Question

6.42

Under risk neutrality, a factory can be worth $500000 or $1000000 in two years, depending on product demand, each with equal probability. The appropriate cost of capital is 6% per year. The factory can be financed with proceeds of $500000 from loans today. What are the promised and expected cash flows and rates of return for the factory (without a loan), the loan, and the levered factory owner?

Answer 1

A factory can be worth $500000 or $1000000 in two years, depending on product demand, each with equal probability

So the worth of factory after 2 years by incorporating the impact of probability is

500000*0.5 + 1000000*0.5

$750000

The worth of factory after 2 years is $ 750000

Now, the cost of capital is 6% per year

The factory can be financed with proceeds of $500000 from loans today

so the outflow for 1st year is 500000*0.06 = $30000

and the outflow for 2nd year is 500000*0.06 = $30000

Now after 2 years the worth of company is 750000

anf for the the cashflow is 560000

So the ultimate gain to the factory owner is $190000