Restaurant Study
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In order to find Virginias net worth we take the present value formula PV=FV/(1+i)^n to evaluate the present value of the $3,000,000 Virginia is receiving one year from now. That calculation equals 2,830,188.68. Then that calculation is added the current $ 2,000,000 cash she has to get a total of $ 4,830,188.68. Virginia can consume 2,000,000 today. If she consumes nothing today, and invests $2,000,000 at the interest rate of 6% she will be able to spend more compared to now. FV=PV x (1+i)^n. $2,000,000 * 1.06 = 2,120,000 plus $ 2,830,188.68 = 4,950,188.68.
Virginia should invest $ 3,000,000 in the restaurant. If she were to take her money to the market place, her payout at the end of the year would have only been $4,240,000. With the restaurant, she will make that money with the $3,000,000. She can invest the $ 1 million left elsewhere if she is not willing to invest the full amount. Virginias wealth grows quicker wit the investment in the restaurant.
If Virginia consumes $3.8 million of the consumption at this point, she will only have $ 200,000 left over which will not be enough for her to invest in this restaurant.
She should make the investment into the restaurant because with a bank loan, she would have to pay about 6% interest, but the rate of return in investing with the restaurant is way higher. For instance, if she borrowed $4 million and paid 6 % interest on it, she would owe the bank $ 4,240,000 at the end of the year. She can use that money to invest in the restaurant. If the restaurant does as expected, the payout will be %5.8 million for the same amount. In the end, she would make $ 1,560,000.
The compromise will be reached at the pint when they calculate at which investment amount is the payout at its premium, highest rate of return. Spenders will want to invest all of the $4,000,000 on the restaurant, rather than pay it out as a dividend. The savers on the other hand, will have to pay a hefty cost of opportunity if they do not invest.
She should not invest in this, as the rate of return will not be as high, and the quality will not be worth the same after.