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Reading 5: The Time Value of Money- LOS d, (Part 4)~ Q4-5

Q4. Given the following cash flow stream:

End of Year             Annual Cash Flow

1                                 $4,000

2                                 $2,000

3                                 -0-

4                                 -$1,000

Using a 10% discount rate, the present value of this cash flow stream is:

A)   $3,415.

B)   $3,636.

C)   $4,606.

Q5. Find the future value of the following uneven cash flow stream. Assume end of the year payments. The discount rate is 12%.

Year 1     -2,000

Year 2     -3,000

Year 3     6,000

Year 4     25,000

Year 5     30,000

A)   $58,164.58.

B)   $65,144.33.

C)   $33,004.15.

答案和详解如下:

Q4. Given the following cash flow stream:

End of Year             Annual Cash Flow

1                                 $4,000

2                                 $2,000

3                                 -0-

4                                 -$1,000

Using a 10% discount rate, the present value of this cash flow stream is:

A)   $3,415.

B)   $3,636.

C)   $4,606.

Correct answer is C)         

PV(1): N = 1; I/Y = 10; FV = -4,000; PMT = 0; CPT → PV = 3,636
PV(2): N = 2; I/Y = 10; FV = -2,000; PMT = 0; CPT → PV = 1,653
PV(3): 0
PV(4): N = 4; I/Y = 10; FV = 1,000; PMT = 0; CPT → PV = -683
Total PV = 3,636 + 1,653 + 0 − 683 = 4,606

Q5. Find the future value of the following uneven cash flow stream. Assume end of the year payments. The discount rate is 12%.

Year 1     -2,000

Year 2     -3,000

Year 3     6,000

Year 4     25,000

Year 5     30,000

A)   $58,164.58.

B)   $65,144.33.

C)   $33,004.15.

Correct answer is A)

N = 4; I/Y = 12; PMT = 0; PV = -2,000; CPT → FV = -3,147.04
N = 3; I/Y = 12; PMT = 0; PV = -3,000; CPT → FV = -4,214.78
N = 2; I/Y = 12; PMT = 0; PV = 6,000; CPT → FV = 7,526.40
N = 1; I/Y = 12; PMT = 0; PV = 25,000; CPT → FV = 28,000.00
N = 0; I/Y = 12; PMT = 0; PV = 30,000; CPT → FV = 30,000.00

Sum the cash flows: $58,164.58.

Alternative calculation solution: -2,000 × 1.124 − 3,000 × 1.123 + 6,000 × 1.122 + 25,000 × 1.12 + 30,000 = $58,164.58.

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