Question

1) The Ewert Exploration Company is considering two mutually exclusive plans for extracting oil on property for which it has mineral rights. Both plans call for the expenditure of $10 million to drill development wells. Under Plan A, all the oil will be extracted in 1 year, producing a cash flow at t = 1 of $12 million; under Plan B, cash flows will be $1.75 million per year for 20 years.

a. What are the annual incremental cash flows that will be available to Ewert Exploration if it undertakes Plan B rather than Plan A? (Hint: Subtract Plan A’s flows from B‘s.)

b. If the company accepts Plan A and then invests the extra cash generated at the end of Year 1, what rate of return (reinvestment rate) would cause the cash flows from reinvestment to equal the cash flows from Plan B?

c. Suppose a firm ’ s cost of capital is 10%. Is it logical to assume that the firm would take on all available independent projects (of average risk) with returns greater than 10%? Further, if all available projects with returns greater than 10% have been taken, would this mean that cash flows from past investments would have an opportunity cost of only 10%, because all the firm could do with these cash flows would be to replace money that has a cost of 10%? Finally, does this imply that the cost of capital is the correct rate to assume for the reinvestment of a project ’ s cash flows?

d. Construct NPV profiles for Plans A and B, identify each project ’ s IRR, and indicate the crossover rate.

***I must have full equations as well as how to put it in your finance calculator (if needed) to get full credit** thanks in advance

Answer 1

Year	Incremental cash flow amounts (Cashflow of B - Cashflow of A) (Amounts in $ millions)
1	= (1.75-12) = -10.25
2 - 20	= (1.75 - 0) = 1.75 * 19 = 33.25

Therefore, total incremental cashflow of B compared to that of A = 33.25 - 10.25 =$ 23 million

b. The extra cash generated by Project A, at the end of year 1 = 12-10 = $ 2 million

Annual cashflow of Project B = $1.75 million

therefore, reinvestment rate per annum for both projects to have same rate of return = 1.75 / 2 = 0.875 = 87.50% of return required per annum.

c. Even if all the projects have a cost of capital of more than 10%, it is not possible for the firm to invest in all of these projects. The major limiting factor for any firm would be the amount of iinvestment available with it. If that limit is reached or exceeded, then, the decision again depends on the rate at which the additional capital required can be raised. Another limiting factor for the same is the scale of operations at which the firm is operating. Even if cost of capital is met, if the scale at which firm will invest is beyond its risk taking size, even then the additional investment is not possible.

Similarly, if all projects with 10% or greater returns are accepted, then the opportunity cost of replacing these projects with the older ones will not be the same 10% all the time. There will be a lot of demographical and behavioural aspects of investment that decide the cost of swithching from one investment to another investment or project. Hence, the opportunity cost in most of the cases will be greater than 10%.

Hence, the cost of capital is not always the correct re-investment rate for any project. It involves different additional opportunity costs and also certain limitations in terms of re-investment size and risk of exceeding portfolio distribution norms.

d.

PARTICULARS	PROJECT A ( Amount in $ milliions)	PROJECT B (Amount in $ millions)
Initial cashoutflow	- 10	- 10
PV of cashflows @10%(Year 1)	= 12*0.9091 = 10.9091	= 1.75*0.9091 = 1.5909
PV of cumulative cashflows ( Year 2 to Year 20)	0	= 1.75*( PV factor of 20 years - PV of year 1) = 1.75*(8.514 - 0.909) = 1.75 * 7.605 = 13.3087
NPV	= 10.9091 - 10 = 0.9091	= 13.3087+ 1.5909 - 10 = 4.89965
IRR	20.00% per annum.	16.70% per annum.

The crossover rate is the rate at which the NPV from both the projects would yield the same. Hence, it can be calculated by take the incremental cash flow approach for cash inflows and outflows ( Project B - Project A), and calculating IRR for such cashflow pattern. Hence, the IRR for above given incremental cashflow pattern is 16.70% per annum.