Question

Please show using step by step mathematics.

Henrie’s Drapery Service is investigating the purchase of a new machine for cleaning and blocking drapes. The machine would cost $170,595, including freight and installation. Henrie’s estimated the new machine would increase the company’s cash inflows, net of expenses, by $45,000 per year. The machine would have a five-year useful life and no salvage value.

Click here to view 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 $40,500 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

Internal rate of return is the rate at which NPV = 0

i.e. present value of cash inflows = Present value of cash outflows

Let the rate be x

45000*PVAF(x%, 5 years) = 170,595

PVAF(x%, 5 years) = 3.791

Using Present value annuity factor table, x = 10%

Hence, machine’s IRR = 10%

b.NPV at 10% = Present value of cash inflows – present value of cash outflows

= 45000*3.791 – 170,595

= 0

NPV at IRR = 0

Hence, IRR = 10%

c.PVAF(x%, 5 years)= 170,595/40,500 = 4.2122

Using table, IRR = 6%

Hence, IRR = 6%