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.

---

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

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

---

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

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.

---

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.

---

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

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.

---

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

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.

---

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

What is the present value of a 10-year, $100 annual annuity due if interest rates are 0%?

A) $900.

B) $1,000.

C) No solution.

---

When I/Y = 0 you just sum up the numbers since there is no interest earned.

mouse123

An investor will receive an annuity of $5,000 a year for seven years. The first payment is to be received 5 years from today. If the annual interest rate is 11.5%, what is the present value of the annuity?

A) $15,000.

B) $13,453.

C) $23,185.

---

With PMT = 5,000; N = 7; I/Y = 11.5; value (at t = 4) = 23,185.175. Therefore, PV (at t = 0) = 23,185.175 / (1.115)4 = $15,000.68.

mouse123

If $2,500 were put into an account at the end of each of the next 10 years earning 15% annual interest, how much would be in the account at the end of ten years?

A) $41,965.

B) $27,461.

C) $50,759.

---

N = 10; I = 15; PMT = 2,500; CPT → FV = $50,759.

karoliukas

Given: an 11% annual rate compounded quarterly for 2 years; compute the future value of $8,000 today.

A) $8,962.

B) $9,939.

C) $9,857.

---

Divide the interest rate by the number of compound periods and multiply the number of years by the number of compound periods. I = 11 / 4 = 2.75; N = (2)(4) = 8; PV = 8,000.