Reading 5: The Time Value of Money-LOS e习题精选 single, 2011, interpret, ordinary, annuity

1215

Session 2: Quantitative Methods: Basic Concepts
Reading 5: The Time Value of Money

LOS e: Calculate and interpret the future value (FV) and present value (PV) of a single sum of money, an ordinary annuity, an annuity due, a perpetuity (PV only), and a series of unequal cash flows.

 

 

An investor deposits $10,000 in a bank account paying 5% interest compounded annually. Rounded to the nearest dollar, in 5 years the investor will have:

A) $12,763.

B) $12,500.

C) $10,210.

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PV = 10,000; I/Y = 5; N = 5; CPT → FV = 12,763.

or: 10,000(1.05)⁵ = 12,763.

cheifmic

 thx

1215

What is the total present value of $200 to be received one year from now, $300 to be received 3 years from now, and $600 to be received 5 years from now assuming an interest rate of 5%?

A) $919.74.

B) $980.89.

C) $905.87.

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200 / (1.05) + 300 / (1.05)³ + 600 / (1.05)⁵ = 919.74.

1215

The following stream of cash flows will occur at the end of the next five years.

Yr 1	-2,000
Yr 2	-3,000
Yr 3	6,000
Yr 4	25,000
Yr 5	30,000

At a discount rate of 12%, the present value of this cash flow stream is closest to:

A) $36,965.

B) $33,004.

C) $58,165.

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N = 1; I/Y = 12; PMT = 0; FV = -2,000; CPT → PV = -1,785.71.
N = 2; I/Y = 12; PMT = 0; FV = -3,000; CPT → PV = -2,391.58.
N = 3; I/Y = 12; PMT = 0; FV = 6,000; CPT → PV = 4,270.68.
N = 4; I/Y = 12; PMT = 0; FV = 25,000; CPT → PV = 15,887.95.
N = 5; I/Y = 12; PMT = 0; FV = 30,000; CPT → PV = 17,022.81.
Sum the cash flows: $33,004.15.

Note: If you want to use your calculator's NPV function to solve this problem, you need to enter zero as the initial cash flow (CF₀). If you enter -2,000 as CF₀, all your cash flows will be one period too soon and you will get one of the wrong answers.

1215

Assuming a discount rate of 10%, which stream of annual payments has the highest present value?

A)    $20       –$5        $20        $110

B) –$100    –$100    –$100    $500

C)    $110      $20       $10         $5

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This is an intuition question. The two cash flow streams that contain the $110 payment have the same total cash flow but the correct answer is the one where the $110 occurs earlier. The cash flow stream that has the $500 that occurs four years hence is overwhelmed by the large negative flows that precede it.

1215

Suppose you are going to deposit $1,000 at the start of this year, $1,500 at the start of next year, and $2,000 at the start of the following year in an savings account. How much money will you have at the end of three years if the rate of interest is 10% each year?

A) $4,000.00.

B) $5,750.00.

C) $5,346.00.

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Future value of  $1,000 for 3 periods at 10% = 1,331
Future value of $1,500 for 2 periods at 10% = 1,815
Future value of $2,000 for 1 period at 10% = 2,200
        Total = $5,346

N = 3; PV = -$1,000; I/Y = 10%; CPT → FV = $1,331
N = 2; PV = -$1,500; I/Y = 10%; CPT → FV = $1,815
N = 1; PV = -$2,000; I/Y = 10%; CPT → FV = $2,200

1215

Given investors require an annual return of 12.5%, a perpetual bond (i.e., a bond with no maturity/due date) that pays $87.50 a year in interest should be valued at:

A) $70.

B) $1,093.

C) $700.

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87.50 ÷ 0.125 = $700.

1215

An annuity will pay eight annual payments of $100, with the first payment to be received one year from now. If the interest rate is 12% per year, what is the present value of this annuity?

A) $1,229.97.

B) $556.38.

C) $496.76.

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N = 8; I/Y = 12%; PMT = -$100; FV = 0; CPT → PV = $496.76.

1215

Renee Fisher invests $2,000 each year, starting one year from now, in a retirement account. If the investments earn 8% or 10% annually over 30 years, the amount Fisher will accumulate is closest to:

8%

10%

A) $225,000 $330,000

B) $225,000 $360,000

C) $245,000 $360,000

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N = 30; I/Y = 8; PMT = -2,000; PV = 0; CPT FV = 226,566.42

N = 30; I/Y = 10; PMT = -2,000; PV = 0; CPT FV = 328,988.05

1215

An investment offers $100 per year forever. If Peter Wallace’s required rate of return on this investment is 10%, how much is this investment worth to him?

A) $10,000.

B) $500.

C) $1,000.

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For a perpetuity, PV = PMT ÷ I = 100 ÷ 0.10 = 1,000.