Jamaica Corp. is adding a new assembly line at a cost of $8.5 million. The firm expects the project to generate cash flows of $2 million, $3 million, $4 million, and $5 million over the next four years. Its cost of capital is 16 percent. What is the internal rate of return that Jamaica can earn on this project? (Do not round intermediate computations. Round final answer to the nearest percent.)
a. 18%
b. 19%
c. 20%
d. 21%
The Correct Answer and Explanation is:
To find the Internal Rate of Return (IRR), we need to determine the discount rate that makes the Net Present Value (NPV) of the project zero. IRR is essentially the rate at which the present value of future cash flows equals the initial investment.
Given:
- Initial investment (outflow): $8.5 million (at time 0)
- Cash inflows:
- Year 1: $2 million
- Year 2: $3 million
- Year 3: $4 million
- Year 4: $5 million
We need to find IRR, i.e., the rate rr that satisfies: 0=−8.5+2(1+r)1+3(1+r)2+4(1+r)3+5(1+r)40 = -8.5 + \frac{2}{(1 + r)^1} + \frac{3}{(1 + r)^2} + \frac{4}{(1 + r)^3} + \frac{5}{(1 + r)^4}
This cannot be solved algebraically, so we use trial and error, interpolation, or a financial calculator/Excel to compute it.
Let’s try:
At 20%:
NPV=−8.5+21.20+31.44+41.728+52.0736\text{NPV} = -8.5 + \frac{2}{1.20} + \frac{3}{1.44} + \frac{4}{1.728} + \frac{5}{2.0736} NPV=−8.5+1.6667+2.0833+2.3148+2.4105=−8.5+8.4753=−0.0247≈0\text{NPV} = -8.5 + 1.6667 + 2.0833 + 2.3148 + 2.4105 = -8.5 + 8.4753 = -0.0247 \approx 0
This is very close to zero, which indicates that the IRR is approximately 20%.
At 19%:
NPV=−8.5+21.19+31.4161+41.6841+52.0031\text{NPV} = -8.5 + \frac{2}{1.19} + \frac{3}{1.4161} + \frac{4}{1.6841} + \frac{5}{2.0031} NPV=−8.5+1.6807+2.1179+2.3753+2.4961=−8.5+8.6699=0.1699>0\text{NPV} = -8.5 + 1.6807 + 2.1179 + 2.3753 + 2.4961 = -8.5 + 8.6699 = 0.1699 > 0
NPV is positive, so 19% is too low.
At 21%:
NPV=−8.5+21.21+31.4641+41.7716+52.1441\text{NPV} = -8.5 + \frac{2}{1.21} + \frac{3}{1.4641} + \frac{4}{1.7716} + \frac{5}{2.1441} NPV=−8.5+1.6529+2.0487+2.2583+2.3325=−8.5+8.2924=−0.2076<0\text{NPV} = -8.5 + 1.6529 + 2.0487 + 2.2583 + 2.3325 = -8.5 + 8.2924 = -0.2076 < 0
NPV is negative, so 21% is too high.
Therefore, the IRR that sets NPV close to zero is 20%.
✅ Correct Answer: c. 20%
Explanation:
The internal rate of return (IRR) is the break-even interest rate where a project’s net present value is zero. It represents the project’s expected rate of return. Jamaica Corp.’s project costs $8.5 million and brings a total of $14 million in future cash inflows over 4 years. We discount these inflows at different rates to find when the present value equals $8.5 million. At 20%, the net present value is nearly zero, making it the IRR. Since 19% gives a positive NPV and 21% a negative one, we confirm that 20% is the correct IRR. This rate is higher than the cost of capital (16%), which indicates the project is financially worthwhile.