Question

Consumers appear to require returns of 25 percent or more before they are prepared to make energy-efficient investments, even though a more reasonable estimate of the cost of capital might be around 15 percent. Here is a highly simplified problem which illustrates that such behavior could be rational.20

Suppose you have the opportunity to invest $1,000 in new space-heating equipment that would generate fuel savings of $250 a year forever given current fuel prices. What is the PV of this investment if the cost of capital is 15 percent? What is the NPV?

Now recognize that fuel prices are uncertain and that the savings could well turn out to be $50 a year or $450 a year. If the risk-free interest rate is 10 percent, would you invest in the new equipment now or wait and see how fuel prices change? Explain.

Answer 1

Suppose you have the opportunity to invest $1,000 in new space-heating equipment that would generate fuel savings of $250 a year forever given current fuel prices. What is the PV of this investment if the cost of capital is 15 percent? What is the NPV?

C0 = 1,000; Annual savings = C = $ 250 in perpetuity; r = 15%

Hence, PV of this investment = PV of perpetuity = C / r = 250 / 15% = $ 1,666.67

And NPV = PV - C0 = $ 1,666.67 - 1,000 = $ 666.67

Now recognize that fuel prices are uncertain and that the savings could well turn out to be $50 a year or $450 a year. If the risk-free interest rate is 10 percent, would you invest in the new equipment now or wait and see how fuel prices change? Explain.

You will need an assured cash saving of at least S such that NPV at risk free rate = 0

i. S / rf - C0 = 0

Or, S / 10% - 1,000 = 0

Hence S = 1000 x 10% = $ 100

A minimum guaranteed annual saving of $ 100 is required for the people to invest in the new equipment. However, in this case, the savings could well turn out to be as low as $50 a year, as well. Hence, the uncertainty (or the riskiness) doesn't warrant investment in the new equipment. People will wait and watch.