Question

Bark company is considering investing in a project that costs $70,000, has an expected useful life of 3 years, no salvage value, and will increase net annual cash flows by $28,650. What is the internal rate of return?

Answer 1

Answer to the question:

Internal rate of return (IRR) – IRR is the discounted rate of return that makes the NPV of all the cash flows of a project equal to zero.

That is IRR is the rate of return at which the present value of all the cash flows is equal to the initial investment.

In the given case

Project cost = $ 70,000

Expected useful life = 3 years

Increase in net annual cash flows = $28,650

In the given case IRR is the rate of return at which present value of $28,650 for 3 years is equal to $70,000

PARTICULARS	CASH FLOW IN $	PV @ 10%	PV @ 12%
YEAR 1	28,650	26,045.45	25580.36
YEAR 2	28,650	23,677.69	22839.60
YEAR 3	28,650	21,525.17	20392.50
TOTAL	85,950	71248.31	68812.46

From the above table we get that PV of the cash flow @10% is higher than the initial investment of $70,000, whereas PV @12% is lower than the initial investment.

Therefore IRR is the rate of return somewhere between 10% and 12%, which can be calculated by the interpolation method.

IRR = 10% + PV of cash flow @ lower interest rate - Initial investment * (higher rate –lower rate

                          PV of cash flow @ (lower interest rate – Higher interest rate)

10% + 71,248.31 – 70,000 * (12%-10%)

           71,248.31 – 68,812.46

On solving the above, we get that IRR = 11.01% i.e. approximately equal to 11%