Question

A company is considering two mutually exclusive expansion plans. Plan A requires a $41 million expenditure on a large-scale integrated plant that would provide expected cash flows of $6.55 million per year for 20 years. Plan B requires a $13 million expenditure to build a somewhat less efficient, more labor-intensive plant with an expected cash flow of $2.91 million per year for 20 years. The firm's WACC is 11%. The data has been collected in the Microsoft Excel Online file below. Open the spreadsheet and perform the required analysis to answer the questions below.

1. Calculate each project's NPV. 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.

   Plan A: $   million

   Plan B: $   million

   Calculate each project's IRR. Round your answer to two decimal places.

   Plan A: %

   Plan B: %

2. By graphing the NPV profiles for Plan A and Plan B, approximate the crossover rate to the nearest percent.

   %

3. Calculate the crossover rate where the two projects' NPVs are equal. Round your answer to two decimal places.

   %

4. Why is NPV better than IRR for making capital budgeting decisions that add to shareholder value? The input in the box below will not be graded, but may be reviewed and considered by your instructor.

Answer 1

Answer - a

Statement showing NPV of Plan A

Year	Particulars	Amount (in m$) (A)	Discount Factor @ 11% (B)	Present Value (in m$)              (A * B)
0	Capital Expenditure	-41.00	1	-41.00
1 to 20	Cash flow	6.55	7.9633	52.16
	Net Present Value	11.16

Statement showing NPV of Plan B

Year	Particulars	Amount        (in m$) (A)	Discount Factor @ 11% (B)	Present Value (in m$)              (A * B)
0	Capital Expenditure	-13.00	1	-13.00
1 to 20	Cash flow	2.91	7.9633	23.17
	Net Present Value	10.17

IRR is the rate of cost of capital at which the present values of inflows and outflows are equal i.e. the net present value comes to zero, here in the question in both plans the present value of cash inflows in twenty years are not equal therefore we have to try trail and error method to calculate the IRR of both the plans and then we try to interpolate the IRR. For this we have to put a discount rate at which NPV from both the plans which results in a negative figure so as to find out a rate in between the positive and negative NPV where the NPV comes to zero approximately.

Plan A -

Let us try the discount rate of 16% and calculate the NPV at this rate,

Statement showing NPV of Plan A at discount rate of 16%

Year	Particulars	Amount (in m$) (A)	Discount Factor @ 16% (B)	Present Value (in m$)              (A * B)
0	Capital Expenditure	-41.00	1	-41.00
1 to 20	Cash flow	6.55	5.9288	38.83
	Net Present Value	-2.17

Hence, the discount rate of 16% would result in a negative NPV from Plan A, now let us interpolate the IRR using the below mentioned formula:

IRR = Lower rate + [Lower rate NPV / (Lower rate NPV - Higher rate NPV)] * Difference in rates

Where -

Lower rate can be considered as 11%

Lower rate NPV at discount rate of 11% is $11.16m (calculated above)

Higher rate is 16%

Higher rate NPV at discount rate of 16% is -$2.17m (calculated above)

Difference in rates = 5% (16% - 11%)

On putting these figures in the above formula, we get -

IRR = Lower rate + [Lower rate NPV / (Lower rate NPV - Higher rate NPV)] * Difference in rates

IRR = 11 + [11.16 / (11.16 + 2.17)] * 5

IRR = 11 + 4.19

IRR = 15.19%

Hence, IRR of Plan A is 15.19% (approx)

Plan B -

Let us try the discount rate of 23% and calculate the NPV at this rate,

Statement showing NPV of Plan B at discount rate of 23%

Year	Particulars	Amount        (in m$) (A)	Discount Factor @ 23% (B)	Present Value (in m$)              (A * B)
0	Capital Expenditure	-13.00	1	-13.00
1 to 20	Cash flow	2.91	4.2786	12.45
	Net Present Value	-0.55

Hence, the discount rate of 23% would result in a negative NPV from Plan B, now let us interpolate the IRR using the below mentioned formula:

IRR = Lower rate + [Lower rate NPV / (Lower rate NPV - Higher rate NPV)] * Difference in rates

Where -

Lower rate can be considered as 11%

Lower rate NPV at discount rate of 11% is $10.17m (calculated above)

Higher rate is 23%

Higher rate NPV at discount rate of 23% is -$0.55m (calculated above)

Difference in rates = 12% (23% - 11%)

On putting these figures in the above formula, we get -

IRR = Lower rate + [Lower rate NPV / (Lower rate NPV - Higher rate NPV)] * Difference in rates

IRR = 11 + [10.17 / (10.17 + 0.55)] * 12

IRR = 11 + 11.38

IRR = 22.38%

Hence, IRR of Plan B is 22.38% (approx)