Solution manual intermediate accounting 7th by nelson spiceland ch06

Monetary assets and monetary liabilities represent cash or fixed claims/commitments to receive/pay cash in the future and are valued at the present value of these fixed cash flows.. Ques

Monetary assets and monetary liabilities represent cash or fixed claims/commitments to

receive/pay cash in the future and are valued at the present value of these fixed cash flows All other assets and liabilities are nonmonetary

Question 6-7

An annuity is a series of equal-sized cash flows occurring over equal intervals of time

Question 6-8

An ordinary annuity exists when the cash flows occur at the end of each period In an annuity

due the cash flows occur at the beginning of each period

Question 6-9

Table 2 lists the present value of $1 factors for various time periods and interest rates The factors in Table 4 are simply the summation of the individual PV of $1 factors from Table 2

QUESTIONS FOR REVIEW OF KEY TOPICS

Answers to Questions (continued)

PVA = Annuity amount x Ordinary annuity factor

Solving for the annuity amount,

Annuity amount = Ordinary annuity factor PVA

The annuity factor can be obtained from Table 4 at the intersection of the 8% column and 5 period row

Question 6-14

Annuity amount = 3.99271 $500

Annuity amount = $125.23

Answers to Questions (concluded)

Question 6-15

Companies frequently acquire the use of assets by leasing rather than purchasing them Leases usually require the payment of fixed amounts at regular intervals over the life of the lease Certain long-term, noncancelable leases are treated in a manner similar to an installment sale by the lessor and an installment purchase by the lessee In other words, the lessor records a receivable and the lessee records a liability for the several installment payments For the lessee, this requires that the leased asset and corresponding lease liability be valued at the present value of the lease payments

Brief Exercise 6-1

Fran should choose the second investment opportunity More rapid compounding has the effect of increasing the actual rate, which is called the effective rate, at which money grows per year For the second opportunity, there are four, three-month periods paying interest at 2% (one-quarter of the annual rate) $10,000 invested will grow to $10,824 ($10,000 x 1.0824*) The effective annual interest rate, often referred

to as the annual yield, is 8.24% ($824 ÷ $10,000), compared to just 8% for the first opportunity

* Future value of $1: n=4, i=2% (from Table 1)

PVA factor, n=7, i=7% = 5.38929

– PVA factor, n=2, i=7% = 1.80802

= PV factor for deferred annuity = 3.58127

Brief Exercise 6-12

PV = $6,000,0001 (12.40904* ) + 100,000,000 (.13137** )

PV = $74,454,240 + 13,137,000 = $87,591,240 = price of the bonds

1 $100,000,000 x 6% = $6,000,000

* Present value of an ordinary annuity of $1: n=30, i=7% (from Table 4)

** Present value of $1: n=30, i=7% (from Table 2)

Brief Exercise 6-13

PVAD = $55,000 (7.24689* ) = $398,579 = Liability

* Present value of an annuity due of $1: n=10, i=8% (from Table 6)

* Present value of an ordinary annuity of $1: n=20, i=2% (from Table 4)

5 years x 4 quarters = 20 periods 8% ÷ 4 quarters = 2%

Exercise 6-15

PV = $12,000,0001 (17.15909* ) + 300,000,000 (.14205** )

PV = $205,909,080 + 42,615,000 = $248,524,080 = price of the bonds

1 $300,000,000 x 4 % = $12,000,000

* Present value of an ordinary annuity of $1: n=40, i=5% (from Table 4)

** Present value of $1: n=40, i=5% (from Table 2)

PVA factor, n=8, i=10% = 5.33493

– PVA factor, n=2, i=10% = 1.73554

= PV factor for deferred annuity = 3.59939

i 4 Simple interest d The amount of money that a dollar will grow to

k 5 Annuity e Amount of money paid/received in excess of amount

l 6 Present value of a single f Obligation to pay a sum of cash, the amount of

c 7 Annuity due g Money can be invested today and grow to a larger

h 11 Nonmonetary asset k A series of equal-sized cash flows

g 12 Time value of money l Amount of money required today that is equivalent to

f 13 Monetary liability m Claim to receive a fixed amount of money

Exercise 6-20

1 a An annuity is a series of cash flows or other economic benefits occurring at

fixed intervals, ordinarily as a result of an investment Present value is the

value at a specified time of an amount or amounts to be paid or received later, discounted at some interest rate In an annuity due, the payments occur at the beginning, rather than at the end, of the periods Thus, the present value of an annuity due includes the initial payment at its undiscounted amount This lease should be evaluated using the present value of an annuity due

2 d Both future value tables will be used because the $75,000 already in the account

will be multiplied times the future value factor of 1.26 to determine the amount

3 years hence, or $94,500 The three payments of $4,000 represent an ordinary annuity Multiplying the three-period annuity factor (3.25) by the payment amount ($4,000) results in a future value of the annuity of $13,000 Adding the two elements together produces a total account balance of $107,500

Problem 6-1

Choose the option with the lowest present value of cash outflows, net of the present value of any cash inflows (Cash outflows are shown as negative amounts; cash inflows as positive amounts)

Machine A:

PV = – $48,000 – 1,000 (6.71008* ) + 5,000 (.46319** )

* Present value of an ordinary annuity of $1: n=10, i=8% (from Table 4)

** Present value of $1: n=10, i=8% (from Table 2)

3 PVAD = $120,000 (9.36492* ) = $1,123,790 = Lease liability

* Present value of an annuity due of $1: n=20, i=10% (from Table 6)

PROBLEMS

* Present value of $1: n=5, i=8% (from Table 2)

Harding should choose option 2

* Present value of an ordinary annuity of $1: n=6, i=10% (from Table 4)

** Present value of $1:, i=10% (from Table 2)

PV = $718,838 < $800,000

Since the PV is less than $800,000, the restaurant should not be purchased

Annuity amount = Annuity factor PVA

Annuity amount = $10,000 = $1,558 = Payment

6.41766*

* Present value of an ordinary annuity of $1: n=10, i=9% (from Table 4)

Problem 6-7

Requirement 1

Annuity amount = Annuity factor PVA

Annuity amount = $250,000 = $78,868 = Payment

* Present value of an ordinary annuity of $1: n=4, i=10% (from Table 4)

Requirement 2

Annuity amount = Annuity factor PVA

Annuity amount = $250,000 = $62,614 = Payment

* Present value $1: n= 3, i= 10% (from Table 2)

Present value of all payments:

PVA factor, n=6, i=10% = 4.35526

– PVA factor, n=3 i=10% = 2.48685

= PV factor for deferred annuity = 1.86841**

Requirement 2

$136,907 x 10% = $13,691 = Interest in the year 2006

* Present value of $1: n=9, i=7% (from Table 2)

John should choose alternative 3

Or, alternatively (for 3):

PV = $50,000 (3.82037* ) = $191,019

(difference due to rounding)

From Table 4,

PVA factor, n=19, i=7% = 10.33560

– PVA factor, n=9, i=7% = 6.51523

= PV factor for deferred annuity = 3.82037*

or, From Table 6,

PVAD factor, n=20, i=7% = 11.33560

— PVAD factor, n=10, i=7% = 7.51523

= PV factor for deferred annuity = 3.82037*

Problem 6-10

PV = $20,000 (3.79079* ) + 100,000 (.62092** ) = $137,908

* Present value of an ordinary annuity of $1: n=5, i=10% (from Table 4)

** Present value of $1: n=5, i=10% (from Table 2)

The note payable and corresponding merchandise should be recorded at $137,908

Problem 6-11

Requirement 1

PVAD = Annuity amount x Annuity factor

Annuity amount = Annuity factor PVAD

Annuity amount = $800,000

7.24689*

* Present value of an annuity due of $1: n=10, i=8% (from Table 6)

Annuity amount = $110,392 = Lease payment

Requirement 2

Annuity amount = $800,000

6.71008*

* Present value of an ordinary annuity of $1: n=10, i=8% (from Table 4)

Annuity amount = $119,224 = Lease payment

Requirement 3

PVAD = (Annuity amount x Annuity factor) + PV of residual

Annuity amount = PVAD – PV of residualAnnuity factor

PV of residual = $50,000 x 46319* = $23,160

* Present value of $1: n=10, i=8% (from Table 2)

Annuity amount = $800,000 – 23,160

7.24689*

* Present value of an annuity due of $1: n=10, i=8% (from Table 6)

Annuity amount = $107,196 = Lease payment

Problem 6-12

Requirement 1

PVA = Annuity amount x Annuity factor

Annuity amount = Annuity factor PVA

Annuity amount = $800,000

7.36009*

* Present value of an ordinary annuity of $1: n=10, i=6% (from Table 4)

Annuity amount = $108,694 = Lease payment

Requirement 2

Annuity amount = $800,000

15.32380*

* Present value of an annuity due of $1: n=20, i=3% (from Table 6)

Annuity amount = $52,206 = Lease payment

Requirement 3

Annuity amount = $800,000

44.9550*

* Present value of an ordinary annuity of $1: n=60, i=1% (given)

Annuity amount = $17,796 = Lease payment

Problem 6-13

Choose the option with the lowest present value of cash outflows, net of the present value of any cash inflows (Cash outflows are shown as negative amounts; cash inflows as positive amounts)

PV = - $160,000 - 5,000 (5.65022* ) + 10,000 (.32197** )

* Present value of an ordinary annuity of $1: n=10, i=12% (from Table 4)

** Present value of $1: n=10, i=12% (from Table 2)

PV = - $160,000 - 28,251 + 3,220

PV = - $185,031

PVAD = - $25,000 (6.32825* ) = - $158,206

* Present value of an annuity due of $1: n=10, i=12% (from Table 6)

Kiddy Toy should lease the machine

Tinkers 7.54879 (n=17) - 1.71252 (n=2) = 5.83627

Evers 7.70162 (n=18) - 2.44371 (n=3) = 5.25791

Chance 7.83929 (n=19) - 3.10245 (n=4) = 4.73684

Total present value $533,756

Amount of annual contribution:

FVAD = Annuity amount x Annuity factor

Annuity amount = Annuity factor FVAD

Annuity amount = $533,756 = $143,881

3.7097*

* Future value of an annuity due of $1: n=3, i=11% (from Table 5)

Analysis Case 6-1

The settlement was determined by calculating the present value of lost future income ($200,000 per year)1 discounted at a rate which is expected to approximate the time value of money In this case, the discount rate, i, apparently is 7% and the number of periods, n, is 25 (the number of years to John’s retirement) John’s settlement was calculated as follows:

$200,000 x 11.65358* = $2,330,716

annuity

amount

* Present value of an ordinary annuity of $1: n=25, i=7% (from Table 4)

Note: In the actual case, John’s present salary was increased by 3% per year to reflect future salary increases

CASES

* Present value of $1: n=2, i=6% (from Table 2)

Sally should choose alternative 3

Or, alternatively (for 3):

PV = $22,000 (2.37897* ) = $52,337

From Table 4,

PVA factor, n=5, i=6% = 4.21236

– PVA factor, n=2, i=6% = 1.83339

= PV factor for deferred annuity = 2.37897*

or, From Table 6,

PVAD factor, n=6, i=6% = 5.21236

– PVAD factor, n=3, i=6% = 2.83339

= PV factor for deferred annuity = 2.37897*

Communication Case 6-3

Suggested Grading Concepts and Grading Scheme:

Content (65%)

25 Explanation of the method used (present value) to

compare the two contracts

30 Presentation of the calculations

49ers PV = $6,989,065 Cowboys PV = $6,492,710 10 Correct conclusion

65 points

Writing (35%)

5 Proper letter format

6 Terminology and tone appropriate to the audience of

a player's agent

12 Organization permits ease of understanding

_ Introduction that states purpose

_ Paragraphs that separate main points

Ethics Case 6-4

The ethical issue is that the 21% return implies an annual return of 21% on an investment and misrepresents the fund’s performance to all current and future stakeholders Interest rates are usually assumed to represent an annual rate, unless otherwise stated Interested investors may assume that the return for $100 would be

$21 per year, not $21 over two years The Damon Investment Company ad should explain that the 21% rate represented appreciation over two years

Judgment Case 6-5

Purchase price of new machine $150,000

Sales price of old machine (100,000)

Incremental cash outflow required $ 50,000

The new machine should be purchased if the present value of the savings in operating costs of $8,000 ($18,000 - 10,000) plus the present value of the salvage value of the new machine exceeds $50,000

PV = ($8,000 x 3.99271* ) + ($25,000 x 68058** )

PV = $31,942 + 17,015

PV = $48,957

* Present value of an ordinary annuity of $1: n=5, i=8% (from Table 4)

** Present value of $1: n=5, i=8% (from Table 2)

The new machine should not be purchased

Real World Case 6-6

* Present value of $1: n= 40, i= ? (from Table 2, i = 2%)

The effective, semiannual interest rate is 2%

We could also solve for the annual rate using the increase in the carrying value of the bonds:

Accretion (interest expense) $23, 619

$23,619 ÷ $584,472 = approximately 4% annual rate

Requirement 2

Using a 2% effective semiannual rate and 40 periods:

PV = $1,000 (.45289* ) = $452.89

* Present value of $1: n=40, i=2% (from Table 2)

The issue price of one, $1,000 maturity value bond was $452.89

Analysis Case 6-7

Requirement 1

The following liabilities are valued using the time value of money concept:

— Long-term debt (Note 6)