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Time Value of Money: The Buy Versus Rent Decision – Case Solution

In this "Time Value of Money: The Buy Versus Rent Decision" case study, a recent MBA graduate had been renting an apartment while a similar flat had been listed for sale. The graduate is now facing the typical buy versus rent decision. Hence the grad decided to apply some of her analytical tools acquired in business school to make this decision for her personal life.

Sean Cleary, Stephen R. Foerster Ivey ( W14403-PDF-ENG ) August 28, 2014

Case questions answered:

Case study questions answered in the first solution:

What is the best solution to take — to rent or to buy?
What are the assumptions you use?

Case study questions answered in the second solution:

Calculate the best route for the graduate’s housing situation, developing your understanding of the time value of money (TVM) concepts and calculations.
Describe your assumptions, methodology, and results in your discussion narrative, and attach a simple spreadsheet supporting your analysis.

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Time Value of Money: The Buy Versus Rent Decision Case Answers

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BACKGROUND – Time Value of Money: The Buy Versus Rent Decision Case Study

The case is about Rebecca Young, who just completed her MBA and moved to Toronto for her new job in the banking industry. She is having a dilemma between renting or buying a condo instead.

A condo unit is an identical unit next door to her rented unit. She has been renting for more than a year, and she really thinks she can afford the monthly amortization, knowing that she has a secured job in the next 5-10 years.

Let us list the facts of the case:

Her monthly rent is $3,000, and this does not include utilities and cable television, but parking is included in the monthly rent.

The purchase price of the unit is $620,000, but Rebecca thinks she can get it for $600,000. 20% of the purchase price is needed for a downpayment. This will also include both a local and provincial deed-transfer tax of 1.5% of the purchase price – this is both payable and due on the purchase date. A closing fee is estimated to be around $2,000. The total cash outlay on the purchase date totals $140,000, broken as follows:

Time Value of Money: The Buy Versus Rent Decision

Rebecca requested to model the amount of the outstanding principal at various points in the future, two, five, and ten years from now, and this was presented to her.

There were also scenario cases that she considered in her analysis before making her final decision. These scenario cases are presented below and are described accordingly:

The condo price remains unchanged.
The condo price drops 10% over the next two years, then increases back to its purchase price by the end of five years, and then increases by a total of 10% from the original price by the end of ten years.
The condo price increases annually by the annual rate of inflation of 2% per year over the next ten years
The condo price increases annually by an annual rate of 5% per year over the next 1ten years.

These scenario cases are properly illustrated and calculated using the Excel platform.

PRESENTATION:

Case 1 is presented to Ms. Young as saying that she is renting the condo and intelligently pursuing to invest the cash outlay of $140,000. The future value of this investment at year 2 is…

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Case study on TVM

Financial management (finman), la salle university.

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International Journal of Research in Finance and Management 2018; 1(1): 18 -

P P-ISSN: 2617- E-ISSN: 2617 - IJRFM 201 8; 1(1): 18 - Received: 10-11-

Accepted: 12-12-201 7

Mohammad Rahman Institute of Business Administration, Jahangirnagar University, Bangladesh

Correspondence Mohammad Rahman Institute of Business Administration, Jahangirnagar University, Bangladesh

Time value of money: A case study on its concept and

Its application in real life problems, mohammad rahman.

Purpose of this case study is to understand the concept of time value of money. Way to calculate future value and to use it real life situations. It is the concept that the value of a rupee to be received in coming future is less than the value of rupee today. Time value of Money is a theory advantage of having money today then latter. The time value of money is a concept, which states money available now has worth more than the same amount of money in future due to its earning capacity. I have studied advantages / significance of TVM and various reasons which lead to requirement of TVM. Major reason behind time value of money is inflation, risk and rate of return; which lead to reduction in value of same money in future period. I have tried to find solution to four real life problems through this case study. Problem includes loan repayment problem, investment problem, asset replacement problem, growth rate of profit earned in various years and implicit return on investment.

Keywords: Time value of money (TVM), present value future value rate of return, number of periods, annuity value

Introduction It is the concept that the value of a rupee to be received in coming future is less than the value of rupee today. I. Time value of Money is a theory advantage of having money today then latter. II. The time value of money is a concept, which states money available now has worth more than the same amount of money in future due to its earning capacity.

To understand the concept of Time value of money
How we can calculate present value/ future value for profiled cash flows?
How time of money can helps us to solve our real life problems?

There are various reasons behind this concept

Investment: Money can be invested for generating more money, so money received today has greater value.
Interest Earning: Value of rupee currently is more than its future value, as it is expected that it can be A rupee today is worth more today than in future because of its opportunity cost of lost earnings.
Inflation: It is expected to increase in price of commodities in coming future due to inflation, which lead to decline in value of today’s money. “Positive rate of Inflation reduce the purchasing power of rupee with passage of time”.
Risk: When someone lends money, there is a risk involved in not paying back the money. Because of that risk interest is charged on the money, which reduces value of money.

Terms attached with Time Value of Money are

Present Value is a series of future payment or future value discounted at a rate of interest up to the current date to reflect the time value of money and result is called present value.

Future Value is amount that is calculated by increasing present value or series of payment at the given rate of interest and result is future value.

Rate of Interest is a charge against use to inflate/discount present value / future value to achieve desire result.

Time Value of Money Principle: It is used to compare two different cash flow statements of two different companies or projects for investment. Purpose is to state return provided by them if we make investment now.

Number of Periods: it represent the time period to which value or payment series discounted / inflated to calculate appropriate return.

Significance of Time Value of Money It is mostly used concept in Finance world; based on this, decisions are made to maximize return on investments. It helps shareholders to invest their fund wisely. Its concept contributes to this aspect to much extent. Its significance are as follows:

Investment Decision is decision to make investment of funds for long term purpose. TVM help us to identify long term cash flow statements which will occur at different point of time. So, if investor have two projects to invest its money in, those two projects can be compared with this technique even if their cash flow statement time period doesn’t matches with each other by providing present value of their future cash flow. Its concept is mostly used in equity or debt securities investment by using valuation models while doing investments.
Financing Decision is decision to make to optimize capital structure of the organization. Raising fund for equity, debt or from any other source. TVM helps in this decision by comparing cost to company through usage of effective rate of interest of each source of finance. And then present value of costs of two alternatives is compared against each other to decide on appropriate source of financing.
Operational Decision: This concept is also used in evaluating creditor cycle and debtors’ cycle in managing cash collection under current assets management.

Tvm Formula FV = PV * [1 + (i/n)] (n * t) FV = Future value of money PV = Present value of money i = Interest rate t = number of years taken into consideration n = number of compounding periods of interest per year

Example: PV = Rs. 10, i = 10% t = 10 years n = 1 p. FV =?

Scenario 1: n changes from 1 to 4 in case 1 Scenario 2: i changes from 10% to 11% in case 1 Scenario 3: t changes from 1 to 4 in case 1

Let see 3 different scenarios; with change in single input how it leads to change in results:

In all three scenarios with increase in any of these inputs leads to increase in future value in all the scenarios and vice versa.

Applications of Time Value of Money in Real Life Problems Asset Replacement Problem A Manager has to find out accumulated sum of money in future date to replace it with existing assets. Example: ABC Ltd has Rs. 100,000 of Debentures (5%). Company want set up a replacement of existing assets after 10 years. This replacement asset earns 8% per year. Required investment will be as follows: Outcome: So ABC Ltd should invest Rs. 46,319 now to get Rs. 100,000 as replacement at 10 years.

i = 8% t = 10 n = 1 FV = 100, PV = Rs. 100,000 / [1 + (0/1)] ^ (1 * 10) PV = Rs. 46,319.

Investment Problem (Rate of Return) Manage wants to calculate implicit rate of return over an investment. Example: Company offering to pay Rs. 201,475 at the end of 10 years with deposit of Rs. 15,000 p. How much implicate rate of return ABC ltd is offering to its customers? Outcome: Company is offering 5% of annual return.

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