A company is considering buying a new piece of machinery that costs $20,000 and has a salvage value of $8,000 at the end of its 5-year useful life. The machinery nets $5,000 per year in annual revenues. MARR = 8%. The internal rate of return (IRR) on this investment is between A. 16% – 17% B. 2% – 3% C. 6% – 7% D. 4% – 5% E. 11% – 12%
The correct answer and explanation is:
Correct Answer: A. 16% – 17%
To determine the internal rate of return (IRR), we need to solve for the interest rate that makes the net present value (NPV) of the cash flows equal to zero.
Given:
- Initial investment = $20,000 (cash outflow at time 0)
- Annual net revenue = $5,000 for 5 years (cash inflow)
- Salvage value = $8,000 at the end of year 5 (additional cash inflow)
- MARR = 8% (not used for IRR, but for comparison)
- IRR is the rate rr that satisfies: 0=−20,000+∑t=155,000(1+r)t+8,000(1+r)50 = -20,000 + \sum_{t=1}^{5} \frac{5,000}{(1 + r)^t} + \frac{8,000}{(1 + r)^5}
This is a trial-and-error or numerical method problem. We test several rates:
Try 16%: NPV=−20,000+[5,000×(P/A,16%,5)]+8,000(1.16)5NPV = -20,000 + \left[5,000 \times (P/A,16\%,5)\right] + \frac{8,000}{(1.16)^5} (P/A,16%,5)≈3.2743;(P/F,16%,5)≈0.4761(P/A,16\%,5) ≈ 3.2743; \quad (P/F,16\%,5) ≈ 0.4761 NPV≈−20,000+(5,000×3.2743)+(8,000×0.4761)=−20,000+16,371.5+3,808.8=+180.3NPV ≈ -20,000 + (5,000 × 3.2743) + (8,000 × 0.4761) = -20,000 + 16,371.5 + 3,808.8 = +180.3
Try 17%: (P/A,17%,5)≈3.1993;(P/F,17%,5)≈0.4406(P/A,17\%,5) ≈ 3.1993; \quad (P/F,17\%,5) ≈ 0.4406 NPV≈−20,000+(5,000×3.1993)+(8,000×0.4406)=−20,000+15,996.5+3,524.8=−478.7NPV ≈ -20,000 + (5,000 × 3.1993) + (8,000 × 0.4406) = -20,000 + 15,996.5 + 3,524.8 = -478.7
At 16%, NPV is positive. At 17%, NPV is negative. Therefore, IRR lies between 16% and 17%.
The internal rate of return helps a company determine the rate at which their investment breaks even in present value terms. Because the IRR is higher than the company’s minimum attractive rate of return (MARR of 8%), this investment is financially viable. Choosing projects where IRR exceeds MARR maximizes value and profitability.