25) You are currently 25 and would like to retire at age 45. You plan to save by making equal investments of
$10,000 at the end of each year for the next 20 years. If you are able to earn 8% per year on your investments, how
much will you have at the end of the 20 years? Please refer to the table below:
Future Value of an Annuity of $1
Periods 8%
12 18.98
13 21.5
14 24.21
15 27.15
16 30.32
17 33.75
18 37.45
19 41.45
20 45.76
A) $216,000
B) $200,000
C) $457,600
D) $576,900
26) Amanda is ready to retire and as a retirement benefit, she can choose to take $380,000 now or $50,000 at the end
of each year for a period of 10 years. To compare the two options, she must calculate the present value of both
alternatives. She believes a discount rate of 5% would be the most appropriate rate to apply. How much is the
present value if she takes the cash as a lump sum right now? Please refer to the following data, if needed:
Present Value of an Annuity of $1
5% 6% 7% 8% 9% 10%
1 0.952 0.943 0.935 0.926 0.917 0.909
2 1.859 1.833 1.808 1.783 1.759 1.736
3 2.723 2.673 2.624 2.577 2.531 2.487
4 3.546 3.465 3.387 3.312 3.240 3.170
5 4.329 4.212 4.100 3.993 3.890 3.791
6 5.076 4.917 4.767 4.623 4.486 4.355
7 5.786 5.582 5.389 5.206 5.033 4.868
8 6.463 6.210 5.971 5.747 5.535 5.335
9 7.108 6.802 6.515 6.247 5.995 5.759
10 7.722 7.360 7.024 6.710 6.418 6.145
A) $380,000
B) $386,100
C) $321,000
D) $399,000
27) Amanda is ready to retire and as a retirement benefit, she can choose to take $380,000 now or $50,000 at the end
of each year for a period of 10 years. To compare the two options, she must calculate the present value of both
alternatives. She believes a discount rate of 5% would be the most appropriate rate to apply. How much is the
present value if she takes the option of $50,000 a year for 10 years? Please refer to the following data, if needed:
Present Value of an Annuity of $1
5% 6% 7% 8% 9% 10%
1 0.952 0.943 0.935 0.926 0.917 0.909
2 1.859 1.833 1.808 1.783 1.759 1.736
3 2.723 2.673 2.624 2.577 2.531 2.487
4 3.546 3.465 3.387 3.312 3.240 3.170
5 4.329 4.212 4.100 3.993 3.890 3.791
6 5.076 4.917 4.767 4.623 4.486 4.355
7 5.786 5.582 5.389 5.206 5.033 4.868
8 6.463 6.210 5.971 5.747 5.535 5.335
9 7.108 6.802 6.515 6.247 5.995 5.759
10 7.722 7.360 7.024 6.710 6.418 6.145
A) $380,000
B) $386,100
C) $321,000
D) $399,000
28) Simms Manufacturing is considering two alternative investment proposals with the following data:
Proposal X Proposal Y
Investment $620,000 $400,000
Useful life 8 years 8 years
Estimated annual net cash inflows for
8 years $130,000 $80,000
Residual value $60,000 $0
Depreciation method Straight-line Straight-line
Discount rate 14% 10%
What is the total present value of future cash inflows from Proposal Y?
Present Value of an Annuity of $1
5% 6% 7% 8% 9% 10%
1 0.952 0.943 0.935 0.926 0.917 0.909
2 1.859 1.833 1.808 1.783 1.759 1.736
3 2.723 2.673 2.624 2.577 2.531 2.487
4 3.546 3.465 3.387 3.312 3.240 3.170
5 4.329 4.212 4.100 3.993 3.890 3.791
6 5.076 4.917 4.767 4.623 4.486 4.355
7 5.786 5.582 5.389 5.206 5.033 4.868
8 6.463 6.210 5.971 5.747 5.535 5.335
9 7.108 6.802 6.515 6.247 5.995 5.759
10 7.722 7.360 7.024 6.710 6.418 6.145
A) $266,750
B) $426,800
C) $436,800
D) $536,800
29) Simms Manufacturing is considering two alternative investment proposals with the following data:
Proposal X Proposal Y
Investment $620,000 $400,000
Useful life 8 years 8 years
Estimated annual net cash inflows for 8 years $130,000 $80,000
Residual value $0 $0
Depreciation method Straight-line Straight-line
Discount rate 9% 10%
What is the total present value of future cash inflows from Proposal X?
Present Value of an Annuity of $1
5% 6% 7% 8% 9% 10%
1 0.952 0.943 0.935 0.926 0.917 0.909
2 1.859 1.833 1.808 1.783 1.759 1.736
3 2.723 2.673 2.624 2.577 2.531 2.487
4 3.546 3.465 3.387 3.312 3.240 3.170
5 4.329 4.212 4.100 3.993 3.890 3.791
6 5.076 4.917 4.767 4.623 4.486 4.355
7 5.786 5.582 5.389 5.206 5.033 4.868
8 6.463 6.210 5.971 5.747 5.535 5.335
9 7.108 6.802 6.515 6.247 5.995 5.759
10 7.722 7.360 7.024 6.710 6.418 6.145
A) $878,340
B) $703,070
C) $614,230
D) $719,550
30) Simms Manufacturing is considering two alternative investment proposals with the following data:
Proposal X Proposal Y
Investment $620,000 $400,000
Useful life 8 years 8 years
Estimated annual net cash inflows for 8 years $130,000 $80,000
Residual value $60,000 $0
Depreciation method Straight-line Straight-line
Discount rate 14% 10%
What is the net present value of Proposal Y, taking into consideration the initial outlay and the subsequent
cash inflows?
Present Value of an Annuity of $1
5% 6% 7% 8% 9% 10%
1 0.952 0.943 0.935 0.926 0.917 0.909
2 1.859 1.833 1.808 1.783 1.759 1.736
3 2.723 2.673 2.624 2.577 2.531 2.487
4 3.546 3.465 3.387 3.312 3.240 3.170
5 4.329 4.212 4.100 3.993 3.890 3.791
6 5.076 4.917 4.767 4.623 4.486 4.355
7 5.786 5.582 5.389 5.206 5.033 4.868
8 6.463 6.210 5.971 5.747 5.535 5.335
9 7.108 6.802 6.515 6.247 5.995 5.759
10 7.722 7.360 7.024 6.710 6.418 6.145
A) $0
B) $26,800 positive
C) $136,800 positive
D) $133, 250 negative
31) Simms Manufacturing is considering two alternative investment proposals with the following data:
Proposal X Proposal Y
Investment $620,000 $400,000
Useful life 8 years 8 years
Estimated annual net cash inflows for 8 years $130,000 $80,000
Residual value $0 $0
Depreciation method Straight-line Straight-line
Discount rate 9% 10%
What is the net present value of Proposal X, taking into consideration the initial outlay and the subsequent
cash inflows?
Present Value of an Annuity of $1
5% 6% 7% 8% 9% 10%
1 0.952 0.943 0.935 0.926 0.917 0.909
2 1.859 1.833 1.808 1.783 1.759 1.736
3 2.723 2.673 2.624 2.577 2.531 2.487
4 3.546 3.465 3.387 3.312 3.240 3.170
5 4.329 4.212 4.100 3.993 3.890 3.791
6 5.076 4.917 4.767 4.623 4.486 4.355
7 5.786 5.582 5.389 5.206 5.033 4.868
8 6.463 6.210 5.971 5.747 5.535 5.335
9 7.108 6.802 6.515 6.247 5.995 5.759
10 7.722 7.360 7.024 6.710 6.418 6.145
A) $23,070 positive
B) $99,550 positive
C) $13,070 negative
D) $4,130 negative
32) If you invest $3,000 today at 7% interest, what is the value of the investment at the end of 5 years?
Future Value of $1
4% 5% 6% 7% 8% 9%
1 1.040 1.050 1.060 1.070 1.080 1.090
2 1.082 1.103 1.124 1.145 1.166 1.188
3 1.125 1.158 1.191 1.225 1.260 1.295
4 1.170 1.216 1.262 1.311 1.360 1.412
5 1.217 1.276 1.338 1.403 1.469 1.539
6 1.265 1.340 1.419 1.501 1.587 1.677
7 1.316 1.407 1.504 1.606 1.714 1.828
8 1.369 1.477 1.594 1.718 1.851 1.993
9 1.423 1.551 1.689 1.838 1.999 2.172
10 1.480 1.629 1.791 1.967 2.159 2.367
A) $3,210
B) $4,367
C) $4,190
D) $4,209
49
33) If you invest $1,000 at the end of each of the next 5 years and the investment earns 4% interest, what is the value
of the investment at the end of 5 years?
Future Value of an Annuity of $1
4% 5% 6% 7% 8% 9%
1 1.000 1.000 1.000 1.000 1.000 1.000
2 2.040 2.050 2.060 2.070 2.080 2.090
3 3.122 3.153 3.184 3.215 3.246 3.278
4 4.246 4.310 4.375 4.440 4.506 4.573
5 5.416 5.526 5.637 5.751 5.867 5.985
6 6.633 6.802 6.975 7.153 7.336 7.523
7 7.898 8.142 8.394 8.654 8.923 9.200
8 9.214 9.549 9.897 10.26 10.64 11.03
9 10.58 11.03 11.49 11.98 12.49 13.02
10 12.01 12.58 13.18 13.82 14.49 15.19
A) $5,416
B) $4,310
C) $5,000
D) $5,200
34) Jim wants to invest $5,000 a year for the next 25 years to prepare for his retirement. If he wants to calculate the
value of his investment at the end of the 25 year period, which of the following tables would be the best for him to
use?
A) Present Value of $1
B) Present Value of an Annuity of $1
C) Future Value of $1
D) Future Value of an Annuity of $1
50
35) Wilhelmina has just received an inheritance of $50,000, and she would like to put it into an investment portfolio
for 20 years. To calculate the value of the investment at the end of the 20 year period, which of the following tables
would be the best for her to use?
A) Present Value of $1
B) Present Value of an Annuity of $1
C) Future Value of $1
D) Future Value of an Annuity of $1
36) Juan has just received a prize which entitles him to receive annual payments of $10,000 for the next 10 years. In
order to calculate the overall value of the prize today, which of the following tables would be the best for him to
use?
A) Present Value of $1
B) Present Value of an Annuity of $1
C) Future Value of $1
D) Future Value of an Annuity of $1
37) Julio has just received a legal judgment in a civil court case which awards him a settlement of $24,000 to be
received two years from now. In order to calculate the overall value of the award today, which of the following
tables would be the best for him to use?
A) Present Value of $1
B) Present Value of an Annuity of $1
C) Future Value of $1
D) Future Value of an Annuity of $1
38) Jim wants to invest $5,000 at the end of each year for the next 10 years to prepare for his retirement. He
believes he can earn 7% on his investments. What will the value of his investment be at the end of 10 years?
Future Value of an Annuity of $1
4% 5% 6% 7% 8% 9%
1 1.000 1.000 1.000 1.000 1.000 1.000
2 2.040 2.050 2.060 2.070 2.080 2.090
3 3.122 3.153 3.184 3.215 3.246 3.278
4 4.246 4.310 4.375 4.440 4.506 4.573
5 5.416 5.526 5.637 5.751 5.867 5.985
6 6.633 6.802 6.975 7.153 7.336 7.523
7 7.898 8.142 8.394 8.654 8.923 9.200
8 9.214 9.549 9.897 10.26 10.64 11.03
9 10.58 11.03 11.49 11.98 12.49 13.02
10 12.01 12.58 13.18 13.82 14.49 15.19
A) $61,060
B) $69,900
C) $62,650
D) $69,100
39) Wilhelmina has just received an inheritance of $50,000, and she would like to put it into an investment portfolio
for 8 years. She believes she can earn 4% on the investment. What will the value of the investment be at the end of
8 years?
Future Value of $1
4% 5% 6% 7% 8% 9%
1 1.040 1.050 1.060 1.070 1.080 1.090
2 1.082 1.103 1.124 1.145 1.166 1.188
3 1.125 1.158 1.191 1.225 1.260 1.295
4 1.170 1.216 1.262 1.311 1.360 1.412
5 1.217 1.276 1.338 1.403 1.469 1.539
6 1.265 1.340 1.419 1.501 1.587 1.677
7 1.316 1.407 1.504 1.606 1.714 1.828
8 1.369 1.477 1.594 1.718 1.851 1.993
9 1.423 1.551 1.689 1.838 1.999 2.172
10 1.480 1.629 1.791 1.967 2.159 2.367
A) $62,400
B) $59,670
C) $68,450
D) $69,220
40) Juan has just received a prize which entitles him to receive annual payments of $10,000 at the end of each year
for the next 10 years. He would like to sell the rights to the prize money to a financial institution, so that he can
have the cash now. In order to estimate the present value of the prize, he will use a discount rate of 5%. What is the
present value of the prize?
Present Value of an Annuity of $1
5% 6% 7% 8% 9% 10%
1 0.952 0.943 0.935 0.926 0.917 0.909
2 1.859 1.833 1.808 1.783 1.759 1.736
3 2.723 2.673 2.624 2.577 2.531 2.487
4 3.546 3.465 3.387 3.312 3.240 3.170
5 4.329 4.212 4.100 3.993 3.890 3.791
6 5.076 4.917 4.767 4.623 4.486 4.355
7 5.786 5.582 5.389 5.206 5.033 4.868
8 6.463 6.210 5.971 5.747 5.535 5.335
9 7.108 6.802 6.515 6.247 5.995 5.759
10 7.722 7.360 7.024 6.710 6.418 6.145
A) $61,450
B) $71,080
C) $77,220
D) $71,080
41) Julio has just received a legal judgment in a civil court case which awards him a settlement of $24,000 to be
received two years from now. He would like to sell the rights to the settlement money to a financial institution, so
that he can have the cash now. In order to estimate the present value of the settlement, he will use a discount rate of
6%. What is the present value of the settlement?
Present Value of $1
5% 6% 7% 8% 9% 10%
1 0.952 0.943 0.935 0.926 0.917 0.909
2 0.907 0.890 0.873 0.857 0.842 0.826
3 0.864 0.840 0.816 0.794 0.772 0.751
4 0.823 0.792 0.763 0.735 0.708 0.683
5 0.784 0.747 0.713 0.681 0.650 0.621
6 0.746 0.705 0.666 0.630 0.596 0.564
7 0.711 0.665 0.623 0.583 0.547 0.513
8 0.677 0.627 0.582 0.540 0.502 0.467
9 0.645 0.592 0.544 0.500 0.460 0.424
10 0.614 0.558 0.508 0.463 0.422 0.386
A) $20,160
B) $21,360
C) $22,360
D) $22,590
2) If a company uses a higher discount rate to calculate NPV of an investment, it reflects a higher level of perceived
risk for the investment.
3) Dakka Company is considering an investment of $500,000 in a financial instrument that is expected to return cash
flows of $80,000 a year for 10 years. The operations manager says that it is a “no-brainer” because the total cash
flows are $800,000, and it has a payback of just over six years. The VP Finance expresses caution. He says that
because Dakka uses a 10% hurdle rate, a more thorough analysis may show that the investment does not qualify
under the company’s investment criteria. Considering the information provided, the company should reject the
investment.
Present Value of an Annuity of $1
5% 6% 7% 8% 9% 10%
1 0.952 0.943 0.935 0.926 0.917 0.909
2 1.859 1.833 1.808 1.783 1.759 1.736
3 2.723 2.673 2.624 2.577 2.531 2.487
4 3.546 3.465 3.387 3.312 3.240 3.170
5 4.329 4.212 4.100 3.993 3.890 3.791
6 5.076 4.917 4.767 4.623 4.486 4.355
7 5.786 5.582 5.389 5.206 5.033 4.868
8 6.463 6.210 5.971 5.747 5.535 5.335
9 7.108 6.802 6.515 6.247 5.995 5.759
10 7.722 7.360 7.024 6.710 6.418 6.145
4) Alpha Company is considering an investment of $1,000,000 in a land development project. It will yield cash
flows of $300,000 for 5 years. Alpha uses a discount rate of 7%. If the company analyzes the project using NPV,
this should be considered a good investment opportunity.
Present Value of an Annuity of $1
5% 6% 7% 8% 9% 10%
1 0.952 0.943 0.935 0.926 0.917 0.909
2 1.859 1.833 1.808 1.783 1.759 1.736
3 2.723 2.673 2.624 2.577 2.531 2.487
4 3.546 3.465 3.387 3.312 3.240 3.170
5 4.329 4.212 4.100 3.993 3.890 3.791
5) Centurion Company is considering a mineral extraction project which requires an initial investment of $2,000,000
and will yield annual cash flows of $300,000 for 8 years. Centurion has an 8% hurdle rate. If Centurion uses the
NPV method of evaluation investments, this would be considered a good investment opportunity.
Present Value of an Annuity of $1
5% 6% 7% 8% 9% 10%
1 0.952 0.943 0.935 0.926 0.917 0.909
2 1.859 1.833 1.808 1.783 1.759 1.736
3 2.723 2.673 2.624 2.577 2.531 2.487
4 3.546 3.465 3.387 3.312 3.240 3.170
5 4.329 4.212 4.100 3.993 3.890 3.791
6 5.076 4.917 4.767 4.623 4.486 4.355
7 5.786 5.582 5.389 5.206 5.033 4.868
8 6.463 6.210 5.971 5.747 5.535 5.335
9 7.108 6.802 6.515 6.247 5.995 5.759
10 7.722 7.360 7.024 6.710 6.418 6.145
6) Using the NPV method of evaluating investments, a company should consider a project a good investment
opportunity as long as the NPV of the total cash flows is positive.
7) La Grange Company is evaluating an opportunity to invest $50,000 in new manufacturing equipment. It will
have a useful life of 3 years, and will generate $10,000 cash flows at the end of Year 1; $20,000 of cash flows at the
end of Year 2; and $30,000 of cash flows at the end of Year 3. If La Grange uses a discount rate of 10% to calculate
NPV, they will accept the opportunity as a good investment.
Present Value of $1
5% 6% 7% 8% 9% 10%
1 0.952 0.943 0.935 0.926 0.917 0.909
2 0.907 0.890 0.873 0.857 0.842 0.826
3 0.864 0.840 0.816 0.794 0.772 0.751
4 0.823 0.792 0.763 0.735 0.708 0.683
5 0.784 0.747 0.713 0.681 0.650 0.621
6 0.746 0.705 0.666 0.630 0.596 0.564
7 0.711 0.665 0.623 0.583 0.547 0.513
8 0.677 0.627 0.582 0.540 0.502 0.467
9 0.645 0.592 0.544 0.500 0.460 0.424
10 0.614 0.558 0.508 0.463 0.422 0.386
58
8) When calculating the net present value of future cash streams, dollars that are received sooner are worth more
than dollars received later.
9) A company has policy to invest in new opportunities if the investment has a positive NPV. See data below:
Initial investment $105,000
Yearly cash flows $30,000
Number of years 4
Residual value $10,000
Present Value of an Annuity of $1
5% 6% 7% 8% 9% 10%
1 0.952 0.943 0.935 0.926 0.917 0.909
2 1.859 1.833 1.808 1.783 1.759 1.736
3 2.723 2.673 2.624 2.577 2.531 2.487
4 3.546 3.465 3.387 3.312 3.240 3.170
5 4.329 4.212 4.100 3.993 3.890 3.791
Present Value of $1
5% 6% 7% 8% 9% 10%
1 0.952 0.943 0.935 0.926 0.917 0.909
2 0.907 0.890 0.873 0.857 0.842 0.826
3 0.864 0.840 0.816 0.794 0.772 0.751
4 0.823 0.792 0.763 0.735 0.708 0.683
5 0.784 0.747 0.713 0.681 0.650 0.621
If the company has a hurdle rate of 9%, this investment will yield a positive NPV and should be accepted.
10) A company has policy to invest in new opportunities if the investment has a positive NPV. See data below:
Initial investment $105,000
Yearly cash flows $30,000
Number. of years 4
Residual value $10,000
Present Value of an Annuity of $1
5% 6% 7% 8% 9% 10%
1 0.952 0.943 0.935 0.926 0.917 0.909
2 1.859 1.833 1.808 1.783 1.759 1.736
3 2.723 2.673 2.624 2.577 2.531 2.487
4 3.546 3.465 3.387 3.312 3.240 3.170
5 4.329 4.212 4.100 3.993 3.890 3.791
Present Value of $1
5% 6% 7% 8% 9% 10%
1 0.952 0.943 0.935 0.926 0.917 0.909
2 0.907 0.890 0.873 0.857 0.842 0.826
3 0.864 0.840 0.816 0.794 0.772 0.751
4 0.823 0.792 0.763 0.735 0.708 0.683
5 0.784 0.747 0.713 0.681 0.650 0.621
If the company has a hurdle rate of 6%, this investment will yield a positive NPV and should be accepted.
11) The internal rate of return (IRR) is the rate of return, based on discounted cash flows, that a company can expect
to earn by investing in a capital asset.
12) Considering the four common methods of evaluating investments payback, rate of return, net present value,
and internal rate of return the discounted cash flow methods are superior because they consider both the time value
of money and the profitability of the investment.
13) When a company invests in lean manufacturing processes or “green” technologies, the efficiencies and
elimination of waste are factors that should NOT be included when conducting a discounted cash flow analysis of
the investment.
14) When evaluating a potential investment, managers should use more than one measure for making a sound
investment decision.
15) Carte Blanco Company is evaluating an investment of $1,000,000 which will yield cash flows of $257,000 per
year for 5 years with no residual value.
Present Value of an Annuity of $1
5% 6% 7% 8% 9% 10%
1 0.952 0.943 0.935 0.926 0.917 0.909
2 1.859 1.833 1.808 1.783 1.759 1.736
3 2.723 2.673 2.624 2.577 2.531 2.487
4 3.546 3.465 3.387 3.312 3.240 3.170
5 4.329 4.212 4.100 3.993 3.890 3.791
If Carte Blanco has a hurdle rate of 10%, they should accept the investment because its internal rate of return is
higher than 10%.