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Chapter 4: 4-9-31BP (page 284)

Question: Beverly Hills started a paper route on January 1. Every three months, she deposits $550 in her bank account, which earns 8 percent annually but is compounded quarterly. Four years later, she used the entire balance in her bank account to invest in an investment at 7 percent annually. How much will she have after three more years?

Short Answer

Expert verified

Answer

The future value of the investment after the three years is $12,809.83.

Step by step solution

01

Identification of the required information

Payment (PMT) = $550

Periods for quarterly compounding (n1) = 16 (4 years*4 quarters)

Interest Rate for quarterly compounding (i1) = 2% (8%/4)

Re-investment period (n2) = 3

Re-investment rate (i2) = 7%

02

Future value of investment after the three years (FV)

FV=PMT脳[1+i1n1+1i1]脳(1+i2)n2$550=脳[(1+2%)16+12%]脳(1+7%)3$12,809.83

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Most popular questions from this chapter

Keller Construction is considering two new investments. Project E calls for the purchase of earthmoving equipment. Project H represents an investment in a hydraulic lift. Keller wishes to use a net present value profile in comparing the projects. The investment and cash flow patterns are as follows:

Project E (\(20,000 Investment)

Year

Cash flows

1

\)5,000

2

6,000

3

7,000

4

10,000

Project H (\(20,000 Investment)

Year

Cash flows

1

\)16,000

2

5,000

3

4,000

  1. Determine the net present value of the projects based on a zero percent discount rate.

  2. Determine the net present value of the projects based on a 9 percent discount rate.

  3. The internal rate of return on Project E is 13.25 percent, and the internal rate of return on Project H is 16.30 percent. Graph a net present value profile for the two investments similar to Figure12-3. (Use a scale up to \(8,000 on the vertical axis, with \)2,000 increments. Use a scale up to 20 percent on the horizontal axis, with 5 percent increments.)

  4. If the two projects are not mutually exclusive, what would your acceptance or rejection decision be if the cost of capital (discount rate) is 8 percent? (Use the net present value profile for your decision; no actual numbers are necessary.)

  5. If the two projects are mutually exclusive (the selection of one precludes the selection of the other), what would be your decision if the cost of capital is (1) 6 percent, (2) 13 percent, (3) 18 percent? Once again, use the net present value profile for your answer.

Sampson Corp. is evaluating the introduction of a new product. The possible levels of unit sales and the probabilities of their occurrence are shown next:

Possible Market Reaction Sales in Units Probabilities

Low response ....................................... 30 0.10

Moderate response .............................. 50 0.20

High response ...................................... 75 0.40

Very high response ............................... 90 0.30

a. What is the expected value of unit sales for the new product?

b. What is the standard deviation of unit sales?

Rita Gonzales won the \(41 million lottery. She is to receive \)1.5 million a year for the next 19 years plus an additional lump sum payment of $12.5 million after 19 years. The discount rate is 14 percent. What is the current value of her winnings?

Tim Trepid is highly risk-averse while Mike Macho actually enjoys taking a risk.

a. Which one of the four investments should Tim choose? Compute coefficients of variation to help you in your choice.

Investments

Returns:

Expected Value

Standard Deviation

Buy stocks ..................................... \( 9,140 \) 6,140

Buy bonds ..................................... 7,680 2,560

Buy commodity futures ................. 19,100 26,700

Buy options ................................... 17,700 18,200

b. Which one of the four investments should Mike choose?

Question:Stagnant Iron and Steel currently pays a $12.25 annual cash dividend (D0). The company plans to maintain the dividend at this level for the foreseeable future as no future growth is anticipated. If the required rate of return by common stockholders (Ke) is 18 percent, what is the price of the common stock?
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