Rani owns and operates a small electronic repair shop. A new instrument, called Rapid Diagnosist, which facilitates faster diagnosis of the items to be repaired, has been marketed recently. Being technologically new, it is however expensive. Based on the past, the costs of such instruments decline

Question

Rani owns and operates a small electronic repair shop. A new instrument, called Rapid Diagnosist, which facilitates faster diagnosis of the items to be repaired, has been marketed recently. Being technologically new, it is however expensive. Based on the past, the costs of such instruments decline fast. Rani predicts that Rapid Diagnosist would sell for $5,000 in the next 5 years. She decides to retain a fixed sum each year from annual profit to raise this capital 5 years hence. The retained sum will be invested regularly in the local bank at 6.5% annually compounded interest rate. How much should be retained each year?

Accepted Answer

First you need to decide whether to draw a cashflow diagram for comprehending the problem statement. This depends on how well you understand the problem. Do you know what is being asked for, what’s the unknown, and what variables are known? If you can comprehend all these without the cashflow diagram, you can avoid sketching it. Let us assume that to be the case. We still need to have a mental picture of the problem.

Note that it is a multi-payment problem with regular deposits. It involves A and F, with A being the unknown. The relevant formula is Equation (4.2a) or (4.2b). Use the latter if you favor the functional notation method.

Next, we gather the values of the variables and proceed with the solution. The given data are: F = $5,000, [latex]i=6.5\%[/latex] (per year), and n = 5 (years). Let us say that we decide to use the functional notation method; so from Equation (4.2b), we have:

[latex]A=5,000\left\lgroup\frac{A}{F,6.5\%,5} ight group[/latex]

Look for the value of A/F-factor in the tables. Since there is no table for 6.5%, look for the values corresponding to 6% and 7% and determine their average (since 6.5% is the average of 6% and 7%). This works out to be:

[latex]{(0.1774+0.1739)}/{2}=0.17565[/latex] , yielding

[latex]A=5,000 imes 0.17565[/latex]

[latex]=\$878[/latex]

Thus, Rani must retain $878 each year from the annual profit.

Question 4.2: Rani owns and operates a small electronic repair shop. A new...

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