NPV = –$750,000 + $310,000 / 1.14 + $430,000 / 1.142 + $330,000 / 1.143 = $75,541.46

Submarine ride:

NPV = –$2,100,000 + $1,200,000

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