Npv - Land and Motel Cost

A parcel of land costs $500,000. For an additional $800,000 you can build a motel on the property. The land and motel should be worth $1,500,000 next year. Suppose that common stocks with the same risk as this investment offer a 10 percent expected return. Would you construct the motel? Why or why not?

NPV = - C_o + C_1/((1+r))

NPV = -($500,000 + $800,000)+($1,500,000/(1+0,10))

NPV = -$1,300,000 + ($1,500,000/1.10) = +$63,636

Since the NPV is positive, I would construct the motel. Alternatively, we can compute r as follows:

r = ($1,500,000/$1,300,000) - 1 = 0.1539 = 15.39%

Since the rate of return is greater than the cost of capital, I would construct the motel.

Norman Gerrymander has just received a $2 million bequest. How should he invest it? There are four immediate alternatives.

Investment in one-year U.S. government securities yielding 5 percent.

A loan to Norman's nephew Gerald, who has for years aspired to open a big Cajun restaurant in Duluth. Gerald had arranged a one-year bank loan for $900,000, at 10 percent, but asks for a loan from Norman at 7 percent.

Investment in the stock market. The expected rate of return is 12 percent.

Investment in local real estate, which Norman judges is about as risky as the stock market. The opportunity at hand would cost $1 million and is forecasted to be worth $1.1 million after one year.

Which of these investments have positive NPVs? Which would you advise Norman to take?

NPV = -$2,000,000 + ($2,000,000/(1+0,05))

NPV = -$95,238.10

NPV = -$2,000,000 + (($2,000,000(1.07))/(1+0,10))

NPV = -$54,545.45

NPV = -$2,000,000 + (($2,000,000+(12% x $2,000,000))/(1+0,12))

NPV = -$2,000,000 + ($2,240,000/1.12)

NPV = $0

NPV = -$1,000,000 + ($1,100,000/(1+0,12))

NPV = -$17,857.14

Norman Gerrymander shouldn't invest on project A, B and D because they have a negative NPV. On project C investing in the stock market will have for Norman Gerrymander NPV= 0 because the correct priced securities always NPV = 0. So better Norman Gerrymander to take only for project C.

Respond to the following comments.

"My company's cost of capital is the rate we pay to the bank when we borrow money."

Because of tax advantages on debt issuance, it will be cheaper to issue debt rather than new equity (this is only true for profitable firms, tax breaks are available only to profitable firms). At some point, however, the cost of issuing new debt will be greater than the cost of issuing new equity. This is because adding debt increases the default risk - and thus the interest rate that the company must pay in order to borrow money. By utilizing too much debt in its capital structure, this increased default risk can also drive up the costs for other sources (such as retained earnings and preferred stock) as well. Management must identify the "optimal mix" of financing - the capital structure where the cost of capital is minimized so that the firm's value can be maximized.

"Net present value is just theory. It has no practical relevance. We maximize profits. That's what shareholders really want."

We should use the NPV in our practical project because NPV is an indicator of how much value an investment or project adds to the firm. If NPV is negative, the project should be rejected because the investment would subtract value from the firm. If NPV is positive, the project may be accepted because the investment would add value to the firm. And if NPV=0, we should be indifferent in the decision whether to accept or reject the project. This project adds no monetary value. Decision should be based on other criteria,