Ginny's Restaurant Case
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 to
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 to