Question

Pedro Spier, the president of Spier Enterprises, is considering two investment opportunities. Because of limited resources, he will be able to invest in only one of them. Project A is to purchase a machine that will enable factory automation; the machine is expected to have a useful life of five years and no salvage value. Project B supports a training program that will improve the skills of employees operating the current equipment. Initial cash expenditures for Project A are $108,000 and for Project B are $33,000. The annual expected cash inflows are $27,766 for Project A and $9,155 for Project B. Both investments are expected to provide cash flow benefits for the next five years. Spier Enterprises’ cost of capital is 6 percent. (PV of $1 and PVA of $1) (Use appropriate factor(s) from the tables provided.)

Required

a-1.	Compute the net present value of each project. (Round your intermediate calculations and final answers to 2 decimal places.)

        

a-2.	Which project should be adopted based on the net present value approach?
	Project B Project A

b-1.	Compute the approximate internal rate of return of each project.

        

b-2.	Which one should be adopted based on the internal rate of return approach?
	Project A Project B

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Answer 1

Answer :

a-1. Net Present value :

NPV = Present value of annual cash flow - Initial Investment

Project A

NPV = [$27,766 x PVAF(6%,5years)] - $108,000

= [$27,766 x 4.212] - $108,000

= $116,950.39 - $108,000

= $8,950.39

Project B

NPV = [$9,155 x PVAF(6%,5years)] - $33,000

= [$9,155 x 4.212] - $33,000

= $38,560.86 - $33,000

= $5,560.86

a.2. Project A should be adopted based on the net present value approach.

b.1. Internal rate of return of each project :

IRR = R1  +  [NPV1 x (R2 - R1)] / (NPV1 - NPV2)

Where:

R1      =   Lower discount rate

R2      =   Higher discount rate

NPV1   =   Higher Net Present Value (derived from R1)

NPV2   =   Lower Net Present Value (derived from R2)

Project A

R1      =   Lower discount rate i.e. 6%

R2      =   Higher discount rate i.e. 8%

NPV1   =   Higher Net Present Value (derived from R1) i.e. $8,950.39

NPV2   =   Lower Net Present Value (derived from R2)

= [$27,766 x PVAF(8%,5years)] - $108,000

= [$27,766 x 3.992] - $108,000

= $2,841.87

IRR = 6% + [$8,950.39 x (8 - 6)] / ($8,950.39 - $2,841.87)

= 6% + ($8,950.39 x 2) / $6,108.52

= 6% + 2.93%

= 8.93 % or 9%

Project B

R1      =   Lower discount rate i.e. 6%

R2      =   Higher discount rate i.e. 8%

NPV1   =   Higher Net Present Value (derived from R1) i.e. $5,560.86

NPV2   =   Lower Net Present Value (derived from R2)

= [$9,155 x PVAF(8%,5years)] - $33,000

= [$9,155 x 3.992] - $33,000

= $3,546.76

IRR = 6% + [$5,560.86 x (8 - 6)] / ($5,560.86 - $3,546.76)

= 6% + ($5,560.86 x 2) / $2,014.1

= 6% + 5.52%

= 11.52 % or 12%

b.2. Project B should be adopted based on the internal rate of return approach.