The Problem Bank - Answers to Part 1, Intermediate

THE PROBLEM BANK - SOLUTIONS
Part 1 - Time Value of Money
Section 2 - Intermediate

1. Sally Guthrie is looking for an investment vehicle that will double her money in five years. If she can't find anything that pays more than 11%, approximately how long will it take to double her investment?

Approximately 5.5 years.
Approximately 6 years.
Approximately 7.5 years.
Approximately 7 years.

ANSWER: d

SOLUTION:

FV = PV [FVF_k,n]
FVF_11,n = 2
n = 6.6 years (approximately 7 years)

KEYSTROKES:

HP TI

1000 [ +/- ] [PV]
2,000 [FV]
11 [I/YR]
[N]
1000 [ +/- ] [PV]
2,000 [FV]
11 [I/Y]
[CPT] [N]

Solution: 6.64 Solution: 6.64

2. Sally Guthrie found an investment vehicle that will double her money in five years. At a rate of 15%, approximately how long will it take to triple her investment?

Approximately 6 years.
Approximately 7.3 years.
Approximately 8 years.
Approximately 9 years.

ANSWER: c

SOLUTION:

FV = PV [FVF_k,n]
FVF_15,n = 3
n = 7.9 years (approximately 8 years)

3. The Mutual Assurance and Life Company is offering an insurance policy under either of the two following terms:
Alternative a) make a series of twelve $1,200 payments at the beginning of each of the next 12 years, with the first payment being made today, or
Alternative b) make a single lump-sum payment today of $10,000 and receive coverage for the next 12 years.
If you had investment opportunities offering an 8 percent annual return, which alternative would you prefer?

Alternative a
Alternative b

ANSWER: a

SOLUTION:

PVAND₀= $1,200 (PVIFA_{.08,12)
(1 + 0.08) = $1,200 (7.536) (1.08)}
= $9,766.66
Alternative b: Present value cost equals $10,000 (given). Therefore, choose Alternative a because it has a lower present value cost.

KEYSTROKES:

HP TI

[ '] [BEG/END]
1,200 [ +/- ] [PMT]
12 [N]
8 [I/YR]
[PV]
[ 2nd] [BEG] [2nd] [ENTER]
1,200 [ +/- ] [PMT]
12 [N]
8 [I/Y]
[CPT] [PV]

Solution: 9,766.76 Solution: 9,766.76

4. Paladin Enterprises manufactures printing presses for small-town newspapers that are often short of cash. To accommodate these customers, Paladin offers the following payment terms:
1/3 on delivery
1/3 after six months
1/3 after 18 months
The Littleton Sentinel is a typically cash-poor newspaper considering one of Paladin's presses. What discount is implied by the terms from Paladin's point of view if it can invest excess funds at 8% compounded quarterly? Assume a price of $300.

ANSWER: d

SOLUTION:

PV = $100 + $100 [PVF_2,2] + $100 [PVF_2,6]
= $100 + $100 (.9612) + $100 (.8880)
= $284.92
Discount = $15.08/$300 = 5%

KEYSTROKES:

HP TI

12 [ '] [P/YR]
4 [ '] [NOM%]
100 [PV] [M]
100 [ +/- ] [FV]
6 [N]
8 [I/YR]
[PV]
Partial solution: 96.09 [M+]

100 [ +/- ] [FV]
18 [N]
[PV]
Partial solution: 88.73 [M+]

300 [-] [RM] [=]
Partial solution: 15.18 [¸] 300 [=]

[2nd] [P/Y] 12 [ENTER] [ ò] 12 [ENTER]
[2nd] [I conv]
8 [ENTER] [ ò] [ ò]
4 [ENTER] [ ñ ] [CPT] [2nd] [QUIT]
100 [ +/- ] [FV]
6 [N]
8 [I/Y]
[CPT] [PV]
Partial solution: 96.09 [STO] [+] 1

100 [ +/- ] [FV]
18 [N]
[CPT] [PV]
Partial solution: 88.73 [STO] [+] 1
300 [-] [RCL] 1 [=]
Partial solution: 15.18 [¸] 300 [=]

Solution: 5% Solution: 5%

5. Mr. Jones bought a building for $60,000, payable on the following terms: a $10,000 down payment and 25 equal annual installment payments to include principal and interest of 10 percent per annum. Calculate the amount of the installment payments. How much of the first year's payment goes toward reducing the principal amount?

$478.39
$508.43
$500.78
$601.02

ANSWER: b

SOLUTION:

PVAN₀ = $60,000 - $10,000 = $50,000
$50,000 = PMT (PVIFA_.10,25) = PMT (9.077)
PMT = $5,508.43
Interest (first year) = .10 ($50,000) = $5,000
Principal reduction = $5,508.43 - $5,000 = $508.43

6. How long will it take a payment of $500 per quarter to amortize a loan of $8,000 at 16% compounded quarterly? Interpolate and give your answer in terms of years and months.

5 years and 8 months
5 years and 2 months
6 years and 1 month
6 years and 4 months

ANSWER: c

SOLUTION:

PVA = PMT [PVFA_k,n]
$8,000 = $500 [PVFA_4,n]
PVFA_4,n = 16
n = 26 quarters = 6.5 years = 6 years 6 months

PVAd = PMT [PVFA_k,n] (1+k)
$8,000 = $500 [PVFA_4,n] (1.04)
PVFA_4,n = 15.3846
n = 24 1/3 quarters = 6 years 1 month

7. What are the monthly mortgage payments on a 30-year loan for $150,000 at 12%?

$1,224.88
$1,972.18
$1,542.92
$1,446.92

ANSWER: c

SOLUTION:

PVA = PMT [PVFA_k,n]
$150,000 = PMT [PVFA_1,360] = PMT (97.2183)
PMT = $1,542.92

8. The Tower family wants to make a home improvement that is expected to cost $60,000. They want to fund as much of the cost as possible with a home equity loan, but can afford payments of only $600 per month. Their bank offers equity loans at 12% compounded monthly for a maximum term of 10 years. Their bank account pays 8% compounded quarterly.
How much cash do they need as a down payment? If they delay starting the project for two years, how much would they have to save each quarter to make the required down payment if the loan rate and estimated cost remains the same?

$18,179.70; $2,118.10
$18,554.32; $1,822.97
$17,645.47; $2,077.35
$17,989.21; $2,158.10

ANSWER: a

SOLUTION:

PVA = PMT [PVFA_k,n] = $600 [PVFA_1,120]
= $600 (69.7005) = $41,820.30
Down payment: $60,000 - $41,820.30 = $18,170.70
Save per quarter: FVA = PMT [FVFA_k,n] = PMT [PVFA_2,8]
$18,179.70 = PMT (8.5830)
PMT = $2,118.10

9. Two investment opportunities are open to you: Investment 1 and Investment 2. Each has an initial cost of $10,000. Assuming that you desire a 10 percent return on your initial investment, compute the net present value of the two alternatives and determine which is the preferred alternative:

Investment 1		Investment 2
Cash Flows	Year	Cash Flows	Year
$5,000	1	$8,000	1
$6,000	2	$7,000	2
$7,000	3	$6,000	3
$8,000	4	$5,000	4

Investment 1
Investment 2

ANSWER: b

SOLUTION:

NPV₁ = -$10,000 + $5,000 (0.909) + $6,000 (0.826) + $7,000 (0.751) + $8,000 (0.683) = $10,222
NPV₂ = -$10,000 + $8,000 (0.909) + $7,000 (0.826) + $6,000 (0.751) + $5,000 (0.683) = $10,975

Investment 2 is the preferred alternative.

10. An investment promises to pay $6,000 at the end of each year for the next 5 years and $4,000 at the end of each year for years 6 through 10. If you require a 12% rate of return on an investment of this sort, what is the maximum amount you would pay for this investment?

$32,014
$29,600
$29,810
$31,500

ANSWER: c

SOLUTION:

PV₀ = $6,000 (PVIFA_.12,5) + $4,000 (PVIFA_.12,5) (PVIF_.12,5)
=$6,000 (3.6048) + $4,000 (3.6048) (0.5674) + $29,810
(Note: $4,000 (PVIFA_.12,5) gives the present value of that annuity at the end of five years. Hence, it must be discounted back to time 0 at a 12% rate.

KEYSTROKES:

HP TI

0 [CFj]
6,000 [CFj]
5 [ '] [Nj]
4,000 [CFj]
5 [ '] [Nj]
12 [I/YR]
[ '] [NPV]

[CF]
0 [ENTER] [ ò]
6,000 [ENTER] [ ò]
5 [ENTER] [ ò]
4,000 [ENTER] [ ò]
5 [ENTER] [ ò] [NPV]
12 [ENTER] [ ò] [CPT]

Solution: 29,810.44 Solution: 29,810.44

11. You are considering investing in a bond that matures 20 years from now. It pays an annual end-of-year coupon rate of interest of 8.75 percent, or $87.50 per year. The bond currently sells for $919. Your marginal income tax rate (applied to interest payments) is 28 percent. Capital gains are taxed at the same rate as ordinary income. What is your after-tax rate of return if you buy this bond today and hold it until maturity?

7%
7.5%
6%
8%

ANSWER: a

SOLUTION:

$919 = $87.5 (1 - 0.28) (PVIFA_i,20) + [ $919 +$1000 - $919)
x (1 - 0.28) ] (PVIF_i,20)
$919 = $63 (PVIFA_i,20) + $977.32 (PVIF_i,20)
Try i = 7%
$919 = $63 (10.594) + $977.32 (0.258) = $919.57
Therefore, i = 7%

12. What payments are due on a 5-year, 10 percent loan, with an initial outstanding balance of $100,000? (At the end of 5 years, the loan will be paid off. All loan payments are equal and occur at the end of the year.)

$27,378
$26,378
$26,746
$26,791

ANSWER: b

SOLUTION:

$100,000 = PMT (PVIFA_.10,5) = PMT (3.791)
PMT = $26,378

13. Payments on a 5-year, 10 percent loan with an initial outstanding balance of $100,000 are $26,378. (At the end of 5 years, the loan will be paid off. All loan payments are equal and occur at the end of the year.) What portion of the year 2 payment is principal and what portion is interest?

Principal, $17,399; interest, $7,543
Principal, $18,539; interest, $8,143
Principal, $18,016; interest, $8,362
Principal, $18,610; interest, $8,603

ANSWER: c

SOLUTION:

Year 1: Interest = 0.10 ($100,000) = $10,000
Principle repayment = $26,378 - $10,000 = $16,378
Year 2: Balance outstanding at beginning of year:
$100,000 - $16,378 = $83,622
Interest = 0.10 ($83,622) = $8,362
Principal repayment = $26,378 - $8,362 = $18,016

14. Mitchell Investments has offered you the following investment opportunity:
$6,000 at the end of each year for the first 5 years, plus
$3,000 at the end of each year from years 6 through 10, plus
$2,000 at the end of each year from years 11 through 20.
How much would you be willing to pay for this investment if you required a 12 percent rate of return?

$33,518
$28,500
$31,401
$32,225

ANSWER: c

SOLUTION:

PV₀ = $6,000 (PVIFA_.12,5)(PVIF_{.12,5)
+ $2,000 (PVIFA_{.12,10)
(PVIF_.12,10)}}
PV₀ = $6,000 (3.605) + $3,000 (3.605) (0.567) + $2,000 (5.650) (0.322)
PV₀ = $31,401

15. Upon retirement, your goal is to spend 5 years traveling around the world. To travel in the style to which you are accustomed will require $250,000 per year at the beginning of each year. If you plan to retire in 30 years, what are the equal, annual, end-of-year payments necessary to achieve this goal? The funds in the retirement account will compound at 10 percent annually.

$5,952.76
$6,337.41
$6,501.22
$6,137.41

ANSWER: b

SOLUTION:

PVAND₃₀ = $250,000 (PVIFA_{.10,5)
(1 + .10)

= $250,000 (3.791) (1.1)

= $1,042,525 ($1,042,466 by calculator)

FVAN_{30 =
$1,042.525 = PMT} (FVIFA_{.10,30)
= PMT (164.494)

PMT = $6,338 ($6337.41 by calculator)}}

16. Upon retirement, you are offered a choice between a $250,000 lump sum payment or a lifetime annuity of $51,300, with annuity payments being made at the end of each year. If you expect to live for 15 years after retirement, at what required rate of return would you be indifferent between the two alternatives (to the nearest whole percent)?

Approximately 19%
Approximately 18%
Approximately 17.8%
Approximately 21%

ANSWER: a

SOLUTION:

$250,000 = $51,300 (PVIFA_i,15)
PVIFA_i,15 = 4.873
From a PVIFA Table, i19%. At any rate greater than 19% you would prefer the lump sum.

17. An investment offers the following year-end cash flows:

End of Year	Cash Flow
1	$20,000
2	$30,000
3	$15.000

Using a 15 percent interest rate, convert this series of irregular cash flows to an equivalent (in present value terms) 3-year annuity.

$23,856
$21,856
$21,871
$22,879

ANSWER: c

SOLUTION:

PV₀ = $20,000 (PVIF_.15,1)+ $30,000 (PVIF_{.15,2)
+ $15,000 (PVIF_.15,3)}
PV₀ = $20,000 (0.8696₎+ $30,000 (0.7561) + $15,000 (0.6575)
PV₀ = $49,937.50
$49.937.50 = PMT (PVIFA_.15,3)= PMT (2.2832)
PMT = $21,871.71

KEYSTROKES:

HP TI

0 [CFj]
20,000 [CFj]
30,000 [CFj]
15,000 [CFj]
15 [I/YR]
[ '] [NPV]
Partial solution 49,938.36
[PV]
0 [FV]
3 [N]
[PMT]

[CF]
0 [ENTER] [ ò]
20,000 [ENTER] [ ò]
1 [ENTER] [ ò]
30,000 [ENTER] [ ò]
1 [ENTER] [ ò]
15,000 [ENTER] [ ò]
1 [ENTER] [ ò] [NPV]
15 [ENTER] [ ò] [CPT]
Partial solution 49,938.36
[STO] 1 [2nd] [QUIT]
[RCL] 1 [PV]
0 [FV]
3 [N]
15 [I/Y]
[CPT] [PMT]

Solution: -21,871.85 (cost) Solution: -21,871.85 (cost)

18. Congratulations! You have just won the Publishers Corporation Sweepstakes. You have been offered a lump sum of $1,000,000, or a lifetime (end-of-year) annuity of $100,000 per year. If you expect to live for 20 years and can earn 15 percent on your investments, which alternative should you choose (ignoring tax consequences)?

Take the million dollars.
Take the annuity.
ANSWER: a

SOLUTION:

PVAN₀= $100,000 (PVIFA_.15,20) = $100,000 (6.259) = $625,900 ($625,933 by calculator)
At 15%, take the million dollars.

19. You are 30 years old and plan to retire on your 60th birthday. You want to start a retirement plan that will require a series of equal, annual, end-of-year deposits into an account that will earn 12 percent annually. The first deposit will be made on your 31st birthday and the last payment will be on your 60th birthday. The plan will allow you to withdraw $120,000 per year for 15 years, beginning on your sixty-first birthday. At the end of the 15th year, you want to withdraw an additional $250,000. What periodic payment must be made into the account to reach your objectives?

$4,221
$3,576
$3,789
$3,992

ANSWER: b

SOLUTION:

Amount needed in account after final deposit on your 60th birthday:
PV₀= $120,000 (PVIFA_.12,15) + $250,000 (0.183)
PV₀= $863,070 ($863,054 by calculator)
$863,070 = PMT (FVIFA_.12,30) = PMT (241.333)
PMT = $3,576

KEYSTROKES:

HP TI

120,000 [PMT]
15 [N]
12 [I/YR]
[PV]
Partial solution: -817,303.74
250,000 [FV]
[PV]
Partial solution: -862,977.80
[ '] [CLEAR ALL]
862,977.80 [FV]
30 [N]
12 [I/YR]
[PMT]

120,000 [PMT]
15 [N]
12 [I/Y]
[CPT] [PV]
Partial solution: -817,303.74
250,000 [FV]
[CPT] [PV]
Partial solution: -862,977.80
[2nd] [CLR TVM]
862,977.80 [FV]
30 [N]
12 [I/Y]
[CPT] [PMT]

Solution: -3,575.88 (cost) Solution: -3,575.88 (cost)

20. Cousin Drusilla has just turned 15. Drusilla plans to go to law school on her twenty-second birthday. Law school is expected to cost $25,000, $26,000, and $27,000 for each of Drusilla's 3 years in school. You plan to provide for Drusilla's education and want the needed funds to be available to Drusilla at the beginning of each year in law school. In addition, you want to give Drusilla a $10,000 per year, 10-year annuity as a graduation gift. Drusilla is to receive the first annuity payment on her twenty-seventh birthday.
You currently have $8,000 to meet these obligations. You want to save an equal amount at the end of each of the next 10 years to meet the remaining obligations. If your investments earn 10% pre-tax and your (and Drusilla's) marginal tax rate is 30%, how much must you save at the end of each of the next 10 years?

$11,051
$10,456
$11,622
$10,075

ANSWER: d

SOLUTION:

10% pretax x (1 - T) = 7% after tax
PV₀ = $25,000 (PVIF_0.07,7) + $26,000 (PVIF_0.07,8) + $27,000 (PVIF_0.07,9) + $10,000 (PVIFA_0.07,10) (1 + 0.07) (PVIF_0.07,12)
= $25,000 (0.623) + $26,000 (0.582) + $27,000 (0.544) + $10,000 (7.024) (1.07) (0.444) = $78,765
Amount needed = $78,765 - $8,000 = $70,765
PVAN₀ = PMT (PVIFA_0.07,10)
$70,765 = PMT (7.024)
PMT = $10,075

21. You have decided to start planning for your retirement by analyzing different retirement plans. The plan offered by IRA Managers requires you to deposit $5,000 at the beginning of each of the next 30 years. The retirement plan guarantees a 10 percent annual compounding rate over the 30-year time period. When you retire at the end of the thirtieth year, the interest earned on the money in the account is guaranteed to increase to a 12 percent annual rate. If you plan on making 20 equal withdrawals at the beginning of each year from the account (with the first withdrawal made at the end of the 30th year-the first year of retirement), how much can you withdraw?

$108,145
$108,731
$107,469
$109,037

ANSWER: a

SOLUTION:

FVAND₃₀ = $5,000 (FVIFA_0.10,30) (1.10)
= $5,000 (164,494) (1.10)
= $904,717
PVAN₀ = PMT (PVIFA_0.12,20) (1.12)
$904,717 = PMT (7.469) (1.12)
PMT = $108,151 ($108,145 by calculator)

22. Linda and Paul Chavez have a son, Mike, who is 15 and plans to go to college 4 years from now. His college expenses are expected to be $30,000 per year, payable at the beginning of each school year. At the end of his fourth year in college, Mike's parents have offered to buy him a car, expected to cost $19,000. Linda and Paul have accumulated a total of $55,000 that can be used to pay the college expenses. They want to know what equal amount they must save (at the beginning of each of the next 6 years) in order to meet their commitments to Mike. Assume Linda and Paul's savings will earn a pretax rate of return of 10 percent, their marginal tax rate is 30 percent, and that these rates will remain unchanged for the next 8 years.

$4,766
$7,642
$9,397
$8,972

ANSWER: b

SOLUTION:

10% pretax x (1 - T) = 7% after tax
PV₀ = $30,000 (PVIFA_0.07,4) (PVIF_0.07,3) + $19,000 (PVIF_0.07,8)
= $30,000 (3.387) (0.816) + $19,000 (0.582)
= $93,972 ($93,977 by calculator)
Amount needed = $93,972 - $55,000 = $38,972
PVAN₀ = PMT (PVIFA_0.07,6) (1.07)
$38,972 = PMT (4.766) (1.07)
PMT = $7,642

23. Crab State Bank has offered you a $1,000,000 5-year loan at an interest rate of 11.25 percent, requiring equal annual end-of-year payments that include both principal and interest on the unpaid balance. Develop an amortization schedule for this loan.

$272,274
$276,374
$281,125
$280,099

ANSWER: a

SOLUTION:

$1,000,000 = PMT (PVIFA_0.1125,5)
PMT = $272,274 (by calculator)

24. Given a 10% discount rate, find the present value of a cash flow stream of $100 at the end of the first year, $200 at the end of the second, $300 at the end of the third, and $400 at the end of the fourth.

$725.61
$754.60
$225.30
$723.20

ANSWER: b

SOLUTION:

PV = ($100) (PVIF_0.10,1) + (200) (PVIF_0.10,2) + (300) (PVIF_0.10,3) + (400) (PVIF_0.10,4)
= ($100) (0.909) + (200) (0.826) + (300) (0.751) + (400) (0.683)
= $90.90 + $165,20 + 225.30 + 273.20
= $754.60

25. Find the present value of a cash flow stream that promises $2,000 per year for the first 10 years and $3,000 per year for the following 10 years given a discount rate of 12%.

$15,650
$16,650
$16,469
$16,757

ANSWER: d

SOLUTION:

PV = (PMT) (PVIFA_0.12,10) + (PMT) (PVIFA_0.12,20 - PVIFA_0.12,10)
= ($2000) (5.650) + (3000) (7.469 - 5.650)
= $11,300 + 5457 + $16,757

26. Frank Tepper will retire in ten years and wishes to set up a personal savings plan to supplement his employer's pension plan. Frank will deposit �2,000 at the end of each of those ten years into an account earning 8%. How much would he have in the account after the last payment is made?

�24,318
�27,794
�28,974
�24,487

ANSWER: c

SOLUTION:

FV = (�2000) (FVIFA_0.08,10)
= (�2000) (14.487) = �28,974

KEYSTROKES:

HP TI

2,000 [+/-] [PMT]
10 [N]
8 [I/YR]
[FV]

2,000 [+/-] [PMT]
10 [N]
8 [I/Y]
[CPT] [FV]

Solution: 28,973.12 Solution: 28,973.12

27. Frank Tepper will retire in ten years and wishes to set up a personal savings plan to supplement his employer's pension plan. Frank will deposit �2,000 at the end of each of those ten years into an account earning 8%. After the last payment is made, Frank will have �28,974 in the account. What is the most that he could withdraw in equal amounts over 10 years, starting 1 year after the last payment has been made into the account?

�4118
�4318
�3285
�4735

ANSWER: b

SOLUTION:

PV = (PMT) (PVIFA_0.08,10)
�28,974 = (PMT) (6.710)
PMT = �28,974 / 6.710 = �4318

28. Lane Manufacturing can purchase a new machine for $240,000 that is expected to generate cash savings of $60,000 per year for the next five years due to lower direct labor costs. Assuming an opportunity cost of 10%, should Lane purchase the machine or continue to bear the higher labor expense?

Lane should purchase the machine.
Lane should continue to bear the high labor expense.

ANSWER: b

SOLUTION:

PV = (Lower Labor Costs) (PVIFA_0.10,5)
= ($60,000) (3.791) = $227,447
Cost of New Machine = $240,000
Since cost is greater than value of savings, Lane should not purchase the new machine.

29. You have just won the $28,000,000 Super Bowl lotto. The winnings are paid in 20 equal annual installments, and the first payment is tomorrow. You have been contacted by a financial services company that is willing to trade an immediate single lump sum for your 20 payments. What lump sum would be acceptable to you if you had an 8% opportunity rate?

$15,000,000
$22,042,671
$14,845,039
$16,342,778

ANSWER: c

SOLUTION:

Annual Cash Payments = $28,000,000 / 20 = $1,400,000
First payment occurs at N=0
PV = $1,400,000 + ($1,400,000) (PVIFA_0.08,19)
= $1,400,000 + ($1,400,000) (9.604)
= $14,845,039
Since PV of the 20 annual payments is $14,845,600, you would accept a lump sum equal to that amount.

30. You have the choice between leasing a new car for $600 per month for 2 years, or purchasing it for $40,000. The estimated value of the car at the end of the 2 years is $30,000. If your opportunity cost is 12%, should the car be leased or purchased?

Lease the car.
Purchase the car.

ANSWER: a

SOLUTION:

Lease: PV = ($600) (PVIFA_0.01,24) = ($600) (21.244) = $12,746
Purchase: PV = $40,000 - (30,000) (PVIF_0.01,24)
= $40,000 - (30,000) (0.788)
= $40,000 - 23,627 = $16,373

The PV of the lease payments is smaller. Thus, the car should be leased.

31. Your monthly statement from your bank credit card shows that the monthly rate of interest is 1.5%. What is the annual effective rate of interest you are being charged on your credit card?

18.2%
15.93%
16.8%
19.56%

ANSWER: d

SOLUTION:

i_eff = (1 + 0.18/12)¹² - 1 = .1956 or 19.56%

32. How much will you have at the end of 5 years in a European vacation account if you deposit $200 per month in an account that is paying a nominal 12 percent per year, compounded monthly?

$15,225
$16,334
$15,977
$16,439

ANSWER: b

SOLUTION:

FVAN = $200 (81.670) = $16,334

33. What is the most you should pay to receive the following cash flows if your required rate of return is 12 percent?

Year 1	$5,000
Year 2	$8,000
Year 3	$12,000
Year 4-10	$15,000

$68,893
$52,321
$66,560
$68,105

ANSWER: d

SOLUTION:

PV = $5,000 (0.893) + $8,000 (0.797) + $12,000 (0.712) + $15,000 (5.650 - 2.402) = $68,105