Question

Henrie’s Drapery Service is investigating the purchase of a new machine for cleaning and blocking drapes. The machine would cost $113,730, 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.

Use Exhibit 13B-1 and Exhibit 13B-2, to determine the appropriate discount factor(s) using table.

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 10%, 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 $27,000 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

1) The internal rate of return is the rate at which the present value of cash inflows is equal to present value of cash outflows.

Cash outflow for machine = Cash Inflows*PVAF(5 yrs, i%)

where, i = internal rate of return

$113,730 = $30,000*PVAF(5 yrs, i%)

PVAF(5 yrs, i%) = $113,730/$30,000

PVAF(5 yrs, i%) = 3.791

The relevant interest rate for 3.791 from the present value ordinary annuity table at the time period of 5 is 10% (approx.)

Hence the machine’s internal rate of return is 10%.

2) Present Value of Cash Inflows = Cash Inflows*PVAF(5 yrs, 10%)

= $30,000*3.79079 = $113,724

Net Present Value = PV of Cash Inflows - Cash Outflows

= $113,724 - $113,730 = -$6

3) Cash outflow for machine = Cash Inflows*PVAF(5 yrs, i%)

where, i = internal rate of return

$113,730 = $27,000*PVAF(5 yrs, i%)

PVAF(5 yrs, i%) = $113,730/$27,000

PVAF(5 yrs, i%) = 4.2122

The relevant interest rate for 4.2122 from the present value ordinary annuity table at the time period of 5 is 6% (approx.)

Hence under these conditions, the machine’s internal rate of return is 6%.