FCF 9th Edition Chapter 06

Chapter 6Problems 1-78Input boxes in tan Output boxes in yellow Given data in blue Calculations in red Answers in green NOTE: Some functions used in these spreadsheets may require that the "Analysis ToolPak" or "Solver Add-In" be installed in Excel. To install these, click on the Office button then "Excel Options," "Add-Ins" and select "Go." Check "Analyis ToolPak" and "Solver Add-In," then click "OK."

require that

Chapter 6Question 1 Input area: Output area:

Discount rate

10%

Year Cash flow 1 $ 950 2 1,040 3 1,130 4 1,075 $ 3,306.37

Chapter 6Question 2 Input area:

Discount rate # of years for X # of years for Y Payment for X Payment for Y $

5% 9 6 6,000 8,000

Output area:

Value of X Value of Y

$ 42,646.93 $ 40,605.54


Discount rate

8%

Year Cash flow 1 $ 940 2 1,090 3 1,340 4 1,405 $ 5,307.71


Payment per year # of years Required rate of return

$

5,300 15 7%

Output area:

Present value PV (forever)

$ 48,271.94 $ 75,714.29


Initial investment $ Interest rate on annuity # of years

34,000 7.65% 15

Output area:

Annuity payment

$

3,887.72


Annual savings # of years Interest rate on annuity

$

73,000 8 8.5%

Output area:

Present value

$ 411,660.36


Annual deposit # of years Interest rate on annuity

$

4,000 20 11.2%

Output area:

Future value

$

262,781.16


Desired amount # of years Interest rate

$

90,000 10 6.8%

Output area:

Annual deposit

$

6,575.77


Desired amount # of years Interest rate

$

50,000 7 7.50%

Output area:

Loan payment

$

9,440.02

Chapter 6Question 10,11 Input area:

Desired amount Interest rate Cost of policy

$

25,000 7.20% 375,000

$

Output area:

Present value Required interest rate

$ 347,222.22 6.67%


Stated rate (APR) # of times per year 8% 4 16% 12 12% 365 15% Infinite

Effective rate 8.24% 17.23% 12.75% 16.18%


Stated rate (APR) # of times per year 8.42% 2 18.20% 12 8.99% 52 15.27% Infinite

Effective rate 8.60% 19.80% 9.40% 16.50%


First National Bank First United Bank

Stated rate (APR) # of times per year 14.2% 12 14.5% 2

Effective rate 15.16% 15.03%


Stated rate (APR) 14.85%

# of times per year 365

Effective rate 16%

The borrower is actually paying annualized interest of 16% per year, not the 14.85% reported on the loan contract.


Deposit # of years Interest rate # of times compounded per year

$

2,100 17 8.4% 2

Output area:

Future value

$8,505.93


Interest rate # of times compounded per year Deposit # of years

$

9.30% 365 4,500 5

Output area:

Future value

$7,163.64


Future value of investment # of years Discount rate # of times compounded per year

$

58,000 7 10% 365

Output area:

Present value of investment

$28,804.71


Interest rate Compounding periods

30% 12

Output area:

APR EAR

360.00% 2229.81%


Future value of investment Discount rate # of years # of times compounded per year

$

68,500 6.9% 5 12

Output area:

Payment Effective interest rate

$

1,353.15 7.12%


Monthly payment Discount rate Current balance

$ $

500 1.3% 18,000.00

Output area:

# of months until paid off

48.86


Present value Future value

$ $

3 4

Output area:

Interest rate per week APR EAR

33.33% 1733.33% 313916515.69%


Monthly payment Contract price

$ $

1,800 95,000

Output area:

Monthly return APR EAR

1.89% 22.74% 25.26%


Monthly deposit # of times compounded per year Interest rate on annuity # of years

$

300 12 10% 30

Output area:

Future value of annuity

$ 678,146.38


Annual deposit # of times compounded per year Interest rate on annuity # of years

$

3,600 12 10% 30

Output area:

EAR Future value of annuity

10.47% $ 647,623.45


Quarterly withdrawal # of times compounded per year # of years Interest rate per quarter

$

2,300 4 4 0.65%

Output area:

Amount needed today

$

34,843.71


Discount rate # of times compounded

11% 4

Year Cash flow 1 $ 725 2 980 3 0 4 1,360 $2,320.36 EAR 11.46%


Discount rate

8.45%

Year Cash flow 1 $ 1,650 2 0 3 4,200 4 2,430 $ 6,570.86


Interest rate # of years

7% 10

Output area:

First Complex Bank interest rate

5.45%


Effective annual rate # of times compounded

17% 12

Output area:

APR Effective rate per period

15.80% 1.32%


Interest rate first six months Interest rate thereafter # of times compounded Balance transferred $

1.50% 18% 12 5,000

Output area:

Accrued interest

$ 508.35


Monthly stock investment Monthly bond investment Stock return Bond return Years to save Retirement return Retirement years

$ $

700 300 11% 6% 30 9% 25

Output area:

FV of stock account FV of bond account Total account FV Monthly withdrawal

$ 1,963,163.82 $ 301,354.51 $ 2,264,518.33 $ 19,003.76


Interest per month 1.17% 1.17%

# of years 1 2 $

Amount invested 1 1

Future value $1.15 $1.32


Amount needed Years to save Return Years to wait before beginning

$ 1,000,000 40 12% -

Output area:

Monthly deposit starting now

$

85.00


Present value Future value Number of periods

$ $

1 3 1

Output area:

Effective annual rate Annual percentage rate Quarterly return

200.00% 126.43% 31.61%


Amount per year in option 1 Amount per year in option 2 Signing bonus in option 2 Interest rate # of times compounded per year

$ $

95,000 70,000 45,000 10% 12

Output area:

EAR Present value of option 1 Present value of option 2 $ $

10.47% 163,839.09 165,723.54


Payment today Length of payments Annual increase Return

$

1,000,000 30 5% 8%

Output area:

Present value of future payments

$

19,016,563.18


Current salary Percent of salary to deposit Return Salary increase Deposit length

$

50,000 5% 11% 4% 40

Output area:

Next year's salary Next year's deposit Present value deposits Future value of deposits

$ $ $ $

52,000 2,600 34,399.45 2,235,994.31


# of years Annuity payment per year Interest rate

$

15 9,000 15%

Output area:

Value of investment

$ 52,626.33

Present value falls as r increases, and rises as r decreases. Future value rises as r increases, and falls as r decreases.


Monthly payment Interest rate Future value of account

$ $

340.00 6% 20,000

Output area:

Number of payments

51.69


Price of sailboat Monthly payment Number of months

$ $

73,000 1,450 60

Output area:

Monthly rate APR

0.594% 7.13%


Number of years Price of house APR Monthly payment

$ $

30 240,000 6.35% 1,150

Output area:

Present value of payments Remaining principal Balloon payment

$ 184,817.42 $ 55,182.58

$ 368,936.54


PV of cash flows Year 1 2 3 4 Discount rate

$ $ $ $ $

6,550 Cash flow 1,700 2,100 2,800 10%

Output area:

Year 1 2 3 4 Total PV of missing CF Value of missing CF

$ $ $ $ $ $ $

PV 1,545.45 1,577.76 1,912.44 5,035.65 1,514.35 1,832.36


First payment $ Annual increase $ Discount rate

1,000,000 500,000 9%

Output area:

Year 0 $ 1 2 3 4 5 6 7 8 9 10 Present value

Payments 1,000,000 1,500,000 2,000,000 2,500,000 3,000,000 3,500,000 4,000,000 4,500,000 5,000,000 5,500,000 6,000,000

$ $ $ $ $ $ $ $ $ $ $ $

Present Value 1,000,000.00 1,376,146.79 1,683,359.99 1,930,458.70 2,125,275.63 2,274,759.85 2,385,069.31 2,461,654.10 2,509,331.40 2,532,352.79 2,534,464.84 22,812,873.40


Number of years Percentage of pruchase price Price of warehouse Monthly payment

$ $

30 80% 2,900,000 15,000

Output area:

Amount of loan Interest rate per month APR EAR

$

2,320,000 0.560% 6.72% 6.93%


Selling price # of years until sale Production cost Discount rate

$ $

165,000 4 94,000 13.0%

Output area:

Present value of sale Profit (loss) Breakeven rate

$ 101,197.59 $ 7,197.59 15.10%


Annual payment Discount rate Year of first payment Year of last payment

$

4,000 10% 8 25

Output area:

PV at beginning of payments Value today

$ $

32,805.65 16,834.48


Monthly payment # of years Interest rate 1 # of years Interest rate 2 # of years

$ 1,500 15 11% 7 7% 8

Output area:

Value today of interest rate 1 payments Value of interest rate 2 payments at rate change Value today of interest rate 2 payments Total present value of the annuity

$ 87,604.36 $ 110,021.35 $ 51,120.33 $ 138,724.68


Investment A: # of years Monthly payment Interest rate Investment B: # of years Interest rate

$

15 1,200 8.50%

15 8%

Output area:

Future value of investment A Lump sum needed

$ $

434,143.62 130,761.55


Interest rate Year to find value Amount of payment Year of first perpetual payment

$

6.2% 7 3,500 15

Output area:

Present value of perpetual stream Present value at requested year

$ $

56,451.61 37,051.41


Quoted interest rate Amount borrowed Interest per year Monthly payment Periods/year

$ $ $

16% 25,000 4,000 2,416.67 12

Output area:

Monthly rate APR EAR

2.361% 28.33% 32.31%


# of years Amount of semiannual payment # of years until first payment Discount rate Compounding periods per year Year to find present value

$

5 7,000 8.50 10% 12 -

Output area:

Semiannual interest rate PV of annuity at year 8 Effective annual rate Present value at requested year

5.105% $ 53,776.72 10.47% $ 24,243.67


Annual payment # of years Discount rate

$

10,000 5 11%

Output area:

a) PV of ordinary annuity PV of annuity due b) FV of ordinary annuity FV of annuity due

$ 36,958.97 $ 41,024.46 $ 62,278.01 $ 69,128.60


Value of lease contract # of months APR

$

68,000 60 7.85%

Output area:

Monthly payment

$1,364.99


Loan amount Interest rate Loan term

$

42,000 8% 5

Output area:

Loan payment

$10,519.17 Total payment Interest paid $ 10,519.17 $ 3,360.00 10,519.17 2,787.27 10,519.17 2,168.71 10,519.17 1,500.68 10,519.17 779.20 $ 10,595.86

Year Beginning balance 1 $ 42,000.00 2 34,840.83 3 27,108.92 4 18,758.47 5 9,739.97 Total interest paid over life of loan =

Principal paid Ending balance $ 7,159.17 $ 34,840.83 7,731.90 27,108.92 8,350.46 18,758.47 9,018.49 9,739.97 9,739.97 -


Loan amount Interest rate Loan term

$

42,000 8% 5

Output area:

Loan payment

$8,400.00 Total payment Interest paid $ 11,760.00 $ 3,360.00 11,088.00 2,688.00 10,416.00 2,016.00 9,744.00 1,344.00 9,072.00 672.00 $ 10,080.00

Year Beginning balance 1 $ 42,000.00 2 33,600.00 3 25,200.00 4 16,800.00 5 8,400.00 Total interest paid over life of loan =

Principal paid Ending balance $ 8,400.00 $ 33,600.00 8,400.00 25,200.00 8,400.00 16,800.00 8,400.00 8,400.00 8,400.00 0.00


Years until retirement Monthly retirement income Years in retirement Years until cabin purchase Cabin price Inheritance Monthly savings for first years Pre-retirement EAR Retirement EAR

$

$ $ $

30 20,000 25 10 380,000 900,000 2,500 10% 7%

Output area:

Pre-retirement APR Retirement APR Savings value until cabin purchase Savings after cabin purchase FV of initial savings PV of retirement spending PV of inheritance Amount needed at retirement Retirement shortfall Savings needed per month $ $ $

9.57% 6.78% 499,659.64 119,659.64 805,010.23

$ 2,885,496.45 $ 165,824.26

$ 3,051,320.71 $ 2,246,310.48 $ 3,127.44


Years for lease Car price Payment today Monthly lease payment Loan rate Resale price

$ $ $ $

3 32,000 99 450 7% 23,000

Output area:

PV of lease payments PV of resale price PV of purchase You should the car since the PV is lower. Breakeven present value Breakeven resale price

$ $ $

14,672.91 18,654.82 13,345.18 Buy

$

17,327.09 $21,363.01


Year 0 1 2 3 4 5 6 Requested signing bonus Requested salary increase Interest rate Compunding periods

$ $ $ $ $ $ $ $ $

7,000,000 4,500,000 5,000,000 6,000,000 6,800,000 7,900,000 8,800,000 9,000,000 1,400,000 5.5% 365

Output area:

EAR PV of salary offer PV of salary with increase Effective quarterly interest rate Quarterly salary

5.65% $ 38,610,482.57 $ 40,010,482.57 1.384% $1,527,463.76


Amount of loan # of years APR

$

25,000 1 15%

Output area:

Amount received EAR

$ 21,250.00 17.65%


Salary for 2 years ago Last year's salary Future salary Years for future salary Pain and suffering Court costs EAR

$ $ $ $ $

47,000 50,000 55,000 5 100,000 20,000 8%

Output area:

APR Value 1 year ago of salary 2 years ago Value today of salary 2 yrs ago Value today of last year's salary Value of next 5 year's salary Total value awarded

7.72%

$ $ $ $

48,699.39 52,595.34 51,807.86 227,539.14

$ 451,942.34


Amount of loan # of years APR Points

$

10,000 1 8% 3%

Output area:

EAR

11.34%


Amount of loan # of years APR # of points

$

10,000 1 11% 2%

Output area:

EAR

13.27%

The effective rate is not affected by the loan amount, since it drops out when solving for R .


# of years Amount of loan Interest rate Fees

$ $

30 240,000 6.80% 2,300

Output area:

Refundable fee: Monthly payment Monthly interest APR EAR Nonrefundable fee: APR EAR

$

1,579.61 0.5745% 6.89% 7.12%

6.80% 7.02%


Amount of loan # of years Interest rate

$

1,000 3 14%

Output area:

Total repayment Monthly payment Monthly interest APR EAR

$ $

1,481.54 41.15 2.30% 27.61% 31.39%

It's called add-on interest because the interest amount of the loan is added to the principal amount of the loan before the loan payments are calculated.


# of years until retirement Annual withdrawal # of years to withdraw Interest rate Employer contribution Trust fund distribution Years until distribution

$

30 105,000 20 7% 1,500 150,000 20

$ $

Output area:

a. Present value of withdrawals Annual deposit until retirement b. Present value in lump sum c. Future value of trust fund deposit Total annual deposit necessary Friend's annual deposit

$ 1,112,371.50 $ $ $ $ $ 11,776.01 146,129.04 295,072.70 8,652.25 7,152.25


Amount of debt Interest rate on current card Interest rate on new card Planned monthly payment Transfer fee

$

$

10,000 19.8% 6.2% 200 2%

Output area:

# of months to pay off current card # of months to pay of new card Difference Amount of bill with fees # of months with fees $

106.50 57.99 48.51 10,200 59.35


Payout at retirement # of years until retirement Year 1 2 3 4 5 6 Interest rate 1 # of years Interest rate 2 # of years

$

500,000 65 Payment 900 900 1,000 1,000 1,100 1,100 12% 6 8% 59

$

Output area:

Year 1 2 3 4 5 6 Total value at year 6 Total value at year 65

Value at Year 6 $ 1,586.11 $ 1,416.17 $ 1,404.93 $ 1,254.40 $ 1,232.00 $ 1,100.00 $ 7,993.60 $ 749,452.56

The policy is not worth buying; the FV of the policy is less than the payout at retirement. We could also compare the PV of the two cash flows. If we compare the PV: Value of deposits Value of payment from insurance company $ 4,049.81

$

2,701.84

Either way, we still choose the same policy.


Amount of loan APR # of years # of years until balloon payment

$

750,000 8.1% 30 8

Output area:

Monthly payment # of payments left after balloon payment Total amount of balloon payment

$

5,555.61 264

$ 683,700.32


Annual payment # of years Annual payout # of years

$

9,000 6 20,000 4

$

Output area:

Year 1 2 3 4 5 6 7 8 9 10 Breakeven rate

$ $ $ $ $ $ $ $ $ $

Cash flow (9,000) (9,000) (9,000) (9,000) (9,000) (9,000) 20,000 20,000 20,000 20,000 8.07%


Plan X: Annual payment # of years Plan Y: Annual payout # of years

$

20,000 In perpetuity

$

28,000 20

Output area:

Discount rate needed

6.46%


Biannual payment APR Compunding periods b. Payments begin in (yrs)

$

15,000 10% 365 4

Output area:

a. EAR Effective 2-year rate Present value of perpetuity Value today b. Value today $ $ $

10.52% 22.14% 67,760.07 74,885.44 55,478.78


Present value of annuity =

$C + $C + + (1 + r) (1 + r)^2

$C (1 + r)^N

Present value of annuity due = $C +

$C ++ $C (1 + r) (1 + r)^(N-1) $C + + (1 + r) $C (1 + r)^N

Present value of annuity due = (1 + r)

= (1 + r) PVA Future value of annuity = $C + $C(1 + r) + $C(1 + r)2 + + $C(1 + r)N-1 Future value of annuity due = $C(1 + r) + $C(1 + r)2 + + $C(1 + r)N Future value of annuity due = (1 + r) ($C + $C(1 + r) + + $C(1 + r)N-1) = (1 + r) FVA


Years until retirement Next year's salary Salary growth rate Investment return Desired retirement value

40 40,000 3% 11% $ 2,000,000 $

Output area:

PV of retirement value Amount to save next year Pecentage of salary

$ 30,768.82 $ 2,591.56 6.48%


Weekly interest rate # of weeks c. Loan amount Loan proceeds Loan payments

$ $ $

7% 1 100 68.92 25.00

Output area:

a. APR EAR b. Weekly rate APR EAR c. Weekly rate APR EAR

364.00% 3272.53% 7.53% 391.40% 4253.98% 16.75% 871.00% 314215.72%

FCF 9th Edition Chapter 06

Documents

Transcript of FCF 9th Edition Chapter 06