Question

A company is considering investing in a new machine that requires a cash payment of $38,209 today. The machine will generate annual cash flows of $15,364 for the next three years. What is the internal rate of return if the company buys this machine? (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

Answer 1

Answer:

The IRR is 10%.

Explanation:

a) Calculation of Internal Rate of Return (IRR):

We choose a discount rate, say 10% and use it to discount the cash flows to their present values.  If the net present value (NPV) of all the cash flows equals zero, then that discount rate is accepted as the IRR.

b) Without 10% discount rate, the discount factors are for:

1st year = 1.1 (1 + discount rate) raised to power 1

2nd year = 1.21 (1 + discount rate) raised to power 2

3rd year = 1.331 (1 + discount rate) raised to power 3

c) These discount factors will divide the cash inflows for each year:

1st year, NPV = $15,364/1.1 = $13,967.27

2nd year, NPV = $15,364/1.21 = $12,697.52

3rd year, NPV = $15,364/1.331 = $11,543.20

Total NPV of inflows                 = $38,209 approximately

NPV of outflows                         -$38,209

NPV of inflows and outflows      $0

So, the IRR is 10%.

IRR is a capital budgeting metric to measure profitability by using a discount rate which makes the net present value of all cash flows to become zero.  To get a suitable rate, trial and error is involved, or one can make use of educated best guess.