Question

1a) What is the discounted free cash in year 5 of a project that has an annual free cash of ~100 million and a discount rate of 20%? Number answer is fine with suitable significant figures.

b) If the capital cost of the project is expected to be 1 billion dollars with a construction schedule of 2 years do you expect this project above (100 million non discounted free cash per year) to be economic at a 20% discount rate. 2/3 sentences

c) What does the 20% discount rate suggest about the project risk? 2/3 sentences

Answer 1

a) The annual free cash = FCF = 100

The discount rate is r = 20% = 0.2

The discounted free cash flow in year n = FCF / ((1 + r)^(n-1))

So, the approximate DCF values are:

DCF in year 1 = 100

DCF in year 2 = 83

DCF in year 3 = 69

DCF in year 4 = 58

DCF in year 5 = 48

b) With such a high initial cost (1 billion) and a high discount rate of 20%,

the annual cash flow should be relatively high. This is not the case here.

The DCF value in year n is represented as 100 / (1 + 0.2)^(n-1)

This is an infinitely decreasing geometric progression,

such that the initial value = b = 100

the common ratio = q = 1 / (1+0.2) = 0.83

So, for an infinitely decreasing geometric progression where the ratio (q) is less than 1,

the sum total is b / (1-q) = 100 / (1-0.83) = 600.

Thus, even if the project continues infinitely, it will generate only 600 million.

It is not economically feasible.

c) The project risk is too high since the discount rate is 20%.