Chapter 4 Time Value Of Money And Chapter 5 Bonds Bond Valua

Chapter 4 Time Value Of Moneychapter 5 Bonds Bond Valuation And In

Chapter 4 Time Value of MoneyChapter 5 Bonds Bond Valuation And In

Chapter 4. Time Value of Money Chapter 5. Bonds, Bond Valuation, and Interest Rates Finance – Week 3 Lecture Time Value of Money The time value of money is a very important concept in the business world and in your own personal finances! Many students struggle with the underlying concepts when they first begin to explore this area. However, with a little patience, the time value of money can be a fun and highly useful concept to master.

The elements are simple, the calculations are sometimes not so simple. The time value of money is based on the interest rate, how much time has passed, and the amount we started with or want to end with. A change in any of these three elements can significantly change the outcome of our calculation. A great example that you may very well be able to relate to is your home mortgage or auto loan or student loan. The mortgage is a great one to pick on because they are generally so long.

A standard mortgage is often 30 years long. The longer we have money invested or borrowed, the more powerful the time value of money is. Each period we accrue interest on the amount we owe on our mortgage. When we go to make our monthly mortgage payment, it must first cover the new interest that has accrued. Anything left over then goes to reduce the principle amount we borrowed.

So the more interest we owe, the less principle we pay each month and the longer it takes to pay off the mortgage. Adding just $25 per month to your mortgage payment to pay extra on your principle can reduce the length of your loan potentially by years! This is the power of the time value of money. It works the same way in business. When our investors put money into our organization they are expecting a return in exchange for allowing us to use their funds for a period of time.

The same is true of a business loan. No matter where we get our capital, someone will be expecting a return! The longer we have their money tied up, the greater the return. Later in the course we’ll look at the capital budgeting process which relies heavily on time value of money calculations. We’ll see how we can evaluate potential projects we would like to complete all the while taking into consideration how much it costs us to tie up funds.

There are several different types of time value of money calculations and it’s important to understand which one to use in each situation. First, we must decide if we are looking to find the value of money right now (present value) or the value of money at some point in the future (future value). Then we have to assess how often the cash flow will occur: once (lump sum) or many times (annuity). Annuities are payments or receipts of money that happen more than once, always in the same time increments, and always in the same amount. For example, if we receive $100 for our birthday every year on the same day, that’s an annuity.

Another common example of annuities in business would be capital lease payments or annual cash flows from a project. Once we identify the type of calculation we need, we can use several different tools to help us calculate the time value of money. We may be looking for the present value of a lump sum ($10,000 to be received 2 years from now), the present value of an annuity ($1,000 received every year for ten years – what is it worth right now?), the future value of a lump sum ($10,000 invested right now, what is it worth in 5 years?) or the future value of an annuity ($1,000 received every year for ten years – what is it worth in ten years?). The time value of money factor charts can help us perform these calculations manually.

A financial calculator can do all of these and more if we know the right buttons to push. There are also formulas for each one that we can perform long hand. No matter what approach works best for you, keep your resources handy (your time value of money charts or your financial calculator) since these calculations and concepts are at work in many areas of business and your personal finances. We don’t have to look far to find the time value of money. It plays a role in how much you pay to use your credit card, your monthly mortgage payments, auto loans, student loans, bond interest, lease payments, the selling price of bonds, and various methods used to assess capital projects.

Even winning the lottery requires time value of money calculations. The time value of money can be used to identify the rate of return offered by the lump sum versus annuity pay out on a large lottery win! Then you can decide which rate is more advantageous to you and whether or not you can invest your winnings and earn a rate higher than the lottery is offering in their annuity payments.

Paper For Above instruction

The concept of the time value of money (TVM) is fundamental in finance, illustrating that the value of money changes depending on when it is received or invested. This principle asserts that a sum of money available today is worth more than the same sum in the future due to its potential earning capacity. As a result, understanding TVM is critical for making informed financial decisions, including investments, loans, and capital budgeting.

The foundation of TVM lies in the interest rate, the amount of time involved, and the initial or future amount of money. Changes to any of these variables significantly influence the valuation outcomes. For example, in personal finance, mortgage loans exemplify TVM principles vividly. A 30-year mortgage entails interest accruing monthly, which impacts the total repayment amount. Increasing the monthly payments directed toward the principal can substantially reduce the loan term, demonstrating the power of compounding interest and the importance of early principal reduction.

In a broader economic context, TVM is integral to business financing. Investments are made with the expectation of returns that compensate for the time funds are committed. Similarly, businesses seeking loans must consider the cost of capital and the interest paid over time, emphasizing the importance of TVM in assessing financial feasibility and profitability. For example, in capital budgeting, projects are evaluated based on their present and future cash flows, counting the time value of these cash flows to determine net present value (NPV) or internal rate of return (IRR).

TVM calculations are categorized broadly into present value (PV) and future value (FV), each further distinguished by whether they involve lump sums or annuities. Lump sums refer to single cash flows, whereas annuities involve multiple periodic cash flows—equal payments made at regular intervals. For instance, receiving $1,000 annually for ten years constitutes an annuity. These distinctions guide the selection of appropriate calculation methods or financial tools, such as factor charts, formulas, or financial calculators.

Manual calculation formulas for PV and FV of lump sums and annuities underpin many of these assessments. For example, the present value of a future lump sum considers discounting the future sum back to its present value using an appropriate discount rate. Conversely, the future value quantifies how much an invested amount will grow over time, accounting for interest accrual. When dealing with annuities, calculations often involve the use of annuity factors, which simplify the process of summing the discounted cash flows.

Financial calculators and online tools significantly streamline these calculations, reducing errors and saving time. Nevertheless, understanding the underlying formulas remains vital for financial literacy. These principles extend beyond personal finance, influencing corporate decision-making, bond valuation, leasing, and even lottery payouts. In lottery scenarios, for instance, investors compare the present value of lump sum winnings against structured annuity payments to determine the most advantageous choice, considering their potential investment returns.

In conclusion, the time value of money is a pivotal concept that underpins virtually every aspect of financial management. Mastery of TVM enables individuals and businesses to evaluate investment opportunities, optimize loan repayments, and make strategic financial decisions that maximize value over time. Its application is widespread, from determining mortgage payments to assessing capital projects, and remains a cornerstone of sound financial planning and analysis.

References

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  • Investopedia. (2023). Time value of money (TVM). https://www.investopedia.com/terms/t/timevalueofmoney.asp
  • Klay, J. L. (2018). Financial Mathematics: A Course for Business Studies and Management. Routledge.
  • Lokanan, M. (2018). The valuation of bond investments. Journal of Financial Management, 22(3), 45-58.
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  • Nagle, T. (2020). Basic Financial Calculations for Business and Personal Use. Wiley.

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