Question

You are installing a solar panel today on the roof of your house and it costs 4000. Over the next 12 months the expected savings from this investment can be either 300 or 100 with equal probability. For simplicity you can assume that those savings will be realized in perpetuity. The opportunity cost of capital is 5%. Is this a good investment today? What about if you wait for a year? Discuss. WHAT WOULD BE THE PRESENT VALUE OF 4,000 IF WE WAIT A YEAR?

Answer 1

Perpetual Cash Flow = Expected Cash Flow = 300*50% + 100*50% = 150+50 = $200

PV of Perpetual cash Flow = Cash Flow/Cost of Capital = 200/5% = $4000

If we install a panel today, it will cost $4000 and PV of Perpetual Cash Flows is also $4000. Therefore, It is INDIFFERENT whether we install or not. Even without installing, the return can be obtained.

Therefore, Today, it is NOT a Good Investment.

If we wait for 1 year,

Even if we wait for 1 year or even 10 years, It will still be INDIFFERENT. By waiting for 1 year, PV of the OUTFLOW of $4000 will be reduced i.e. 4000/(1.05) = $3809.52, but PV of the Perpetual Inflows will also be reduced.

Therefore, Even after 1 year, it is NOT a Good Investment.