Question

Henrie’s Drapery Service is investigating the purchase of a new machine for cleaning and blocking drapes. The machine would cost $163,700, including freight and installation. Henrie’s estimated the new machine would increase the company’s cash inflows, net of expenses, by $50,000 per year. The machine would have a five-year useful life and no salvage value.

Required:

1. What is the machine’s internal rate of return? (Round your answer to whole decimal place i.e. 0.123 should be considered as 12%.)

2. Using a discount rate of 16%, what is the machine’s net present value? Interpret your results.

3. Suppose the new machine would increase the company’s annual cash inflows, net of expenses, by only $41,000 per year. Under these conditions, what is the internal rate of return? (Round your answer to whole decimal place i.e. 0.123 should be considered as 12%.)

Answer 1

Answer :

1. Machine’s internal rate of return :

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

Where:

R1      =   Lower discount rate i.e 15%

R2      =   Higher discount rate i.e. 16%

NPV1   =   Higher Net Present Value (derived from R1)

NPV2   =   Lower Net Present Value (derived from R2)

NPV1 = [Annual cash inflow x PVAF(15%,5years] - Initial investment

= [$50,000 x 3.35215] - $163,700

= $3,925

NPV2 = [Annual cash inflow x PVAF(16%,5years] - Initial investment

= [$50,000 x 3.27429] - $163,700

= $14.5

IRR

= 15% + [$3,925 x(16 - 15)] / ($3,925 - $14.5)

= 15% + [$3,925 / $3,910.5)

= 15% + 1.003

= 16%

2. Machine’s net present value :

Net present value = Present value of annual cash inflow - Initial investment

NPV

= [Annual cash inflow x PVAF(16%,5years] - Initial investment

= [$50,000 x 3.27429] - $163,700

= $14.5

3. Internal rate of return :

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

Where:

R1      =   Lower discount rate i.e 8%

R2      =   Higher discount rate i.e. 10%

NPV1   =   Higher Net Present Value (derived from R1)

NPV2   =   Lower Net Present Value (derived from R2)

NPV1 = [Annual cash inflow x PVAF(8%,5years] - Initial investment

= [$41,000 x 3.99271] - $163,700 = $1.11

NPV2 = [Annual cash inflow x PVAF(10%,5years] - Initial investment

= [$41,000 x 3.79078] - $163,700 = -$8,278

IRR

= 8% + [$1.11 x(10 - 8)] / [$1.11 - (-$8,278)]

= 8% + ($2.22 / $8,279.11)

= 8% + 0.0002

= 8%