# [Solved] ginnys restaurant case

## Valuation of Virginia’s assets

Present value: PV = \$2,000,000 + \$3,000,000/(1+0. 06)1 = \$2,000,000 + \$2,830,189 = \$4,830,189

Future Value (1 year): FV = 2,000,000(1+0. 06)1 + 3,000,000 = 2,120,000 + 3,000,000 = 5,120,000

## Valuation of Viginia’s assets with investment

\$1 million investment PV = \$1,800,000/(1+0. 06)1 + \$3,000,000 = \$1,698,113 + \$3,000,000 = \$4,698,113

\$2 million investment PV = \$3,300,000/(1+0. 06)1 + \$2,000,000 = \$3,113,208 + \$2,000,000 = \$5,113,208

\$ 3 million investment PV = \$4,400,000/(1+0. 06)1 + \$1,000,000 = \$4,150,943 + \$1,000,000 = \$5,150,943

\$4 million investment PV = \$5,400,000/(1+0. 6)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.

## 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.

## 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.

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 spend the money in the present and profit from the spread between the interest rate and return. If the spenders refused to invest, they would have less money to spend in the present day, which is no rationale.