Ch06tutoria 2o4b62

Tutorial 6

ing and the Time Value of Money

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E6-4 (Computation of Future Values and Present Values) Using the appropriate interest table, answer the following questions (each case is independent of the others).

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(a) What is the future value of 20 periodic payments of $4,000 each made at the beginning of each period and compounded at 8%? Answer

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Future value of an ordinary annuity of $4,000 a period for 20 periods at 8% Factor (1 + .08) Future value of an annuity due of $4,000 a period at 8%

X

$183,047.8 ($4,000 X 45.76196) 1.09 $197,691.66

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(b) What is the present value of $2,500 to be received at the beginning of each of 30 periods, discounted at 10% compound interest? Answer Present value of an ordinary annuity of $2,500 for 30 periods at 10% Factor (1 + .10) Present value of annuity due of $2,500 for 30 periods at 10%

$23,567.28 ($2,500 X 9.42691) X 1.10

$25,924.00 (Or see Table 6-5 which gives $25,924.03)

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(c) What is the future value of 15 deposits of $2,000 each made at the beginning of each period and compounded at 10%? (Future value as of the end of the fifteenth period.) Answer Future value of an ordinary annuity of $2,000 a period for 15 periods at 10% Factor (1 + 10) Future value of an annuity due of $2,000 a period for 15 periods at 10%

$63,544.96 ($2,000 X 31.77248) X 1.10

$69,899.46

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(d) What is the present value of six receipts of $1,000 each received at the beginning of each period, discounted at 9% compounded interest? Answer Present value of an ordinary annuity of $1,000 for 6 periods at 9% Factor (1 + .09)

$4,485.92 ($1,000 X 4.48592) X 1.09

Present value of an annuity date of $1,000 for 6 periods at 9%

$4,889.65 (Or see Table 6-5)

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E6-7 (Computation of Bond Prices) What would you pay for a $50,000 debenture bond that matures in 15 years and pays $5,000 a year in interest if you wanted to earn a yield of: (a) 8%? Answer (a)

$50,000 X .31524

= $15,762.00

+ $5,000 X 8.55948

=

42,797.40

$58,559.40

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(b) 10%? Answer (b)

$50,000 X .23939

=

+ $5,000 X 7.60608

=

$11,969.5 0

38,030.40 $49,999.9 0

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(c) 12%? Answer (c)

$50,000 X .18270

=

+ $5,000 X 6.81086

=

$ 9,135.00

34,054,30 $43,189.3 0

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E6-12 (Analysis of Alternatives) The Black Knights Inc., a manufacturer of high-sugar, low-sodium, low-cholesterol TV dinners, would like to increase its market share in the Sunbelt. In order to do so, Black Knights has decided to locate a new factory in the Panama City area. Black Knights will either buy or lease a site depending upon which is more advantageous. The site location committee has narrowed down the available sites to the following three buildings. Building A: Purchase for a cash price of $600,000, useful life 25 years. Building B: Lease for 25 years with annual lease payments of $69,000 being made at the beginning of the year. Building C: Purchase for $650,000 cash. This building is larger than needed; however, the excess space can be sublet for 25 years at a net annual rental of $7,000. Rental payments will be received at the end of each year. The Black Knights Inc. has no aversion to being a landlord. Instructions In which building would you recommend that The Black Knights Inc. locate, assuming a 12% cost of funds?

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Answer Building A—PV = $600,000. Building B— Rent X (PV of annuity due of 25 periods at 12%) = PV $69,000 X 8.78432 = PV $606,118.08 = PV Building C— Rent X (PV of ordinary annuity of 25 periods at 12%) = PV $7,000 X 7.84314 = PV $54,901.98 = PV Cash purchase price of

$650,000.00

PV of rental income

– 54,901.98

Net present value

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$595,098.02

Answer: Lease Building C since its present value of its net cost is the  smallest.

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E6-19 (Computation of Bond Liability) Your client, Faith Hill Inc., has acquired Tracy Lawrence Manufacturing Company in a business combination that is to be ed for as a purchase transaction (at fair market value). Along with the assets and business of Tracy Lawrence, Faith Hill assumed an outstanding debenture bond issue having a principal amount of $8,000,000 with interest payable semiannually at a stated rate of 8%. Tracy Lawrence received $7,300,000 in proceeds from the issuance 5 years ago. The bonds are currently 20 years from maturity. Equivalent securities command a 12% rate of interest, interest paid semiannually.

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Instructions Your client requests your advice regarding the amount to record for the acquired bond issue.

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Answer Time diagram: i = 6% per six months Principal $8,000,000 Interest P=?

$320,000

0 39

$320,000

1

$320,000

$320,000

$320,000

2

38

40 n = 40 six-month periods

Present value of the principal FV (PVF40, 6%) = $8,000,000 (.09722) Present value of the interest payments R (PVF–OA40, 6%) = $320,000 (15.04630) Total present value of bond liability

$

777,760

4,814,816 $5,592,576

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E6-24 (Determine Interest Rate) On July 17, 2000, Tim McGraw borrowed $42,000 from his grandfather to open a clothing store. Starting July 17, 2001, Tim has to make ten equal annual payments of $6,500 each to repay the loan. Instructions What interest rate is Tim paying?

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Answer

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10

?

N

I/YR.

8.85%

42,000

PV

6,500

PMT

0

FV

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P6-1 (Various Time Value Situations) Answer each of these unrelated questions. (a) On January 1, 2001, Rather Corporation sold a building that cost $250,000 and that had accumulated depreciation of $100,000 on the date of sale. Rather received as consideration a $275,000 non-interest-bearing note due on January 1, 2004. There was no established exchange price for the building, and the note had no ready market. The prevailing rate of interest for a note of this type on January 1, 2001, was 9%. At what amount should the gain from the sale of the building be reported?

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Answer

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(a) Given no established value for the building, the fair market value of the note would be estimated to value the building. Time diagram: i = 9% PV = ? FV = $275,000

1/1/01

1/1/02

1/1/03

1/1/04

n=3

Formula: PV = FV (PVFn, i) PV = $275,000 (PVF3, 9%) PV = $275,000 (.77218) PV = $212,349.50

Cash equivalent price of building Less book value ($250,000 – $100,000) Gain on disposal of the building

$212,349.50 150,000.00 $ 62,349.50

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(b) On January 1, 2001, Rather Corporation purchased 200 of the $1,000 face value, 9%,10-year bond of Walters Inc. The bonds mature on January 1, 2011, and pay interest annually beginning January 1, 2002. Rather Corporation purchased the bonds to yield 11%. How much did Rather pay for the bonds?

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Answer (b) Time diagram: i = 11% Principal $200,000 Interest PV–OA = ?

$18,000

$18,000

$18,000

$18,000

1/1/01

1/1/02

1/1/03

1/1/2010 1/1/2011 n = 10 PROBLEM 6-1 (Continued) Present value of the principal FV (PVF10, 11%) = $200,000 (.35218)

=$

70,436.00

Present value of the interest payments R (PVF–OA10, 11%) = $18,000 (5.88923) Combined present value (purchase price)

=

106,006.14 $176,442.14

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(c) Rather Corporation bought a new machine and agreed to pay for it in equal annual installments of $4,000 at the end of each of the next 10 years. Assuming that a prevailing interest rate of 8% applies to this contract, how much should Rather record as the cost of the machine? Answer (a)

Time diagram: i = 8% PV–OA = ?

$4,000

$4,000

$4,000

$4,000

0 8

$4,000

9

1 10 n = 10

Formula: PV–OA = R (PVF–OAn,i) PV–OA = $4,000 (PVF–OA10, 8%) PV–OA = $4,000 (6.71008) PV–OA = $26,840.32 (cost of machine)

2

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(d) Rather Corporation purchased a special tractor on December 31, 2001. The purchase agreement stipulated that Rather should pay $20,000 at the time of purchase and $5,000 at the end of each of the next 8 years. The tractor should be recorded on December 31, 2001, at what amount, assuming an appropriate interest rate of 12%? Answer (d) Time diagram: i = 12% PV–OA = ? $20,000 $5,000

5

$5,000

$5,000

$5,000

$5,000

$5,000

$5,000

$5,000

0 6

1 7

2 8 n=8

Formula: PV–OA = R (PVF–OAn,i) PV–OA = $5,000 (PVF–OA8, 12%) PV–OA = $5,000 (4.96764) PV–OA = $24,838.20 Cost of machine = $20,000 + $24,838.20 = $44,838.20

3

4

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(e) Rather Corporation wants to withdraw $100,000 (including principal) from an investment fund at the end of each year for 9 years. What should be the required initial investment at the beginning of the first year if the fund earns 11%? Answer (e) Time diagram: i = 11% PV–OA = ? $100,000

$100,000

$100,000

$100,000

0 8

1

9 n=9 Formula: PV–OA = R (PVF–OAn, i) PV–OA = $100,000 (PVF–OA9, 11%) PV–OA = $100,000 (5.53705) PV–OA = $553,705

2

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P6-3 (Investment Problem) Mack Aroni, a bank robber, is worried about his retirement. He decides to start a savings . Mack deposits annually his net share of the "loot," which consists of $75,000 per year, for 3 years beginning January 1, 2001. Mack is arrested on January 4, 2003 (after making the third deposit), and spends the rest of 2003 and most of 2004 in jail. He escapes in September of 2004. He resumes his savings plan with semiannual deposits of $30,000 each beginning January 1, 2005. Assume that the bank's interest rate was 9% compounded annually from January 1, 2001, through January 1, 2004, and 12% annual rate compounded semiannually thereafter.

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(Instructions) When Mack retires on January 1, 2008 (6 months after his last deposit), what is the balance in his savings ?

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Answer Time diagram: FV–OA = ? i = 6% per six months

i = 9% per year

$75,000 $75,000 $30,000

1/1/01 1/1/07

$75,000

$30,000

$30,000

$30,000

$30,000

$30,000

1/1/02

1/1/03

1/1/04

1/1/05

1/1/06

1/1/08

This problem can be solved more easily by first computing the future value of the $75,000 payments and adding to it the future value of the $30,000 payments. Future value of $75,000 annuity due on 1/1/04 $75,000 X (Future value of an ordinary annuity for 3 periods at 9% X 1.09) $75,000 X (3.27810 X 1.09) $75,000 X 3.57313 $267,984.75 Future value of $267,984.75 on 1/1/08 FV = $267,984.75 (FVF8, 6%) FV = $267,984.75 (1.59385) FV = $427,127.49 Future value of $30,000 annuity due on 1/1/01 $30,000 X (Future value of an ordinary annuity for 6 periods at 6% X 1.06) $30,000 X (6.97532 X 1.06) $30,000 X 7.39384 FV = $221,815.20 Future value of $267,984.75 on 1/1/08 Future value of $30,000 annuity due on 1/1/08

$427,127.49 221,815.20 $648,942.69

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P6-7 (Analysis of Alternatives) Sally Brown died, leaving to her husband Linus an insurance policy contract that provides that the beneficiary (Linus) can choose any one of the following four options.

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(a) $55,000 immediate cash. (b) $3,700 every 3 months payable at the end of each quarter for 5 years. (c) $18,000 immediate cash and $1,600 every 3 months for 10 years, payable at the beginning of each 3-month period. (d) $4,000 every 3 months for 3 years and $1,200 each quarter for the following 25 quarters, all payments payable at the end of each quarter.

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Instructions If money is worth 2'/z% per quarter, compounded quarterly, which option would you recommend that Linus exercise?

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Answer (a)

The present value of $55,000 cash paid today is $55,000.

(b)

Time diagram: i = 2½% per quarter PV–OA = ?

$3,700

$3,700

0

R= $3,700

$3,700

$3,700

1

2 n = 20 quarters

Formula: PV–OA = R (PVF–OAn, i) PV–OA = $3,700 (PVF–OA20, 2½%) PV–OA = $3,700 (15.58916) PV–OA = $57,679.89

18

19

20

(b)

Time diagram: i = 2½% per quarter $18,000 PV–AD = R = $1,600

$1,600

$1,600

$1,600

$1,600

0

1

2 n = 40 quarters

38

39

Formula: PV–AD = R (PVF–ADn, i) PV–AD = $1,600 (PVF–AD40, 2½%) PV–AD = $1,600 (25.73034) PV–AD = $41,168.54 The present value of option (c) is $18,000 + $41,168.54, or $59,168.54.

40

(b)

Time diagram: i = 2½% per quarter PV–OA =

R=

?

$1,200

$1,200

$1,200

$1,200 PV–OA = ?

R= $4,000

0 13 14 n = 12 quarters

$4,000

1

$4,000

11 36

12 37 n = 25 quarters

Formulas: PV–OA = R (PVF–OAn,i) PV–OA = R (PVF–OAn,i) PV–OA = $4,000 (PVF–OA12, 2½%) PV–OA = $1,200 (PVF–OA37–12, 2½%) PV–OA = $4,000 (10.25776) PV–OA = $1,200 (23.95732 – 10.25776) PV–OA = $41,031.04 PV–OA = $16,439.47

The present value of option (d) is $41,031.04 + $16,439.47, or $57,470.51. Present values: (a) $55,000. (b) $57.679.89. (c) $59,168.54. (d) $57,470.51. Option (c) is the best option, based upon present values alone.

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P6-9 (Purchase Price of a Business) During the past year, Nicole Bobek planted a new vineyard on 150 acres of land that she leases for $27,000 a year. She has asked you as her ant to assist her in determining the value of her vineyard operation.

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The vineyard will bear no grapes for the first 5 years (1-5). In the next 5 years (6-10), Nicole estimates that the vines will bear grapes that can be sold for $60,000 each year. For the next 20 years (11-30) she expects the harvest will provide annual revenues of $100,000. But during the last 10 years (31-40) of the vineyard's life she estimates that revenues will decline to $80,000 per year.

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During the first 5 years the annual cost of pruning, fertilizing, and caring for the vineyard is estimated at $9,000; during the years of production, 6-40; these costs will rise to $10,000 per year. The relevant market rate of interest for the entire period is 12%. Assume that all receipts and payments are made at the end of each year.

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Instructions Dick Button has offered to buy Nicole’s vineyard business by assuming the 40-year lease. On the basis of the current value of the business what is the minimum price Nicole should accept?

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Answer

Time diagram: i = 12% PV–OA = ? R = 23,000 $63,000 $63,000

($36,000) $63,000 $63,000 $43,000

0 10

11 12

29

1 30 31

($36,000) $23,000 $43,000 $43,000

5 39 40

n=5

n=5

n = 20

(0 – $27,000 – $9,000)

($60,000 – $27,000 – $10,000)

($100,000 – $27,000 – $10,000)

6

Formulas: PV–OA = R (PVF–OAn, i) PV–OA = R (PVF–OAn, i) PV–OA = R (PVF–OAn, i) PV–OA =R (PVF–OAn, i) PV–OA = ($36,000)(PVF–OA5, 12%) PV–OA = $23,000 (PVF–OA10-5, 12%) PV–OA = $63,000 (PVF–OA30–10, 12%) PV–OA = $43,000 (PVF–OA40–30, 12%) PV–OA = ($36,000)(3.60478) PV–OA = $23,000 (5.65022–3.60478) PV–OA = $63,000 (8.05518–5.65022) PV–OA = $43,000 (8.24378–8.05518) PV–OA =($129,772.08) PV–OA = $23,000 (2.04544) PV–OA = $63,000 (2.40496) PV–OA = $43,000 (.18860) PV–OA = $47,045.12 PV–OA = $151,512.48 PV–OA = $8,109.80 Present value of future net cash inflows: $(129,772.08) 47,045.12 151,512.48 $

8,109.80 76,895.32

Nicole Bobek should accept no less than $76,895.32 for her vineyard business.

n = 10

($80,000 – $27,00 $10,000)

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ETHICS CASE

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James Qualls, newly appointed controller of KBS, is considering ways to reduce his company's expenditures on annual pension costs. One way to do this is to switch KBS's pension fund assets from First Security to NET Life. KBS is a very well-respected computer manufacturer that recently has experienced a sharp decline in its financial performance for the first time in its 25-year history. Despite financial problems, KBS still is committed to providing its employees with good pension and postretirement health benefits.

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Under its present plan with First Security, KBS is obligated to pay $43 million to meet the expected value of future pension benefits that are payable to employees as an annuity upon their retirement from the company. . On the other hand NET Life requires KBS to pay only $35 million for identical future pension benefits. First Security is one of the oldest and most reputable insurance companies in North America. NET Life has a much weaker reputation in the insurance industry. In pondering the significant difference in annual pension costs, Qualls asks himself, "Is this too good to be true?" (c) Who are the stakeholders that could be affected by Qualls's decision?

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Instructions Answer the following questions: (a) Why might NET Life's pension cost requirement be $8 million less than First Security's requirement for the same future value? Answer The time value of money would suggest that NET Life’s discount rate was substantially lower than First Security’s. The actuaries at NET Life are making different assumptions about inflation, employee turnover, life expectancy of the work force, future salary and wage levels, return on pension fund assets, etc. NET Life may operate at lower gross and net margins and it may provide fewer services.

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(b) What ethical issues should James Qualls consider before switching KBS's pension fund assets?

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(B) As the controller of KBS, Qualls assumes a fiduciary responsibility to the present and future retirees of the corporation. As a result, he is responsible for ensuring that the pension assets are adequately funded and are adequately protected from most controllable risks. At the same time, Qualls is responsible for the financial condition of KBS. In other words, he is obligated to find ethical ways of increasing the profits of KBS, even if it means switching pension funds to a less costly plan. At times, Qualls’ role to retirees and his role to the corporation can be in conflict, especially if Qualls is a member of a professional group such as As or CMAs.

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(c) Who are the stakeholders that could be affected by Qualls's decision?

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Answer  (a)

If KBS switched to NET Life

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The primary beneficiaries of Qualls’ decision would be the corporation and its many stockholders by virtue of reducing 8 million dollars of annual pension costs.

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The present and future retirees of KBS may be negatively affected by Qualls’ decision because the change of losing a future benefit may be increased by virtue of higher risks (as reflected in the discount rate and NET Life’s weaker reputation).

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If KBS stayed with First Security

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In the short run, the primary beneficiaries of Qualls’ decision would be the employees and retirees of KBS given the lower risk pension asset plan.

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KBS and its many stakeholders could be negatively affected by Qualls’ decision to stay with First Security because of the company’s inability to trim 8 million dollars from its operating