Math Problem Statement

You are considering the following two mutually exclusive projects. The required return on each project is 12 percent. Which project should you accept and what is the best reason for that decision?

Year Cash Flow (A) Cash Flow (B) 0 −$ 32,000 −$ 26,000 1 11,500 3,500 2 15,900 5,800 3 13,200 24,900

Multiple Choice

Project B, because it has the higher internal rate of return

Project A, because it has the higher internal rate of return

Project A, because it has the higher net present value

Project B, because it has the higher net present value

Project A, because it pays back faster

Solution

To determine which project to accept, we will calculate the Net Present Value (NPV) for both projects at a discount rate of 12% and compare their values. The decision will be based on the project with the higher NPV, as it maximizes value for the company.


Formula for NPV:

NPV=t=0nCt(1+r)tNPV = \sum_{t=0}^{n} \frac{C_t}{(1 + r)^t} where:

  • CtC_t = Cash flow at time tt
  • rr = Discount rate (12% or 0.12)
  • tt = Year

Calculations:

Project A:

NPVA=32,000(1.12)0+11,500(1.12)1+15,900(1.12)2+13,200(1.12)3NPV_A = \frac{-32,000}{(1.12)^0} + \frac{11,500}{(1.12)^1} + \frac{15,900}{(1.12)^2} + \frac{13,200}{(1.12)^3} NPVA=32,000+11,5001.12+15,9001.2544+13,2001.4049NPV_A = -32,000 + \frac{11,500}{1.12} + \frac{15,900}{1.2544} + \frac{13,200}{1.4049} NPVA=32,000+10,267.86+12,675.34+9,394.80NPV_A = -32,000 + 10,267.86 + 12,675.34 + 9,394.80 NPVA=347.99NPV_A = 347.99

Project B:

NPVB=26,000(1.12)0+3,500(1.12)1+5,800(1.12)2+24,900(1.12)3NPV_B = \frac{-26,000}{(1.12)^0} + \frac{3,500}{(1.12)^1} + \frac{5,800}{(1.12)^2} + \frac{24,900}{(1.12)^3} NPVB=26,000+3,5001.12+5,8001.2544+24,9001.4049NPV_B = -26,000 + \frac{3,500}{1.12} + \frac{5,800}{1.2544} + \frac{24,900}{1.4049} NPVB=26,000+3,125+4,624.43+17,725.51NPV_B = -26,000 + 3,125 + 4,624.43 + 17,725.51 NPVB=525.06NPV_B = -525.06


Decision:

  • Project A NPV = $347.99
  • Project B NPV = -$525.06

Since Project A has the higher NPV, it should be accepted. The best reason is that it maximizes the net present value.


Correct Answer:

Project A, because it has the higher net present value.


Do you want further details on these calculations?
Here are some related questions to expand understanding:

  1. How is the internal rate of return (IRR) calculated, and how does it compare with NPV?
  2. What are the advantages of using NPV over payback period for decision-making?
  3. How does the discount rate affect the NPV of a project?
  4. Can mutually exclusive projects both have positive NPVs? If so, how should decisions be made?
  5. What happens if the required return changes from 12% to another value?

Tip: Always prioritize projects with higher NPV when comparing mutually exclusive options, as it directly reflects added value to the firm.

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Math Problem Analysis

Mathematical Concepts

Net Present Value (NPV)
Discounted Cash Flow (DCF)
Decision-making in mutually exclusive projects

Formulas

NPV = Σ (Ct / (1 + r)^t)
Ct = Cash flow at time t
r = Discount rate
t = Time in years

Theorems

Principle of Maximizing Net Present Value in capital budgeting

Suitable Grade Level

Undergraduate Finance or MBA