mouse123

A firm is evaluating an investment that promises to generate the following annual cash flows:

End of Year	Cash Flows
1	$5,000
2	$5,000
3	$5,000
4	$5,000
5	$5,000
6	-0-
7	-0-
8	$2,000
9	$2,000

Given BBC uses an 8% discount rate, this investment should be valued at:

A) $19,963.

B) $22,043.

C) $23,529.

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PV(1 - 5): N = 5; I/Y = 8; PMT = -5,000; FV = 0; CPT → PV = 19,963
PV(6 - 7): 0
PV(8): N = 8; I/Y = 8; FV = -2,000; PMT = 0; CPT → PV = 1,080
PV(9): N = 9; I/Y = 8; FV = -2,000; PMT = 0; CPT → PV = 1,000
Total PV = 19,963 + 0 + 1,080 + 1,000 = 22,043.

mouse123

Compute the present value of a perpetuity with $100 payments beginning four years from now. Assume the appropriate annual interest rate is 10%.

A) $683.

B) $751.

C) $1000.

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Compute the present value of the perpetuity at (t = 3). Recall, the present value of a perpetuity or annuity is valued one period before the first payment. So, the present value at t = 3 is 100 / 0.10 = 1,000. Now it is necessary to discount this lump sum to t = 0. Therefore, present value at t = 0 is 1,000 / (1.10)3 = 751.

mouse123

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

mouse123

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

mouse123

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

A)    $110      $20       $10         $5

B)    $20       –$5        $20        $110

C) –$100    –$100    –$100    $500

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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.

mouse123

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.

mouse123

If $2,000 a year is invested at the end of each of the next 45 years in a retirement account yielding 8.5%, how much will an investor have at retirement 45 years from today?

A) $100,135.

B) $90,106.

C) $901,060.

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N = 45; PMT = –2,000; PV = 0; I/Y = 8.5%; CPT → FV = $901,060.79.

mouse123

An investor wants to receive $1,000 at the beginning of each of the next ten years with the first payment starting today. If the investor can earn 10 percent interest, what must the investor put into the account today in order to receive this $1,000 cash flow stream?

A) $6,145.

B) $6,759.

C) $7,145.

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This is an annuity due problem. There are several ways to solve this problem.
Method 1:

PV of first $1,000 = $1,000
PV of next 9 payments at 10% = 5,759.02
Sum of payments = $6,759.02

Method 2:

Put calculator in BGN mode.
N = 10; I = 10; PMT = -1,000; CPT → PV = 6,759.02
Note: make PMT negative to get a positive PV. Don’t forget to take your calculator out of BGN mode.

Method 3:

You can also find the present value of the ordinary annuity $6,144.57 and multiply by 1 + k to add one year of interest to each cash flow. $6,144.57 × 1.1 = $6,759.02.

mouse123

An investor purchases a 10-year, $1,000 par value bond that pays annual coupons of $100. If the market rate of interest is 12%, what is the current market value of the bond?

A) $1,124.

B) $887.

C) $950.

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Note that bond problems are just mixed annuity problems. You can solve bond problems directly with your financial calculator using all five of the main TVM keys at once. For bond-types of problems the bond’s price (PV) will be negative, while the coupon payment (PMT) and par value (FV) will be positive. N = 10; I/Y = 12; FV = 1,000; PMT = 100; CPT → PV = –886.99.

mouse123

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) $700.

C) $1,093.

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87.50 ÷ 0.125 = $700.