Key Lab 6 Problems

1. SOLUTION: a., b., c. Connecticut Computer Company

10% Debt40% Debt75% Debt

Debt (TL)$ 10,000$ 40,000$ 75,000

Equity 90,000 60,000 25,000

Total Assets$100,000$100,000$100,000

Shares @ $5 18,000 12,000 5,000

EBIT $18,000 $18,000 $18,000

Interest (15%) 1,500 6,000 11,250

EBT $16,500 $12,000 $ 6,750

Tax (40%) 6,600 4,800 2,700

EAT $ 9,900 $ 7,200 $ 4,050

ROE 11.0% 12.0% 16.2%

EPS $.55 $.60 $.81

Time Value of Money

Some of the answers in this key (and choices in the list of multiple choices) assume that the problem is being worked by using tables rather than a calculator. In AGEC 424 you are expected to use a financial calculator and you are expected to list your calculator inputs and outputs, which constitutes “showing your work.” Some of your answers will be a little different than the key due to the rounding involved when using time value of money tables. In the lab we demonstrated timelines, using your financial calculator and listing calculator inputs and outputs.

Multiple Choice Problems

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  1. ANS:C

Calculator:

n 2; I 5; cpt PV $907.03; PMT 0; FV 1000

  1. ANS:B

100 FV 24 n 1 I/Y Solve for PV = $78.76

  1. ANS:A

Calculator steps: -1000 PV; 1254.70 FV; 2 n; Solve for I/Y = 12.01%

  1. ANS:D

n 5; I 8; PV -1000; PMT 0; cpt FV $1469.33

  1. ANS:C

–1 PV; 2 FV; 12 I/Y; Solve for n = 6.12 years

  1. ANS:C

n 3; cpt I 8.00; PV -7938; PMT 0; FV 10,000

Calculator 8.00%

  1. ANS:C

n 5; cpt I 14.87%; PV -1; PMT 0; FV 2

Calculator: 14.87%

  1. ANS:B

n 8; cpt I 3.00 ; PV -3947; PMT 0; FV 5000

Calculator: 3.00%x2 = 6%

When you compute a periodic rate for a period less than a year, multiply by the number of periods to get an annual rate for your answer.

  1. ANS:D

Calculator steps: –1,000 PV 9 I/Y 3000 FV Solve for n = 12.75

  1. ANS:B

n 40; I 12; PV -10000; PMT 0; cpt FV 930,509.70

  1. ANS:B

n 20; I 8; cpt PV -2454536.85; PMT 250000; FV 0

  1. N 40, I 10, 2400 PMT, 0 PV, solve FV = 1,062,222.13
  2. N 60, I 1, PV -10,000, FV 0, solve PMT = 222.44
  3. ANS:C

PV = 100,000 (.650) = $65,000

Calculator: 5 n 9 I/Y –100,000 FV Solve for PV = $64,993

  1. ANS:A

Calculator steps: 9 n; –30,000 PV; 83,190 FV; Solve for I/Y = 12.0%

  1. ANS:A

Calculator:

Use CFj function on your calculator. Always start with CF0 using $0 if there is no cash flow at time zero and always ‘clear all’ first.

CF0 = 0

CF1 = 120000

CF2 = 180000

CF3 = 240000

I = 11

Solve NPV = $429,686.08

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  1. ANS:C

Calculator solution: use CFj function and find NPV = $68,109.08

Use $0 CF for CF0 and when you get to the part where you repeat $15,000 you do not have to re-enter the $15,000, just keep pushing the CFj key until the number 10 shows on your calculator screen for the period.

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  1. ANS:B

Calculator steps: PV 130000 I/Y .666666667 N 180. Solve for PMT = $1,242.35

Month / Beg. Bal / PMT / Interest / Principal / End Bal
1 / $130,000.00 / $1,242.35 / $866.67 / $375.68 / $129,624.32
2 / $129,624.32 / $1,242.35 / $864.16 / $378.19 / $129,246.13
  1. ANS:D

EAR = (1 + .10/12)12 – 1 = .1047, or 10.47%

  1. ANS:C

EAR = (1 + .18/12)12 – 1 = .1956, or 19.56%

You could just start with the given monthly rate of 0.015 instead of .18/12.

  1. ANS:C

$60,000/.08 = $750,000

  1. ANS:C

Calculator Steps: 1,500 PMT .667 I/Y 360 n Solve for PV = $204,425

Down Payment = $220,000 - $204,425 = $15,575

  1. ANS:C

$20/.10 = $200

  1. ANS:D

Calculator Steps: 60 n 1 I/Y 750 PMT Solve for PV = 33,716

Down Payment = $40,000 – $33,716 = $6,284

Perpetual Annuity problems

1. 200/.05 = 200*20 = 4000

2. 4000 + 200 = 4200

3. N=9, I=5, FV=4000, PMT=0, solve for PV=$2578.44

Problems from the book

33. SOLUTION: First calculate how much the known source of funding ($100,000 per quarter) will grow to by the end of 13 years

n = 13 x 4 = 52; I/Y = 8/4 = 2; PV = 0; PMT = 100,000 CPT FV = $9,001,640.93

The remainder $10,998,359.07 will have to be raised from the other divisions and becomes the FV of the second annuity problem

n = 156; I/Y = .5; PV = 0; FV = 10,998,359.07 CPT PMT = $46,712.61

34. SOLUTION:

First, we need to calculate how much money Carol will need when she starts college. That’s the present value of $2,500 per month for four years.

n = 48; I/Y = .5; PMT = 2,500; FV = 0 CPT PV = $106,450.79

The money from her uncle will contribute the future value of an annuity of $300 per month for 13 years:

n = 156; I/Y = .5; PV = 0; PMT = 300 CPT FV = $70,634.20

The shortfall is the difference of $35,816.59 which must be made up by her parent’s contributions over the last 8 years before Carol starts college.

n = 96; I/Y = .5; FV = 35,816.59; PV=0; CPT PMT = $291.60

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