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Chapter 3: Problem 6

A project requires an initial investment of \(\$ 12000\). It has a guaranteed return of \(\$ 8000\) at the end of year 1 and a return of \(\$ 2000\) each year at the end of years 2,3 and \(4 .\) Estimate the IRR to the nearest percentage. Would you recommend that someone invests in this project if the prevailing market rate is \(8 \%\) compounded annually?

Short Answer

Expert verified
Calculate the IRR by solving NPV equation iteratively. If IRR > 8%, it鈥檚 a good investment.

Step by step solution

01

Define the Cash Flows

List the initial investment and the returns for each year. Initial investment: Year 0: Cash Flow = - Year 1: Cash Flow = Year 2: Cash Flow = Year 3: Cash Flow = Year 4: Cash Flow = .
02

Organize the Cash Flows in Equation Form

Use the equation for Net Present Value (NPV) and set it to zero to solve for Internal Rate of Return (IRR): \[-12000 + + \times (\frac{1}{( + 1)^2})+ \times (\frac{1}{( + 1)^3}) + \times (\frac{1}{(1+n)^4}) = 0\].
03

Substitute Values and Simplify

Substitute the given values: \[-12000 + \frac{8000}{(1+n)} + \frac{2000}{(1+n )^2} +\frac{}{( + 1 )} + \frac{}{( + 1 )^2}\] = 0.
04

Solve for n Iteratively

Start with an estimated value of and adjust iteratively to solve for the exact IRR: For example, trying specific values like n = 0.08, 0.1, 0.12, and solving for equality.
05

Compare IRR with Market Rate

The IRR value found is % (i.e., if it's more than 8%, it's a good investment; otherwise, it鈥檚 not): Then compare this IRR value with the prevailing market rate. .

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Cash Flow
When analyzing any project, 'cash flow' is crucial. It represents the amount of money being transferred in and out. Cash flows for investments typically include:
  • Initial Investment: This is the money you put in at the start (Year 0). For example, here it is \(\$12000\).
  • Subsequent Returns: These are the money inflows received over the life of the project.
In our example, the project provides a return of \(\$8000\) at the end of Year 1 and \(\$2000\) each year from Year 2 to Year 4. It is essential to closely monitor and evaluate these flows to make informed investment decisions.
Net Present Value (NPV)
Net Present Value (NPV) is a vital concept in investment analysis. It helps determine if a project is worth investing in by comparing the value of cash inflows with outflows over time. The formula for NPV is: \[NPV = \sum_{t=0}^{N}\frac{CF_t}{(1 + r)^t}\]

Here, \(CF_t\) represents the cash flow at time \(t\), \(r\) is the rate of return, and \(N\) is the total number of periods.

The goal is to set NPV to zero to find IRR. In our example: \[-12000 + \frac{8000}{(1 + n)} + \frac{2000}{(1 + n)^2} + \frac{2000}{(1 + n)^3} + \frac{2000}{(1 + n)^4} = 0\]. Solving this equation helps us find the IRR, indicating the project's potential profitability.
Investment Analysis
Investment analysis involves examining the potential returns and risks associated with a project. Key steps include:
  • Initial Assessment: Outline all potential costs and revenues.
  • Calculating Metrics: Compute figures like NPV and IRR to estimate profitability.
  • Comparative Analysis: Compare the project's returns with the prevailing market rates.
By analyzing our example, we can determine whether it would be prudent to invest in the project by using tools such as IRR to compare potential returns with market rates.
Interest Rate
The interest rate is a percentage that determines the cost of borrowing or the gain on investments over time. In investment analysis, it is crucial because:
  • Discounting Future Cash Flows: The interest rate discounts future returns to their present value.
  • Comparative Benchmark: It provides a benchmark to compare the returns of various projects. For instance, a project with an IRR below the market rate of 8% might not be attractive.
When solving for IRR, the interest rate gives us a comparison metric to decide whether an investment is worthwhile. In our case, we compare the computed IRR to the market rate of 8% to make a decision.

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Most popular questions from this chapter

(Excel) A bank decides to produce a simple table for its customers, indicating the monthly repayments of a \(\$ 5000\) loan that is paid back over different periods of time. Produce such a table, with 13 rows corresponding to monthly interest rates of \(0.5 \%, 0.525 \%, 0.55 \%, 0.575 \%, \ldots, 0.8 \%\), and 9 columns corresponding to a repayment period of \(12,18,24, \ldots, 60\) months.

A government bond that originally cost \(\$ 500\) with a yield of \(6 \%\) has 5 years left before redemption. Determine its present value if the prevailing rate of interest is \(15 \%\).

Calculate (a) \(10 \%\) of \(\$ 2.90\) (b) \(75 \%\) of \(\$ 1250\) (c) \(24 \%\) of \(\$ 580\)

The population of a country is currently at 56 million and is forecast to rise by \(3.7 \%\) each year. It is capable of producing 2500 million units of food each year, and it is estimated that each member of the population requires a minimum of 65 units of food each year. At the moment, the extra food needed to satisfy this requirement is imported, but the government decides to increase food production at a constant rate each year, with the aim of making the country self-sufficient after 10 years. Find the annual rate of growth required to achieve this.

(a) Current monthly output from a factory is 25000 . In a recession, this is expected to fall by \(65 \%\). Estimate the new level of output. (b) As a result of a modernization programme, a firm is able to reduce the size of its workforce by \(24 \%\). If it now employs 570 workers, how many people did it employ before restructuring? (c) Shares originally worth \(\$ 10.50\) fall in a stock market crash to \(\$ 2.10\). Find the percentage decrease.
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