# Investments: Net Present Value and Investment Assignment

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Initial investment An initial investment is the money a business owner needs to start up a firm. It might include the business owner’s own money, money borrowed from an array of sources including family and friends or banks, or capital raised from investors. The term initial investment is also used as the money a business owner uses to invest in a capital investment venture such as a piece of equipment or a building. IRR The higher a projects internal rate of return, the more desirable it is to invest in the project.

Some ways to use the IRR method are: ??? Discounted Cash Flow Analysis – Find the interest rate return that you would receive as your investment return rate. ??? Capital Budget Planning – Go through the capital budget process so that you make the best economic decision. ??? Discounted Cash Flow Analysis – When you calculate IRR you will have one number for an objective comparison between capital projects. ??? Investment Calculator – Determine if a potential investment is a good choice or not. ??? Compound Rate of Return – Understand the compounding effect of interest on investments. (“Calculating internal rate,”)

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Deciding between investments You are deciding between two mutually exclusive investment opportunities. Both require the same initial investment of \$10 million. Investment A will generate \$2 million per year (starting at the end of the first year) in perpetuity. Investment B will generate \$1. 5 million at the end of the first year and its revenues will grow at 2% per year for every year after that. a. Which investment has the higher IRR? a) Since IR is defined as the rate of return that makes the NPV = 0: Investment A: Setting NPV = \$0, and solving for r \$0 = [pic] [pic][pic] r = [pic] IRR = 20%

Investment B: Setting NPV = \$0, and solving for r \$0 = [pic] [pic][pic] r -0. 02 = [pic] r ??? 0. 02 = 0. 15 r = 0. 15 + 0. 02 IRR = 17% b. Which investment has the higher NPV when the cost of capital is 7%? b) Substituting r = 0. 07 into the NPV formulas derived in part a: Investment A: NPV = [pic] = \$18,571,428. 57 Investment B: NPV = [pic] = \$20,000,000 Investment B has the higher NPV c. In this case, when does picking the higher IRR give the correct answer as to which investment is the best opportunity? c) At the crossover rate, the NPV rule and the IRR rule lead to equal decisions.

We accept the investment using their rule if the required rate of return is below the crossover rate. The NPV would be positive at any discount rate less than the crossover rate, so we will accept the investment using the NPV rule as well. The two rules are the same in this case. To calculate the crossover rate, we set NPVA = NPVB [pic][pic] [pic] 1,500,000r = 2,000,000r – \$400,000 0. 5 r = 0. 04 r = 0. 08 = 8% References Calculating internal rate of return. (n. d. ). Retrieved from http://www. business-analysis-made-easy. com/Calculating-Internal-Rate-Of-Return. html

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