Question

Timing Differences

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 $9.5 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 $10.5 million; under Plan B, cash flows will be $1.4 million per year for 20 years.

1. 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.) 

2. 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? Round your answer to two decimal places.

   
   

3. 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?

   I. No, the firm would not take on all available independent projects with greater than 10% returns. If taken, risk remains the same among projects and the cost of capital does not vary with the amount of capital raised.
   II. Yes, the firm would take on all available independent projects with greater than 10% returns. If taken, risk varies with projects and the cost of capital varies with the amount of capital raised.
   III. Yes, the firm would take on all available independent projects with greater than 10% returns. If taken, risk remains the same among projects and the cost of capital does not vary with the amount of capital raised.
   
   

4. Select the correct graph for NPV profiles for Plans A and B.

Answer 1

a) Incremental Cash flow on choosing B over A

Year 1 : $1.4 million - $10.5 million = -$9.1 million

Year 2-20 : $1.4 million - 0 = $1.4 million

b) Extra cash generated from Plan A in 1st year = $10.5 million - $1.4 million = $9.1 million

To generate a cashflow equal to that of B, the rate should be such that the present value of all the remaining 19 cashflows of B be equal to $9.1 million

So, 1.4/(1+r) + ... + 1.4/(1+r)^19 = 9.1

=> 1.4/r* (1-1/(1+r)^19) = 9.1

Using hit and trial method ., r = 0.141373 or 14.14%

c) The firm must take all available projects having return greater than the cost of capital . Once taken , risk does not vary with the project and cost of capital does not vary with capital raised. (option III)

d) The NPV of a normal project decreases with the increase in the cost of capital. So graph A and B are incorrect. Further, B's NPV is more sensitive to changes in interest rates because of the long duration of cash flows. Hence C is the correct graph of A and B's NPV profiles

IRR of project A (r) is given by the rate where NPV profile crosses the X-axis i.e when NPV =0

9.5 =10.5/(1+r)

=> r= 10.5/9.5-1 = 0.105263

or 10.53%

IRR of project B (r) is given by the rate where NPV profile crosses the X-axis i.e when NPV =0

9.5 =1.4/r* (1-1/(1+r)^20)  

By hit and trial, r = 0.13583 or 13.58%

Crossover rate is when NPV profile of B crosses NPV profile of A .

Crossover rate is the rate calculated in part b) above i.e. 14.14%