In: Advanced Math

This is your lucky day. You have won a $20,000 prize. You are setting aside $8,000 for taxes and partying expenses, but you have decided to invest the other $12,000. Upon hearing the news, two different friends have offered you an opportunity to become a partner in two different entrepreneurial ventures, one planned by each friend. In both cases, this investment would involve spending some of your time next summer as well as putting up cash. Becoming a full partner in the first friend’s venture would require an investment of $10,000 and 400 hours, and your estimated profit (ignoring the value of your time) would be $9,000. The corresponding figures for the second friend’s venture are $8,000 and 500 hours, with an estimated profit to you of $9,000. However, both friends are flexible and would allow you to come in at any fraction of a full partnership you would like. If you choose a fraction of a full partnership, all the above figures given for a full partnership (money investment, time investment, and your profit) would be multiplied by this fraction. Because you were looking for an interesting summer job anyway (maximum 600 hours), you have decided to participate in one or both friends’ ventures in whichever combination that would maximize your total estimated profit. You need to solve the problem of finding the best combination.

a) Use the graphical solution method to solve this problem. Clearly display the feasible region of the problem and its optimal solution.

b) What profit would the first friend have to offer you in order to be optimal to invest your money and time to become his full partner?

INVESTING YOUR OWN PORTFOLIO
You have won the jackpot of a European Lottery with a prize of
€30 000. After distributing a portion of the prize to a local
charity, you decide that it is a good idea to invest the rest of
the prize. However, you are doubtful about which asset class or
financial vehicle is more suitable given the current international
context.
Bear in mind that you are in your early twenties and that your
financial restrictions are...

INVESTING YOUR OWN PORTFOLIO
You have won the jackpot of a European Lottery with a prize of
€30 000. After distributing a portion of the prize to a local
charity, you decide that it is a good idea to invest the rest of
the prize. However, you are doubtful about which asset class or
financial vehicle is more suitable given the current international
context.
Bear in mind that you are in your early twenties and that your
financial restrictions are...

You have just received notification that you have won the $2.04
million first prize in the Centennial Lottery. However, the prize
will be awarded on your 100th birthday (assuming you’re around to
collect), 82 years from now.
What is the present value of your windfall if the appropriate
discount rate is 8 percent?

You have just received notification that you have won the $1
million first prize in the Centennial Lottery. However, the prize
will be awarded on your 100th birthday (assuming you’re around to
collect), 80 years from now. What is the present value of your
windfall if the appropriate discount rate is 8.45 percent? (Do not
round intermediate calculations and enter your answer in dollars,
not millons of dollars, rounded to 2 decimal places, e.g.,
1,234,567.89.)

You have just received notification that you have won the $2
million first prize in the Centennial Lottery. However, the prize
will be awarded on your 100th birthday (assuming you’re around to
collect), 70 years from now.
What is the present value of your windfall if the appropriate
discount rate is 8 percent? (Do not round intermediate
calculations and round your final answer to 2 decimal places, e.g.,
32.16.)

6. You won the big prize in the California lottery and you have
to choose one of the following two payment plans:
Payment Plan 1: If you choose this payment plan, you will
receive semiannual payments for a fixed period of time. The first
payment of Rs. 150,000 will be paid on January 01, 2007 and it will
grow by 2% every six months. You will receive the last payment on
January 01, 2016
Payment Plan 2: If you choose...

1. You have just won the prize in the State lottery. A recent
innovation is to offer prize winners a choice of payoffs. You must
choose one of the following prizes:
a. $1,000,000 paid immediately
b. $600,000 paid exactly one year from today, and another $600,000
paid exactly 3 years from today
c. $70,000 payment at the end of each year forever (first payment
occurs exactly 1 year from today)
d. An immediate payment of $600,000, then beginning exactly 5...

You have won a competition , and can choose any one of the
following prize:
a. 100,000 now
b. 180,000 at the end of give of five years from
c. 11,400 forever
d. 19,000for each of the 10 years
e . 6,500next year, and increaseing by 5% per year forever after
If the interest rate is 12% what do you choose?

Manuel just won the lottery and the prize was $ 1 million. You have
the option of receiving a lump sum of $ 312,950 or $ 50,000 per
year for the next 20 years. If Miguel can invest the single amount
at 9% or invest the annual payments at 7%; Which one should I
choose?
a. one-time amount of 312,950
b. b. annual payments of 50,000

Congratulations! You have won the $ 1 million lottery grand
prize. You have been presented with several payout alternatives,
and you have to decide which one to
accept.
The alternatives are as follows:
$1
million today
$1.2
million lump- sum in two years.
$1.5
million lump-sum in five years.
$2
million lump-sum in eight years.
Your cousin, s stockbroker, advises you that over the long-term
you should be able to earn ten percent on an investment
portfolio.
You are intrigued...

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