A company is evaluating two different projects. Project A requires an initial investment of $100,000 and is expected to generate annual cash flows of $30,000 for 5 years. Project B requires an initial investment of $150,000 and is expected to generate annual cash flows of $50,000 for 5 years. If the company's cost of capital is 8%, which project has the higher Net Present Value (NPV)?
Explanation: To determine which project has the higher NPV, we need to calculate the present value of each project's cash flows using the cost of capital (8%) as the discount rate. Project B generates higher annual cash flows and, although it requires a larger initial investment, the higher cash flows often result in a higher NPV.
For precise comparison, use the NPV formula: NPV=∑CFt(1+r)t−Initial InvestmentNPV = \sum \frac{CF_t}{(1 + r)^t} - Initial \, InvestmentNPV=∑(1+r)tCFt−InitialInvestment Where CFtCF_tCFt is the cash flow in year ttt, rrr is the discount rate, and ttt is the year.
Project A NPV: NPVA=30,000(1+0.08)1+30,000(1+0.08)2+30,000(1+0.08)3+30,000(1+0.08)4+30,000(1+0.08)5−100,000NPV_A = \frac{30,000}{(1 + 0.08)^1} + \frac{30,000}{(1 + 0.08)^2} + \frac{30,000}{(1 + 0.08)^3} + \frac{30,000}{(1 + 0.08)^4} + \frac{30,000}{(1 + 0.08)^5} - 100,000NPVA=(1+0.08)130,000+(1+0.08)230,000+(1+0.08)330,000+(1+0.08)430,000+(1+0.08)530,000−100,000 Project B NPV: NPVB=50,000(1+0.08)1+50,000(1+0.08)2+50,000(1+0.08)3+50,000(1+0.08)4+50,000(1+0.08)5−150,000NPV_B = \frac{50,000}{(1 + 0.08)^1} + \frac{50,000}{(1 + 0.08)^2} + \frac{50,000}{(1 + 0.08)^3} + \frac{50,000}{(1 + 0.08)^4} + \frac{50,000}{(1 + 0.08)^5} - 150,000NPVB=(1+0.08)150,000+(1+0.08)250,000+(1+0.08)350,000+(1+0.08)450,000+(1+0.08)550,000−150,000
Calculations will show that Project B typically has a higher NPV.