Question

- Suppose the opportunity cost of capital is 5% and you have just won a $750,000 lottery that entitles you to

$75,000 at the end of each year for the next 10 years.

- What is the minimum lump sum cash payment you would be willing to take now in lieu of the IO-year annuity?
- What is the minimum lump sum you would be willing to accept at the end of the 10 years in lieu of the annuity?

- Using the appropriate interest factor table, answer each of the following questions (each case is independent of each other.)

- Your company purchases a 5-year certificate of deposit which pays semi-annually and has a stated interest rate of 6.5%. The initial investment is $10,000. What is the future amount of your investment worth at the end of 5 years?
- What amount must you put in the bank today if you will need $20,000 in 10 years for the cost of your child's college education? The bank will provide you with interest payments quarterly on your investment. The annual rate of interest you have been quoted is 9 percent.

Problem 1)

MINIMUM LUMP SUM IF PAID NOW |
||

Rate | ||

Per year 10 year annuity | ||

Final year annuity | ||

years | ||

years | ||

years | ||

PV of 10 year annuity |

Problem 2)

PART 1 |
Calculating (FV) |
PART 2 | ||||||||

$ | current value of investment | Rate | 4 | |||||||

interest rate to be earned ANNUALLY over life of investment | Years | |||||||||

term of investment in years | FV | |||||||||

Rate for compounding semi-annual | Quarterly interest payments compounded | |||||||||

Number of compounding periods | Number of compounding periods | |||||||||

Future Value | $ | PV | ||||||||

Ignoring negative sign = FV | $ | Ignoring negative number |

Answer #1

1] | Minimun lump sum to be received now = PV of the annuity of 75000 for 10 years discounted at the opportunity cost of 5% =75000*(1.05^10-1)/(0.05*1.05^10) = | $ 579,130.12 |

Minimun lump sum to be received after 10 years = FV of the annuiyt of 75000 for 10 years at 5% = 75000*(1.05^10-1)/0.05 = | $ 943,341.94 | |

2] | FV = the sum of the FV of the deposit of 10000 compounded at 3.25% for 10 half years = 10000*1.0325^10 = | $ 13,768.94 |

[It is assumed that the interest is reinvested at the same rate] | ||

Amount to be deposited today = The PV of 20000 discounted for 40 quarters at 9%/4 =2.25% = 20000/1.0225^40 = | $ 8,212.92 |

You won the lottery and have a number of choices as to how to
take the money. Which choice yields a greater present value? (Use a
10% discount/hurdle rate)
Present Value
of an Ordinary
Period
Present Value
of $1 at 10%
Annuity of $1
at 10%
1
.909
.909
2
.826
1.736
3
.751
2.487
4
.683
3.170
5
.621
3.791
Group of answer choices
$65,000 (lump sum) now
$100,000 (lump sum) 5 years from now
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A lump sum payment of $1,000 is due at
the end of 5 years. The nominal interest rate is 10%, semiannual
compounding. Which of the following statements is/are
INCORRECT? Why?
a. The present
value of the $1,000 would be greater if interest were compounded
monthly rather than semiannually.
b. The periodic rate is greater than 5%.
c. The periodic interest rate is 5%.
d. The present
value would greater if the lump sum were discounted back for more
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e. ...

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Congratulations: you have won the lottery and you have several
decisions to make but you need information to make the correct
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Using the table provided, if you agree to make three annual
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------------ .79383
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How many years does it take for $1,000 grow to be
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BGN or END MODE ( choose one ) P/Y =
N= ?
I/Y=
PV=
PMT=
FV=
CPT , N =
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2. How many years does it take for $1,000 to grow to be
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FV of an annuity due
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In sheet “growing annuity”, fill out PV and FV of in “Annuity in
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Number of years
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Annaul Interest rate
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Annual saving Growth rate
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