Question

A company is considering two mutually exclusive expansion plans. Plan A requires a $40 million expenditure on a large-scale integrated plant that would provide expected cash flows of $6.39 million per year for 20 years. Plan B requires a $11 million expenditure to build a somewhat less efficient, more labor-intensive plant with an expected cash flow of $2.47 million per year for 20 years. The firm's WACC is 11%.

a. 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: %

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

%

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

%

d. 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

WACC = 11% = 0.11

period of cash inflows , n = 20

PVIFA( 11% , 20 years) = present value interest rate factor of annuity

= [((1+r)ⁿ - 1)/((1+r)ⁿ*r)] = [((1.11)²⁰ - 1)/((1.11)²⁰*0.11)] = 7.96332812

a) PLAN A

initial investment , I = 40 million

annual cash flow , A = 6.39 million

Present value of cash inflows from project = A*PVIFA

FOR r = 11% = 0.11

Present value of cash inflows from project (PV)= 6.39*7.96332812 = 50.88566667 million

NPV = PV - I = 50.88566667 - 40 = 10.88566667 or $10.89 million ( rounding off to 2 decimal places)

PLAN B

initial investment , I = 11 million

annual cash flow , A = 2.47 million

Present value of cash inflows from project = A*PVIFA

FOR r = 11% = 0.11

Present value of cash inflows from project (PV)= 2.47*7.96332812 = 19.66942045 million

NPV = PV - I = 19.66942045 - 11 = 9.66942045 or $9.67 million ( rounding off to 2 decimal places)

IRR FOR PLAN A

IRR is the rate of return for which NPV = 0

NPV = Present value of cash inflows of the project - initial investment

Putting NPV = 0

Present value of cash inflows of the project = initial investment

A*PVIFA = 40

6.39*[((1+IRR)ⁿ - 1)/((1+IRR)ⁿ*r)] = 40

6.39*[((1+IRR)²⁰ - 1)/((1+IRR)²⁰*r)] = 40

[((1+IRR)²⁰ - 1)/((1+IRR)²⁰*r)] = 40/6.39 = 6.259780908

we have to find IRR by trial and error which satisfies the above equation

by trial and error we find that , IRR = 0.15 or 15%

IRR for Plan B

IRR is the rate of return for which NPV = 0

NPV = Present value of cash inflows of the project - initial investment

Putting NPV = 0

Present value of cash inflows of the project = initial investment

A*PVIFA = 11

2.47*[((1+IRR)ⁿ - 1)/((1+IRR)ⁿ*r)] = 11

2.47*[((1+IRR)²⁰ - 1)/((1+IRR)²⁰*r)] = 11

[((1+IRR)²⁰ - 1)/((1+IRR)²⁰*r)] = 11/2.47 = 4.453441296

we have to find IRR by trial and error which satisfies the above equation

by trial and error we find that , IRR = 0.2204 or 22.04%

b)

WE can see from the graph , the approximate crossover rate is the one where the NPV profiles for the 2 plans cross each other , marked with a cross , approximate crossover rate = 0.12 or 12%

c)

d)

since firm value after taking on a capital budgeting project can be directly added to the existing firm alue , we can directly compare if the firm adds value or decreases the value of the firm.

and NPV assumes that the cash inflows from the project / Plans are reinvested at WACC ( or required return) , but IRR rule assumes that the cash flows are reinvested at IRR , since NPV's assumption is more realistic than IRR's , NPV is considered the best method for making captal budgeting decisions