Principles of Finance, 6e
Besley/Brigham
Chapter 09
Principles of Finance, 6e
Besley/Brigham
Chapter 09
TOPICS:
Annuity Payment
a.
$15,373
to be able to purchase the Nissan in 7 years?
$4,945.57
$3,933.93
$7,714.72
$3,450.82
$6,030.43
ANSWER:
b
RATIONALE:
Cash flow time line:
Equation
solution: Price of car on 27th birthday FV = $30,000(1 + 0.05)7 = $42,213. Annual
investment required
Financial
calculator solution: Price of car on 27th birthday Inputs: N = 7; I = 5; PV = −30,000.
Output: FV = $42,213.01 ≈ $42,213. Annual investment required Inputs: N = 7; I = 14; FV
= 42,213. Output: PMT = −$3,933.93.
POINTS:
1
DIFFICULTY:
Moderate
Principles of Finance, 6e
Besley/Brigham
Chapter 09
$10,000
15,000
15,000
15,000
15,000
20,000
a.
$66,909
b.
$57,323
c.
$61,815
d.
$52,345
$16,550
$32,290
$38,352
$13,975
ANSWER:
b
RATIONALE:
Cash flow time line:
Equation
solution: Financial calculator solution:
Calculate the FV of the withdrawals which is how much her actual account fell short of
her plan. END mode. Inputs: N = 3; I = 10; PMT = −5,000. Output: FV = $16,550.
Alternative solution: Calculate FV of original plan. BEGIN mode. Inputs: N = 5; I = 10;
PMT = −8,000. Output: FV = $53,724.80. Calculate FV of actual deposits less
withdrawals, take the difference. Inputs: = 8,000; = 8,000; N1 = 2; = 3,000;
N2 = 2; = −5,000; I = 10. Output: NFV = $37,174.80. Difference: $53,724.80 −
$37,174.80 = $16,550.
POINTS:
1
DIFFICULTY:
Moderate
ACCREDITING STANDARDS:
Blooms Taxonomy-2 – Application
Business Program-3 – Analytic
DISC-FIN-05 – Financial Analysis and Cash Flows
DISC-FIN-09 – Investments
Time Estimate-a – 5 min.
TOPICS:
Annuity Payment
41. Assume that your required rate of return is 12 percent and you are given the following stream of cash flows:
Year
Cash Flow
Principles of Finance, 6e
Besley/Brigham
Chapter 09
$62,029
ANSWER:
a
RATIONALE:
Cash flow time line:
Equation solution:
Financial
calculator solution: Using cash flows Inputs: = 10,000; = 15,000; N1 = 4; =
20,000; I = 14. Output: NPV = $66,908.77 ≈ $66,909.
POINTS:
1
DIFFICULTY:
Moderate
ACCREDITING STANDARDS:
Blooms Taxonomy-2 – Application
Business Program-3 – Analytic
DISC-FIN-05 – Financial Analysis and Cash Flows
DISC-FIN-09 – Investments
Time Estimate-a – 5 min.
TOPICS:
PV of an Uneven CF Stream
42. Express Airlines is considering the purchase of an aircraft to supplement its current fleet. In estimating the impact of
adding this aircraft to the fleet, management has developed the following expected cash flows:
End of Year
1
−$ 1,000
2
$100,000
3
$100,000
4
$100,000
5
$100,000
6
$100,000
7
−$300,000
If the discount rate is 10 percent, what is the present value of these estimated flows?
$379,080
$224,211
$189,760
$154,869
$199,000
ANSWER:
c
RATIONALE:
Cash flow time line:
Principles of Finance, 6e
Besley/Brigham
Chapter 09
POINTS:
1
DIFFICULTY:
Moderate
44. You are given the following cash flow information. The appropriate discount rate is 12 percent for Years 1−5 and 10
percent for Years 6−10. Payments are received at the end of the year.
Year
Amount
1–5
$20,000
6–10
$25,000
What should you be willing to pay right now to receive the income stream above?
$166,866
$158,791
$225,000
$125,870
$198,433
ANSWER:
d
RATIONALE:
Cash flow time line:
Equation solution: Solve for PV at time = 0 of $20,000 annuity
Solve for PV at time = 5 of $25,000
Principles of Finance, 6e
Besley/Brigham
Chapter 09
a.
$2,000
TOPICS:
PV of an Uneven CF Stream
45. A project with a 3-year life has the following probability distributions for possible end of year cash flows in each of
the next three years:
Year 1
Year 2
Year 3
Prob
Cash Flow
Prob
Cash Flow
Prob
Cash Flow
0.30
$300
0.15
$100
0.25
$200
0.40
500
0.35
200
0.75
800
0.30
700
0.35
600
0.15
900
Using an interest rate of 8 percent, find the expected present value of these uncertain cash flows. (Hint: Find the expected
cash flow in each year, then evaluate those cash flows.)
$1,204.95
$835.42
$1,519.21
$1,580.00
$1,347.61
ANSWER:
e
RATIONALE:
Cash flow time line:
Calculate expected cash flows E(CF1) = (0.30) ($300) + (0.40) ($500) + (0.30) ($700) =
$500 E(CF2) = (0.15) ($100) + (0.35) ($200) + (0.35) ($600) + (0.15) ($900) = $430
E(CF3) = (0.25) ($200) + (0.75) ($800) = $650 Equation solution:
Financial Calculator Solution: Using
cash flows Inputs: = 0; = 500; = 430; = 650; I = 8. Output: NPV =
$1,347.61.
POINTS:
1
DIFFICULTY:
Moderate
ACCREDITING STANDARDS:
Blooms Taxonomy-2 – Application
Business Program-3 – Analytic
DISC-FIN-05 – Financial Analysis and Cash Flows
DISC-FIN-09 – Investments
Time Estimate-a – 5 min.
TOPICS:
PV of Uncertain Cash Flows
46. The present value (t = 0) of the following cash flow stream is $5,979.04 when discounted at 12 percent annually. What
is the value of the missing (t = 2) cash flow?
Principles of Finance, 6e
Besley/Brigham
Chapter 09
$2,391
$3,000
$3,391
$4,237
ANSWER:
c
RATIONALE:
Cash flow time line:
Equation
solution: Solve for PV of given payments
Solve for PV of missing payment
PVMissing PMT = PVAll − PVGiven payments $2,391.59 = $5,979.04 − $3,587.45 Solve for PV
of missing payment FV = $2,391.59(1 + 0.12)2 = $3,000. Financial calculator solution:
Solve for PV of given payments Inputs: = 0; = 1,000; = 0; = 2,000; =
2,000; I = 12. Output: NPV = $3,587.45. Solve for PV of missing payment PVMissing PMT =
PVAll − PVGiven payments $2,391.59 = $5,979.04 − $3,587.45 Solve for PV of missing
payment Inputs: N = 2; I = 12; PV = −2,391.59. Output: FV = $3,000.01 ≈ $3,000.
POINTS:
1
DIFFICULTY:
Moderate
ACCREDITING STANDARDS:
Blooms Taxonomy-2 – Application
Business Program-3 – Analytic
DISC-FIN-05 – Financial Analysis and Cash Flows
DISC-FIN-09 – Investments
Time Estimate-a – 5 min.
TOPICS:
Value of Missing Payment
47. If you buy a factory for $250,000 and the terms are 20 percent down, the balance to be paid off over 30 years at a 12
percent rate of interest on the unpaid balance, what are the 30 equal annual payments?
$20,593
$31,036
$24,829
$50,212
$6,667
ANSWER:
c
Principles of Finance, 6e
Besley/Brigham
Chapter 09
POINTS:
1
DIFFICULTY:
Hard
TOPICS:
perpetuity, and at the end of time period 10 you will receive the first payment on an additional $200 in perpetuity. If you
52. Your mother’s employer offers a tax-deferred retirement plan (a 401-b plan, which was authorized by Congress to
encourage savings) which would permit her to invest, tax-free until she retires, up to 15 percent of her salary. Once you
are out of school (one year from today), she figures she can save $1,000 every 6 months, or $2,000 per year. The
insurance company which manages the retirement fund promises to pay a stated (or simple) rate of 12 percent per year,
but with quarterly compounding. If your mother invests $1,000 each six months, starting six months after you graduate (or
18 months from today), how much will she have 5 years from now, assuming the last payment is made at the end of Year
5? (Hint: She will make a total of 8 payments.)
$12,300
$12,462
$9,897
$9,929
$10,000
ANSWER:
d
RATIONALE:
Cash flow time line: In thousands
Begin by finding the quarterly or periodic rate, which is 12/4 = 3%. Equation solution: A
way to solve the problem is to recognize that we have an 8-period annuity of $1,000 per
period. Note, though, that the effective 6-month interest rate must be used. The effective
annual rate of (1.03)4 − 1 = 12.55%, but that rate cannot be used for the annuity because
the payments are semiannual. What you must do is get the effective 6-month rate, found
as follows: (1.03)2 − 1 = 0.0609 = 6.09%. (Note that (1.0609)2 − 1 = 12.55%.) Calculate
the effective 6-month rate
Calculate the FV of the annuity
Principles of Finance, 6e
Besley/Brigham
Chapter 09
a.
$528.21
b.
$1,329.00
c.
$792.49
d.
$1,046.41
e.
$875.18
RATIONALE:
require a 10 percent rate of return, what is the combined present value of these three perpetuities?
$2,349.50
$2,526.85
$2,685.42
$2,779.58
$2,975.40
ANSWER:
d
RATIONALE:
Cash flow time line:
Equation solution: PVp1 at Time = 0: $100/0.10 = $1,000 PVp2 at Time = 5; $150/0.10 =
$1,500 PVp3 at Time = 9; $200/0.10 = $2,000
Financial calculator
solution: Calculate the undiscounted values of each of three perpetuities at the point in
time where they begin, using numerical methods, then calculate PV at t = 0 of the
combined perpetuity values. PVp1 at Time = 0: $100/0.10 = $1,000 PVp2 at Time = 5;
$150/0.10 = $1,500 PVp3 at Time = 9; $200/0.10 = $2,000 Inputs: = 1,000; = 0;
N1 = 4; = 1,500; = 0; N3 = 3; = 2,000; I = 10. Output: NPV = $2,779.577 ≈
$2,779.58.
POINTS:
1
DIFFICULTY:
Hard
ACCREDITING STANDARDS:
Blooms Taxonomy-2 – Application
Business Program-3 – Analytic
DISC-FIN-05 – Financial Analysis and Cash Flows
DISC-FIN-09 – Investments
Time Estimate-a – 5 min.
TOPICS:
PV of a Perpetuity
54. Find the present value of an income stream which has a negative flow of $100 per year for 3 years, a positive flow of
Principles of Finance, 6e
Besley/Brigham
Chapter 09
Cengage Learning Testing, Powered by Cognero
Page 35
Equation solution: Calculate the PV of CFs
4−8 as of time = 3 at I = 5%
Calculate PV of
the FV of the positive CFs at Time = 3 Total PV = $1,070 −
$277.51 = $792.49 Financial calculator solution: Inputs: = 0; = −100; N1 = 3; I =
4. Output: NPV = −277.51. Calculate the PV of CFs 4−8 as of time = 3 at I = 5% Inputs:
= 0; = 200; = 300; N2 = 4; I = 5. Output: NPV = $1,203.60. Calculate PV of
the FV of the positive CFs at Time = 3 Inputs: N = 3; I = 4; FV = −1,203.60. Output: PV =
$1,070. Total PV = $1,070 − $277.51 = $792.49
POINTS:
1
DIFFICULTY:
Hard
ACCREDITING STANDARDS:
Blooms Taxonomy-2 – Application
Business Program-3 – Analytic
DISC-FIN-05 – Financial Analysis and Cash Flows
DISC-FIN-09 – Investments
Time Estimate-a – 5 min.
TOPICS:
PV of an Uneven CF Stream
55. Your parents start saving for your sister’s college education. She will begin college when she turns age 18 and will
need $4,000 at that time and at the end of each of the following 3 years. They will make a deposit at the end of this year in
an account which pays 6 percent compounded annually, and an identical deposit at the end of each year with the last
deposit occurring when she turns age 18. If an annual deposit of $1,484 will allow them to reach their goal, how old is
your sister now?
13
8
14
12
10
ANSWER:
e
RATIONALE:
Cash flow time line:
Principles of Finance, 6e
Besley/Brigham
Chapter 09
$14,922.85
ANSWER:
d
RATIONALE:
Cash flow time line:
Principles of Finance, 6e
Besley/Brigham
Chapter 09
e.
10.42%
ANSWER:
c
The following question(s) may require the use of a financial calculator.
58. You want to borrow $1,000 from a friend for one year, and you propose to pay her $1,120 at the end of the year. She
agrees to lend you the $1,000, but she wants you to pay her $10 of interest at the end of each of the first 11 months plus
$1,010 at the end of the 12th month. How much higher is the effective annual rate under your friend’s proposal than under
your proposal?
0.00%
0.45%
0.68%
0.89%
1.00%
ANSWER:
c
RATIONALE:
Your proposal: rEAR 1 = $120/$1,000 rEAR 1 = 12% Your friend’s proposal: Interest is
being paid each month ($10/$1,000 = 1% per month), so it compounds, and the rEAR is
higher than rSIMPLE = 12%: Difference = 12.68% −
12.00% = 0.68% You could also visualize your friend‘s proposal in a cash flow time line
format: Insert those
cash flows in the cash flow register of a calculator and solve for IRR. The answer is 1%,
but this is a monthly rate. The simple rate is 12 (1%) = 12%, which converts to an ER of
12.68% as follows: Input into a financial calculator the following: P/YR = 12, NOM% = 12,
and solve for EFF% = 12.68%
POINTS:
1
DIFFICULTY:
Easy
ACCREDITING STANDARDS:
Blooms Taxonomy-2 – Application
Business Program-3 – Analytic
DISC-FIN-05 – Financial Analysis and Cash Flows
DISC-FIN-09 – Investments
Time Estimate-a – 5 min.
TOPICS:
Effective Annual Rate
59. Bank One currently charges a 10 percent simple rate on a car loan where the interest is compounded semiannually.
Bank Two offers a car loan where the interest is compounded quarterly. What simple rate would Bank Two have to charge
in order to earn the same effective annual rate that is earned by Bank One?
9.25%
9.88%
10.00%
10.25%