Question

Imagine that the net present value of a hydroelectric plant with a life of 70 years is $23.73 million and that the net present value of a thermal electric plant with a life of 35 years is $18.77 million. Rolling the thermal plant over twice to match the life of the hydroelectric plant thus has a net present value of ($18.77 million) + ($18.77 million)/(1 + 0.05)35 = $22.17 million.

      

Now assume that at the end of the first 35 years, there will be an improved second 35-year plant. Specifically, there is a 30 percent chance that an advanced solar or nuclear alternative will be available that will increase the net benefits by a factor of three; a 60 percent chance that a major improvement in thermal technology will increase net benefits by 50 percent; and a 10 percent chance that more modest improvements in thermal technology will increase net benefits by 10 percent.

       a. Should the hydroelectric or thermal plant be built today?

       b. What is the quasi-option value of the thermal plant?

Answer 1

Greetings,

a) whenever we have two mutually exclusive projects ie only one has to be accepted then we should choose the project having highest NPV provided there are comparable in terms of risk, life etc. Whenever the projects have unequal lives, then we need to either find out Annualised benefit or repeat the shorter project for more than once and try it to equate it with the life of the longer project. For instance - if project A is 6 yrs long and project B is 2 years long, then B can be repeated 3 times during the life time of A. So NPV of B will be standing at t=0, 2 and 4 and hence discounting is required accordingly.

In the given case, second approach is followed ie second project can be repeated twice, hence NPV of 18.77m stand at t =0 and at t=35, hence 2nd NPV needs further discounting and final answer is 22.17m which is less than first project hence we should go with the first project today ie hydroelectric plant should be built today.

b) After completion of 35 years, first project can not be undone as it is for 70 yrs, but second one may not be repeated again if we don't find it to be worthy in future. Hence second project gives us the option of repeating it after 35 years or do not repeat it. So our decision today shall be based upon the value of that option as well which it offers.

We need to find out the weighted average NPV during second period of 35 years given the improved model or improvements in the existing model.

Ist Scenario - NPV will increase by a factor of 3. Interpreting it to be in the manner that NPV will treble is it will become 18.77*3=56.31m with 30% probability giving us 56.31*.30=16.893m

2nd scenario - NPV will increase by 50% and become 18.77*1.5=28.155m with 60% probability giving 28.155*.6=16.893m again

3rd scenario - NPV will increase by 10% ie it will become 18.77*1.1=20.647 with 10% probability giving us 2.0647m

Adding up the 3 figures NPV come to be 35.85m approx. This will be discounted 35 yrs back @5% hence PV of NPV = 35.85/1.05^35 =6.5M approx.

So total NPV of second project considering real option is 18.77+6.5=25.27m. It is more than the NPV of first plant, hence we should construct second plant after considering the value of option.

Value of option = 25.27m-22.17m =3.1m ie the value by which NOV of second plant increased.

Note- Please acknowledge that there is second interpretation of the words "increase by a factor of three" as increase by 33.33%. If this is the case then there will be changes in the scenario 1 and the wwhol answer accordingly.