Problem 8-9 Calculating NPV [LO 4] Consider the following cash flows: Year Cash Flow 0 –$ 32,000 1 14,200 2 17,500 3 11,600

Problem 8-9 Calculating NPV [LO 4]

Consider the following cash flows:

Year	Cash Flow
0		–$	32,000
1			14,200
2			17,500
3			11,600

Requirement 1:

What is the NPV at a discount rate of zero percent? (Do not round intermediate calculations.) Net present value $   Requirement 2: What is the NPV at a discount rate of 10 percent? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)   Net present value $   Requirement 3: What is the NPV at a discount rate of 20 percent? (Do not round intermediate calculations. Negative amount should be indicated by a minus sign.Round your answer to 2 decimal places (e.g., 32.16).)   Net present value $   Requirement 4: What is the NPV at a discount rate of 30 percent? (Do not round intermediate calculations. Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places (e.g., 32.16).)   Net present value $   Explanation: 1: The NPV of a project is the PV of the outflows plus the PV of the inflows. At a zero discount rate (and only at a zero discount rate), the cash flows can be added together across time. So, the NPV of the project at a zero percent required return is:   NPV = – $32,000 + 14,200 + 17,500 + 11,600 NPV = $11,300   2: The NPV at a 10 percent required return is:   NPV = – $32,000 + $14,200 / 1.10 + $17,500 / 1.102 + $11,600 / 1.103 NPV = $4,087.15   3: The NPV at a 20 percent required return is:   NPV = – $32,000 + $14,200 / 1.20 + $17,500 / 1.202 + $11,600 / 1.203 NPV = –$1,300.93   4: And the NPV at a 30 percent required return is:   NPV = – $32,000 + $14,200 / 1.30 + $17,500 / 1.302 + $11,600 / 1.303 NPV = – $5,441.97   Notice that as the required return increases, the NPV of the project decreases. This will always be true for projects with conventional cash flows. Conventional cash flows are negative at the beginning of the project and positive throughout the rest of the project.     Calculator solution:   Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.    CFo  –$32,000 CFo  –$32,000 C01  $14,200 C01  $14,200 F01  1 F01  1 C02  $17,500 C02  $17,500 F02  1 F02  1 C03  $11,600 C03  $11,600 F03  1 F03  1   I = 0%   I = 10%   NPV CPT   NPV CPT   $11,300.00   $4,087.15     CFo  –$32,000 CFo  –$32,000 C01  $14,200 C01  $14,200 F01  1 F01  1 C02  $17,500 C02  $17,500 F02  1 F02  1 C03  $11,600 C03  $11,600 F03  1 F03  1   I = 20%   I = 30%   NPV CPT   NPV CPT   –$1,300.93   –$5,441.97