Question

The market capitalization of this company is $140 million, it's beta is 0.75, the risk free rate is 2% and the market risk premium is 6%.

The project costs $1 million and has expected cashflows of $75,000 a year forever. This same firm now realizes that the project they were considering before has a timing option. Specifically, they can wait a year to see if the product the project will create will catch on in the market, or not. At time 1, they will see whether the product will do well ($100k per year forever), or badly ($50k a year forever). There is an equal probability of the product doing well or badly. If they start the project if it does well, they will pay $1.25million since many of the raw materials to produce this product will be in demand (as opposed to $1 million if they start immediately). If they start the project if it does badly, they will still only pay $1 million to start it.

a) What is the NPV, at time 1, of starting the project?

b) What is the NPV of doing the project at time 1 if the product doesn't do well?

c) What is the overall value of waiting at time 0? (remember to factor in the appropriate decisions to not do the project if the NPV is 0 at time 1, and also to discount time 1 cashflows to time 0).

Answer 1

Expected rate of return (cost of equity) = Risk free rate + Beta * Market risk premium = 0.02 +0.75 x 0.06 = 0.065 or 6.5%

Expected Cash outflows at time 1 = $ 1,250,000 x 0.5 +$ 1,000,000 x 0.5 = $1,125,000

Expected cash inflows per year at time 1 = $100,000 x 0.5 + $50,000 x 0.5 = $75,000

PV of annuity in perpetuity = a / r where a = Expected cash inflows and r(discount rate) = 0.065

PV of cash inflows at time 1 = $75,000/0.065 = $ 1,153,846

PV of cash outflows at time 1 = $ 1,125,000

a) Therefore NPV at time 1 of starting the project = $ 1,153,846 - $ 1,125,000 = $ 28,846

b) If the product doesn't do well , then NPV at time 1 = $1,000,000 - 50000/0.065 = - $ 230,769

c) If the project is started at time 0

NPV at time 0 = -$1,000,000 +$ 75000/0.065 = $ 153,846

If the project is started at time 1, NPV at time 1 = -$ 1,250,000 +$100,000/0.065 = $ 288,462

NPV at time 0 if project started at time 1 = $288,462/(1+0.065) = $270,856

Hence Overall value of waiting at time 0 = $ 270,856 - $ 153,846 = $ 117,010