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.
Ham business investment
PV = $3,400,000/(1+0. 06)1 = 3,207,547 NPV = 3,207,547 – 2,500,000 = 707,547
While the project generates a positive net present value, I don’t recommend the investment in the ham business. The only way to invest in the Ham business without borrowing money or using the companies retained earnings would be to issue 357,143 new shares at the current $7 per share price. However, the valuation of the company (per share) would drop to $2. 87 per share after the Ham company investment and thus it is not in the best interest of the shareholders to make this investment.
