Question

Henrie’s Drapery Service is investigating the purchase of a new machine for cleaning and blocking drapes. The machine would cost $102,990, including freight and installation. Henrie’s estimated the new machine would increase the company’s cash inflows, net of expenses, by $30,000 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 14%, 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 $25,790 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

(1)-Machine’s internal rate of return (IRR)

The Present Value factor for determining IRR = Initial Investment Cost / Net Annual Cash Inflow

= $102,990 / $30,000 per year

= 3.433

From the given Present Value Annuity Factor Table (PVAIF Table), the discount rate (IRR) corresponding to the factor of 3.433 for 5 Years is closest to 14%

“The Machine’s internal rate of return (IRR) will be 14%”

(2)-Machine’s net present value using the discount rate of 14%

Net Present Value (NPV) = Present Value of annual cash inflows – Initial Investment

= $30,000[PVIFA 14%, 5 Years] - $102,990

= [$30,000 x 3.433] - $102,990

= $102,990 - $102,990

= $0 [Zero]

NOTE

-The formula for calculating the Present Value Annuity Inflow Factor (PVIFA) is [{1 - (1 / (1 + r)ⁿ} / r], where “r” is the Discount Rate/Cost of capital and “n” is the number of years.

(3)-Machine’s internal rate of return (IRR)

The Present Value factor for determining IRR = Initial Investment Cost / Net Annual Cash Inflow

= $102,990 / $25,790 per year

= 3.993

From the given Present Value Annuity Factor Table (PVAIF Table), the discount rate (IRR) corresponding to the factor of 3.993 for 5 Years is closest to 8%

“The Machine’s internal rate of return (IRR) will be 8%”