Test Bank For Accounting for Decision Making and Control Jerald Zimmerman 10 Edition
Chapter 03 Test Bank – Static Key
Multiple Choice Questions
1. A lump sum of $5,000 is invested at 10% per year for five years. The company’s cost of capital is 8%. Which is true?
A. The investment has a future value of $7,347
B. The investment has a future value of $8,053
C. The investment has a present value of $5,000
D. The investment has a net present value of $5,000
E. None of the above
$5,000 (1 0.1)5 = $8,053
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Topic: Future Values
Topic: Present Values
2. Cash of $12,000 will be received in year 6. Assuming an opportunity cost of capital of 7.2%, which of the following is true?
A. The future value is $18,212
B. The present value is $7,996
C. The present value is $7,907
D. Provide data for tax purposes
E. None of the above
$12,000 × (1 0.072)−6 = $7,907
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Topic: Future Values
Topic: Present Values
3. Gorgeous George is evaluating a five-year investment in an oil-change franchise, which costs $120,000 paid up front. Projected net operating cash flows are $60,000 per year. If Gorgeous George buys shares instead of the franchise, he expects an annual return of 12%. Which is true?
A. The future value of the franchise is $216,287
B. The net present value of the franchise is $216,287
C. The future value of the franchise is $138,900
D. The net present value of the franchise is $96,287
E. None of the above
|
NPV |
= |
Sum PV(Op Cash Flows) − Investment |
|
$96,287 |
= |
$216,287 − $120,000 |
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Blooms: Apply
Difficulty: 3 Hard
Topic: Annuities
Topic: Decision to Open a Day Spa
Topic: Future Values
Topic: Present Values
4. Furious Fred expects cash flows from an investment as follows:
Yr 1 $3,000, Yr 2 $5,000, Yr 3 $8,000
Using an opportunity cost of capital of 5.6%, the present value is:
A. $14,118
B. $14,523
C. $14,361
D. $14,909
E. none of the above
|
PVi |
= |
FVi × PVFi |
|
$14,118 |
= |
$3,000 × (1 0.056)−1 $5,000 × (1.056)−2 $8,000 × (1.056)−3 |
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Topic: Present Value of a Cash Flow Stream
5. Which is true?
A. The present value of a 20-year annuity of $1,900 at 8% is $16,854
B. A $100,000 bond with a 5% coupon will sell at a premium when the market rate of interest is 6%
C. The issue price of a $150,000 zero coupon bond that matures in 6 years when the market rate of interest is 6% is $105,744
D. The present value of a perpetual income stream of $4,000 when the market rate of interest is 8% is $50,000
E. None of the above
|
PV of perpetuity |
= |
Annual income/interest rate |
|
$50,000 |
= |
$4,000/0.08 |
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Blooms: Apply
Difficulty: 3 Hard
Topic: Annuities
Topic: Present Values
6. Harriet Harvester (HH) plans to buy a haymaker. It costs $180,000 and is expected to last for five years. She presently hires 10 workers at $3,000 per month for each of the six harvesting months each year. The equipment would eliminate the need for six workers. HH uses straight-line depreciation and projects a salvage value of $23,000. Her tax rate is 21% and opportunity cost of funds is 8.0%. Which is true?
A. The present value of cash flows in year 5 is $24,466
B. NPV is −$24,466
C. NPV is $155,534
D. NPV is −$155,534
E. None of the above
|
|
Yr 0 |
1 |
2 |
3 |
4 |
5 |
||||||||||||
|
INV |
−$ |
180,000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Labor savings* |
|
|
|
$ |
36,000 |
|
$ |
36,000 |
|
$ |
36,000 |
|
$ |
36,000 |
|
$ |
36,000 |
|
|
Tax @ 21% |
|
|
|
− |
7,560 |
|
− |
7,560 |
|
− |
7,560 |
|
− |
7,560 |
|
− |
7,560 |
|
|
Tax shield of depreciation** |
|
|
|
|
6,594 |
|
|
6,594 |
|
|
6,594 |
|
|
6,594 |
|
|
6,594 |
|
|
Salvage value |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
23,000 |
|
|
Net cash flows |
−$ |
180,000 |
|
$ |
35,034 |
|
$ |
35,034 |
|
$ |
35,034 |
|
$ |
35,034 |
|
$ |
58,034 |
|
|
NPV @ 8% |
−$ |
24,466 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
*$3,000 × 6 × 6
**S-L depreciation = (HC − Salvage)/Life = ($180,000 − $23,000)/5 = $31,400
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Blooms: Apply
Difficulty: 3 Hard
Topic: Annuities
Topic: Essential Points about Capital Budgeting
Topic: Multiple Cash Flows per Year
Topic: Present Values
7. Samuel Survivor is planning to save for retirement 35 years from now. He expects to live 25 years beyond that, and would like an annual retirement income of $38,500 after tax of 30%. What is the lump sum needed to fund retirement, at an expected annual return of 11.2%?
A. $357,888
B. $319,561
C. $456,515
D. $479,118
E. None of the above
|
Annual pre-tax income |
= |
Target income/(1 − tax rate) |
|
$55,000 |
= |
$38,500/(1 − 0.3) |
|
PV Annuity |
= |
Annuity × PVFAn |
|
$456,515 |
= |
$55,000 × 8.30028 |
|
PVFAn |
= |
(1 − (1 0.112)−25)/0.112 |
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Blooms: Apply
Difficulty: 3 Hard
Topic: Annuities
8. Samuel Survivor is planning to save for retirement 35 years from now. He expects to live 25 years beyond that, and would like an annual retirement income of $38,500 after tax of 30%. How much must Samuel Survivor save each year to accumulate the lump sum needed to fund retirement, at an expected annual return of 11.2%?
A. $893
B. $4,062
C. $1,339
D. $937
E. None of the above
|
Annual pre-tax income = Target income/(1 − tax rate) $55,000 = $38,500/(1 − 0.3) PV Annuity = Annuity × PVFAn $456,515 = $55,000 × 8.30028 PVFAn = (1 − (1 0.112)−25)/0.112 Annuity = FV/FVFAn $1,275 = $456,515/357.888 FVFAn = ((1 0.112)35 − 1)/0.112 |
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AICPA: BB Industry
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Blooms: Apply
Difficulty: 3 Hard
Topic: Annuities
Topic: Taxes and Depreciation Tax Shields
9. Mirtha Mudflat has sufficient funds to choose one of two investments. The same amount will be invested in either case. Choice one: ten year $100,000 5% Treasury bonds issued to yield 4% per annum, the market rate. Choice two: a risky bond of the same amount that has expected cash flows of $9,000 per year for the same period.
What is the issue price of the Treasury bond?
A. $100,000
B. $108,110
C. $92,278
D. $125,000
E. None of the above
Issue price of the bond:
|
Par value × PVF |
= |
$100,000 × (1.04)-10 |
= |
$ |
67,556 |
|
Annuity × PVFAn |
= |
$5,000 × (1 − (1.04)-10)/0.04 |
= |
$ |
40,554 |
|
|
|
|
|
$ |
108,110 |
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Difficulty: 3 Hard
Topic: Annuities
Topic: Present Values
10. Mirtha Mudflat has sufficient funds to choose one of two investments. The same amount will be invested in either case. Choice one: ten year $100,000 5% Treasury bonds issued to yield 4% per annum, the market rate. Choice two: a risky bond of the same amount that has expected cash flows of $9,000 per year for the same period.
What is the risk premium that makes Mirtha indifferent between the two investments?
A. 7.80%
B. 5.66%
C. 3.80%
D. 5.00%
E. None of the above
First, solve for the issue price of the bond:
|
Par value × PVF |
= |
$100,000 × (1.04)-10 |
= |
$ |
67,556 |
|
Annuity × PVFAn |
= |
$5,000 × (1 − (1.04)-10)/0.04 |
= |
$ |
40,554 |
|
|
|
|
|
$ |
108,110 |
Then, solve for the IRR, then subtract riskless rate:
|
INV |
= |
Annuity × PVFAn Bond maturity × PVF |
|
PVFAn |
= |
(INV – PV bond)/Annuity |
|
|
= |
($108,110 − $47,171)/$9,000 = 6.77104(IRR = x%, t = 10) |
|
IRR – riskless |
= |
7.8% − 4% = 3.8% |
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Difficulty: 3 Hard
Topic: Annuities
Topic: Internal Rate of Return (IRR)
Topic: Present Values
11. Mirtha Mudflat has sufficient funds to choose one of two investments. The same amount will be invested in either case. Choice one: ten year $100,000 5% Treasury bonds issued to yield 4% per annum, the market rate. Choice two: a risky bond of the same amount that has expected cash flows of $9,000 per year for the same period. Assume Mirtha purchased the risky bond for $105,000 and the market rate is 6%. Which is false?
A. Net present value is $17,080
B. Payback occurs at the end of year 10
C. IRR is 8.25%
D. Present value of the cash flows is $122,080
E. None of the above
All are true.
|
|
Yr 0 |
1 |
2 − 9 |
10 |
||||
|
INV |
$ |
105,000 |
|
|
|
|
|
|
|
OPCF |
|
|
$ |
9,000 |
$ |
9,000 |
$ |
9,000 |
|
Par |
|
|
|
|
|
|
|
100,000 |
|
Net cash flows |
$ |
105,000 |
$ |
9,000 |
$ |
9,000 |
$ |
109,000 |
NPV $17,080; PV $122,080; IRR 8.25%
Payback is not accomplished by the annual cash flows ($9,000; 10 years). The payback shortfall is covered by the redemption of the bond.
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Blooms: Apply
Difficulty: 3 Hard
Topic: Annuities
Topic: Decision to Open a Day Spa
Topic: Internal Rate of Return (IRR)
Topic: Payback
Topic: Present Values
12. Peter Pontificator is proposing to purchase a paddle machine, which will cost $5 million, last ten years and have a salvage value of $80,000. Given a tax rate of 21%, and a cost of capital of 8%:
What is the present value of the tax shield if straight-line depreciation is used?
A. $600,000
B. $643,234
C. $745,671
D. $693,286
E. None of the above
SL depreciation = (HC − Salvage)/Life
= ($5,000,000 − $80,000)/10 = $492,000
Annual tax shield = 21% × $492,000 = $103,320 per year
PV of Annuity of $103,320 per year at 8% for 10 years = $693,286
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Blooms: Apply
Difficulty: 3 Hard
Topic: Annuities
Topic: Taxes and Depreciation Tax Shields
13. Peter Pontificator is proposing to purchase a paddle machine, which will cost $1 million, last eight years and have a salvage value of 20%. Given a tax rate of 35%, and a cost of capital of 6%:
If double-declining balance depreciation is used, and PP switches to straight-line depreciation in year 6, the present value of the depreciation tax shield is:
A. $287,506
B. $230,005
C. $286,513
D. $229,211
E. none of the above
Double declining rate = 2 × (1/life) = 2 × (1/8) = 25%
The depreciable amount = purchase price. Salvage value is ignored in this method.
|
|
|
|
Yr 1 |
|
|
Yr 2 |
|
|
Yr 3 |
|
|
Yr 4 |
|
|
|
Double declining dep |
|
|
$ |
250,000 |
|
$ |
187,500 |
|
$ |
140,625 |
|
$ |
105,469 |
|
|
Depreciation tax shield |
35 |
% |
$ |
87,500 |
|
$ |
65,625 |
|
$ |
49,219 |
|
$ |
36,914 |
|
|
|
|
|
Yr 5 |
|
|
Yr 6 |
|
|
Yr 7 |
|
|
Yr 8 |
|
|
|
Double declining dep |
|
|
$ |
79,102 |
|
$ |
79,102 |
|
$ |
79,102 |
|
$ |
79,102 |
|
|
Depreciation tax shield |
|
|
$ |
27,686 |
|
$ |
27,686 |
|
$ |
27,686 |
|
$ |
27,686 |
|
|
NPV |
$ |
287,506 |
|
|
|
|
|
|
|
|
|
|
|
|
AACSB: Knowledge Application
Accessibility: Keyboard Navigation
AICPA: BB Industry
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Blooms: Apply
Difficulty: 3 Hard
Topic: Annuities
Topic: Present Values
Topic: Taxes and Depreciation Tax Shields
Essay Questions
14. Annuity
Suppose the opportunity cost of capital is 10 percent and you have just won a $1 million lottery that entitles you to $100,000 at the end of each of the next ten years.
Required:
a. What is the minimum lump sum cash payment you would be willing to take now in lieu of the ten-year annuity?
b. What is the minimum lump sum you would be willing to accept at the end of the ten years in lieu of the annuity?
c. Suppose three years have passed and you have just received the third payment and you have seven left when the lottery promoters approach you with an offer to “settle-up for cash.” What is the minimum you would accept (the end of year three)?
d. How would your answer to part (a) change if the first payment came immediately (at t = 0) and the remaining payments were at the beginning instead of at the end of each year?
Feedback:
A. The minimum lump sum you should take is the present value of the cash payments.
|
PV |
= |
$100,000 × Annuity Factor (i = 0.10, t = 10) |
|
|
= |
$100,000 × 6.145 |
|
|
= |
$614,500 |
b. This question is essentially (a) in reverse. You are looking for the future value of the cash payments. Looking in the future value in arrears table, the annuity factor is 15.937.
|
PV |
= |
$100,000 × 15.937 |
|
|
= |
$1,593,700 |
c. This is similar to (a). This time, t = 7.
|
PV |
= |
$100,000 × Annuity Factor (i = 0.10, t = 7) |
|
|
= |
$100,000 × 4.868 |
|
|
= |
$486,800 |
d. To convert an end-of-year payment schedule to a beginning-of-year schedule, we need only multiply by 1 r. The minimum payment is $614,500 × 1.10 = $675,950.
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AICPA: BB Industry
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Blooms: Apply
Difficulty: 3 Hard
Topic: Annuities
Topic: Future Values
Topic: Opportunity Cost of Capital
Topic: Present Values
15. Identifying the Opportunity Cost of Capital
Don Phelps recently started a dry cleaning business. He would like to expand the business and have a coin-operated laundry also. The expansion of the building and the washing and drying machines will cost $100,000. The bank will lend the business $100,000 at 12 percent interest rate. Don could get a 10 percent interest rate loan if he uses his personal house as collateral. The lower interest rate reflects the increased security of the loan to the bank, because the bank could take Don’s home if he doesn’t pay back the loan. Don currently can put money in the bank and receive 6 percent interest.
Required:
Provide arguments for using 12 percent, 10 percent, and 6 percent as the opportunity cost of capital for evaluating the investment.
Feedback:
The 12 percent rate that the bank wants to charge without the security of the home mortgage probably best reflects the risk of the project. Therefore, the 12 percent interest rate is probably the most appropriate discount rate to use.
The 10 percent rate reflects the interest rate that Don Phelps would have to pay if he uses his personal house as collateral. This rate reflects the interest rate for Don’s total portfolio of assets including his house.
The 6 percent rate reflects the interest rate that Don receives in interest for his bank deposits. If Don decided to use his own cash and not borrow money for the investment, Don’s forgone opportunity of using the cash would be the 6 percent interest if no other investment were available.
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Blooms: Understand
Difficulty: 2 Medium
Topic: Opportunity Cost of Capital
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