Question

NPV PROFILES: TIMING DIFFERENCES

An oil-drilling company must choose between two mutually exclusive extraction projects, and each costs $12 million. Under Plan A, all the oil would be extracted in 1 year, producing a cash flow at t = 1 of $14.4 million. Under Plan B, cash flows would be $2.1323 million per year for 20 years. The firm's WACC is 11.4%.

1. Construct NPV profiles for Plans A and B. Round your answers to two decimal places. Do not round your intermediate calculations. Enter your answers in millions. For example, an answer of $10,550,000 should be entered as 10.55. If an amount is zero enter "0". Negative value should be indicated by a minus sign.

   Discount Rate	NPV Plan A	NPV Plan B
   0%	$  million	$  million
   5	million	million
   10	million	million
   12	million	million
   15	million	million
   17	million	million
   20	million	million

   Identify each project's IRR. Round your answers to two decimal places. Do not round your intermediate calculations.

   Project A  %

   Project B  %

   Find the crossover rate. Round your answer to two decimal places. Do not round your intermediate calculations.
   %
2. 
   
3. Is it logical to assume that the firm would take on all available independent, average-risk projects with returns greater than 11.4%?
   -Select-YesNoItem 18
   
   If all available projects with returns greater than 11.4% have been undertaken, does this mean that cash flows from past investments have an opportunity cost of only 11.4%, because all the company can do with these cash flows is to replace money that has a cost of 11.4%?
   -Select-YesNoItem 19
   
   Does this imply that the WACC is the correct reinvestment rate assumption for a project's cash flows?
   -Select-YesNo

Answer 1

Working Tables

Year	Project A Cash flows	Project B Cash flows	Cross over rate Cash flow
Cash Out Flow	-12.0000	-12.0000	0.000
1	14.4000	2.1323	12.2677
2	0.000	2.1323	-2.1323
3	0.000	2.1323	-2.1323
4	0.000	2.1323	-2.1323
5	0.000	2.1323	-2.1323
6	0.000	2.1323	-2.1323
7	0.000	2.1323	-2.1323
8	0.000	2.1323	-2.1323
9	0.000	2.1323	-2.1323
10	0.000	2.1323	-2.1323
11	0.000	2.1323	-2.1323
12	0.000	2.1323	-2.1323
13	0.000	2.1323	-2.1323
14	0.000	2.1323	-2.1323
15	0.000	2.1323	-2.1323
16	0.000	2.1323	-2.1323
17	0.000	2.1323	-2.1323
18	0.000	2.1323	-2.1323
19	0.000	2.1323	-2.1323
20	0.000	2.1323	-2.1323

We first prepare the cash flow table as above, in which we have the cash in-flow for project A as $14.4 million at the end of year one and cash flow for Project B as $2.1323 million each year for 20 years.

Cash out flow remains same for both projects at $12 million.

Answer A

Discount Rate	NPV Plan A	NPV Plan B
0%	2.40	30.65
5%	1.71	14.57
10%	1.09	6.15
12%	0.86	3.93
15%	0.52	1.35
17%	0.31	0.00
20%	0.00	-1.62
WACC @ 11.4%	0.93	4.55
IRR	20.00%	17.0%

Cross over rate

16.41%

In excel we would use the formula for calculating NPV formula stated as "=NPV(rate, value 1, value2,....)". In manual calculation this formula is based as NPV = Cash outflow + (Cash Inflow year 1)/(1+Rate)^Period....for n number of periods.

The rate would be the discount rate we have used in the above table starting at 0% to 5% until 20%. We have also calculated the NPV of both the projects at WACC rate of 11.4%.

IRR is calculated by using the formula in excel "=IRR(values,guess), where the values would be in the working table i.e. project A and B cash flows. IRR is a value at which the NPV of the project becomes Zero, hence manually we need to put Zero in the NPV formula above and solve for the Rate.

Answer B

Cross over rate is the rate at which both the project would coincide at a common rate is calculated by subtracting cashflows of project A from cash flow of project B resulting in common cash flows. In NPV way to calculate the cross over rate we simply put the cash flows of project A = project B and solve for Rate.

In our working table above, we have calculated the difference between cash flows of project A and B and then used IRR function on the difference cash flow to calculate the Cross over rate which is 16.41%.

Answer C

a) No, the IRR is considered inferior to NPV method and hence the company should always choose projects with higher NPV because it results in wealth creation and IRR does not take into account the cash flow timing hence, it can result in incorrect decision for investments. IRR is always used in conjunction to NPV and not in isolation.

b) No, the opportunity cost of each project could differ and it is impossible for companies to replace capital at the stated rate i.e. 11.4% because the market fluctuates.

c) Yes - because the company is borrowing capital at that rate of 11.4% i.e. equity and debt to initiate the project.