Ginny's Restaurant Case

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1. Valuation of Virginia’s assets
a. Present value:

PV = $2,000,000 + $3,000,000/(1+0.06)1
= $2,000,000 + $2,830,189
= $4,830,189

b. Future Value (1 year):

FV = 2,000,000(1+0.06)1 + 3,000,000
= 2,120,000 + 3,000,000
= 5,120,000

2. Valuation of Viginia’s assets with investment

c. $1 million investment
PV = $1,800,000/(1+0.06)1 + $3,000,000
= $1,698,113 + $3,000,000
= $4,698,113

d. $2 million investment
PV = $3,300,000/(1+0.06)1 + $2,000,000
= $3,113,208 + $2,000,000
= $5,113,208

e. $ 3 million investment
PV = $4,400,000/(1+0.06)1 + $1,000,000
= $4,150,943 + $1,000,000
= $5,150,943

f. $4 million investment
PV = $5,400,000/(1+0.06)1
= $5,094,340

Virginia’s optimal investment in the restaurant is $3 million, which give her a total of $5,150,943 at the end of year 1. This is approximately a 29% increase in her wealth.

3. PV of investment with $2.8m borrowed

FV= Restaurant Future Cash flows – [Principle(1+0.06)]
= $4,400,000 – [$2,800,000(1.06)]
= $4,400,000 - $2,968,000
= $1,432,000
PV = $1,432,000/1.06
= $1,350,943

Assuming that Virginia can borrow the balance of the $3 million investment at a 6% interest rate, she should make the investment regardless.

4. PV of investment with $3m borrowed

FV = Restaurant Future Cash flows – [Principle(1+0.06)]
= $4,400,000 – [$3,000,000(1.06)]
= $4,400,000 - $3,180,000
= $1,220,000
= $1,220,000/1.06
PV= $1,150,943

Yes, she should still make the investment as it will net her $1,150,000.

5. Assuming both are rational, it is in the best interest of both the savers and the spenders to invest $3 million in the restaurant. While the savers are likely to reinvest their earnings from the investment, the spenders would take out a loan in the amount of their share of the future value of the investment less the interest rate allowing them...
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