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Chapter 26: Q19RQ (page 1464)

How is the present value of a lump sum determined?

Short Answer

Expert verified

Answer

PV=FV11+r°

Step by step solution

01

Meaning of Present Value

Present value compares the acquiring control of a future dollar to that of a current dollar. It is a money-related calculation that gauges the worth of a future amount of cash or stream of installments in today's dollars adjusted for interest and inflation.

02

Determination of the present value of a lump sum.

The following formula is used to calculate the present value (PV) of a lump sum: PV factor for future value for interest rate and time.

In which the future value FV is divided by a factor of 1 + I for each interval between present and future dates.

To calculate the PV, enter these figures into the present value calculator:

FV stands for the sum of future values.

“n” in the formula is the number of time periods (years).

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Most popular questions from this chapter

Hamilton Company is considering two capital investments. Both investments have an initial cost of \(7,000,000 and total net cash inflows of \)16,000,000 over 10 years. Hamilton requires a 20% rate of return on this type of investment. Expected net cash inflows are as follows:

Year

Plan Alpha

Plan Beta

1

\(1,600,000

\)1,600,000

2

\(1,600,000

2,200,000

3

\)1,600,000

2,800,000

4

\(1,600,000

2,200,000

5

\)1,600,000

1,600,000

6

\(1,600,000

1,500,000

7

\)1,600,000

1,300,000

8

\(1,600,000

1,100,000

9

\)1,600,000

900,000

10

\(1,600,000

800,000

Total

\)16,000,000

\(16,000,000

Requirements

1. Use Excel to compute the NPV and IRR of the two plans. Which plan, if any, should the company pursue?

2. Explain the relationship between NPV and IRR. Based on this relationship and the company’s required rate of return, are your answers as expected in Requirement 1? Why or why not?

3. After further negotiating, the company can now invest with an initial cost of \)6,500,000. Recalculate the NPV and IRR. Which plan, if any, should the company pursue?

How can spreadsheet software, such as Excel, help with sensitivity analysis?

What is capital rationing?

Using payback, ARR, and NPV with unequal cash flows

Hughes Manufacturing, Inc. has a manufacturing machine that needs attention. The company is considering two options. Option 1 is to refurbish the current machine at a cost of \(2,600,000. If refurbished, Hughes expects the machine to last another eight years and then have no residual value. Option 2 is to replace the machine at a cost of \)3,800,000. A new machine would last 10 years and have no residual value. Hughes expects the following net cash inflows from the two options:

Year

Refurbish current machine

Purchase new machine

1

\(1,760,000

\)2,970,000

2

440,000

490,000

3

360,000

410,000

4

280,000

330,000

5

200,000

250,000

6

200,000

250,000

7

200,000

250,000

8

200,000

250,000

9

250,000

10

250,000

Total

\(3,640,000

\)5,700,000

Hughes uses straight-line depreciation and requires an annual return of 10%.

Requirements

1. Compute the payback, the ARR, the NPV, and the profitability index of these two options.

2. Which option should Hughes choose? Why?

Question: Using payback to make capital investment decisions Consider the following three projects. All three have an initial investment of \(800,000.

Net Cash Inflows

Project LProject MProject N

Year

Annual

Accumulated

Annual

Accumulated

Annual

Accumulated

1

\) 100,000

\( 100,000

\)

200,000

\( 200,000

\)

400,000

$ 400,000

2

100,000

200,000

250,000

450,000

400,000

800,000

3

100,000

300,000

350,000

800,000

4

100,000

400,000

400,000

1,200,000

5

100,000

500,000

500,000

1,700,000

6

100,000

600,000

7

100,000

700,000

8

100,000

800,000

Requirements

  1. Determine the payback period of each project. Rank the projects from most desirable to least desirable based on payback.
  2. Are there other factors that should be considered in addition to the payback period?
See all solutions

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