Week 3 - Tools for Financial Decision Making - Time Value of Money (1) Flashcards
(11 cards)
The goal of finance is to maximise wealth (also called value) by making optimal financial decisions.
For financial decisions:
- We need to identify the relevant costs and benefits of the decision
- Since costs and benefits may occur at different points in time or in different currencies, they must be converted to a common unit, such as dollars today
- Once converted to a common unit, an optimal financial decision is one where the benefits exceed the costs
Identify the role of competitive markets in decision-making
A competitive market is one in which a good can be bought and sold at the same price. In a competitive market, the price determines the value of the good.
→ A business decision is good for a firm if it increases the value of a firm where the benefits exceed costs
→ Whernever a good trades in a competitive market, that price determines the value of the good
A firms’ financial manager makes decisions on behalf of the firms investors (benefits exceeding costs, which will increase the firms value). Real world opportunities are often difficult to quantify and involve using skills from other management disciplines.
- Marketing (increasing revenue from advertising)
- Economics (impact on demand from lowering prices)
- Organisational behaviour (change in management structure on productivity)
- Strategy (competitors’ response to your price drop)
Operations (production costs after upgrading your plant)
The Valuation Principle
→ The value of a commodity or an asset to the firm or its investors is determined by its competitive market price. The benefits and costs of a decision should be evaluated using those market prices. When the value of the benefits exceed the value of the costs, the decision will increase the market value of the firm
→ We can not have two different competitive market prices for the same good - otherwise, we would arrive at two different values e.g if gold was trading simultaneously for two different prices, you and everyone else who noticed the difference would buy at the low price and sell at the high price for as many ounces of gold as possible, making instant risk-free profits. These forces establish the Law of One Price which states that in the competitive markets the same good or securities must have the same price - more generally, securities that produce exactly the same cash flows must have the same price
The practice of buying and selling equivalent goods in different markets to take advantage of a price difference is known as arbitrage. We refer to any situation in which it is possible to make a profit without taking any risk or making any investment as an arbitrage opportunity. Because an arbitrage opportunity’s benefits are more valuable than its costs, whenever an arbitrage opportunity appears in financial markets, investors will race to take advantage of it and their trades will ultimately eliminate the opportunity
Time Value of Money
→ If there is a cost of 100,000 today and benefit 105,000, calculating the projects’ net value as 5000 is incorrect as it ignores the timing of costs and benefits i.e. it trats money today as equivalent to money in a year
→ Thus, the interest rate is the price for exchanging money today for money in a year - we can use the interest rate to determine values in the same way that we used competitive market prices
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→ By depositing money into a savings account, we can convert money today into money in the future with no risk. Similarly, by borrowing money from the bank, we can exchange money in the future for money today.
→ The rate at which we can exchange money today for money in the future is determined by the current interest rate
→ In the same way that an exchange rate allows us to convert money from one currency to another, the interest rate allows us to convert money from one point in time to another; in essence, an interest rate is like an exchange rate across time; it tells us the market price today of money in the future
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→ We define the interest rate “r” for a given period as the interest rate at which money can be borrowed or lent over that period;
→ We are to “(1 + r) as the interest rate factor for cash flows; it defines how we convert cash flows across time and has units of $ in one year/ $ today
→ The interest rate equates the supply of savings to the demand for borrowing
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→ The amount 1/(1+r) is called the one-year discount factor, the interest rate is also referred to as the discount rate for an investment
→ The format for this is usually timelines
→ To track cash flows, we interpret each point on the timeline as a specific date - the space between date 0 and date 1 represents the first year of the loan.
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Calculate the future value and present value of a single cash flow.
- A timeline is a linear representation of the timing of potential cash flows
- Drawing a timeline will help visualise a financial problem
- Timelines can represent cash flows that take place at the beginning or end of any time period (years, months, etc.)
- Identifying dates on a time: Date 0 is today, the beginning of the first year
- Inflows are positive cash flows
- Outflows are negative cash flows
Three Rules of Valuing Cash Flows
Rule 1: Comparing and Combining Values:
○ Only cash flows in the same units can be compared or combined
○ To compare of combine cash flows that occur at different points in time, you first need to convert the cash flows into the same units by moving them to the same point in time
Common Mistake: simply treating all cash flows as comparable regardless of when they are received or paid e.g in 2023, Australian NBA forward Josh Green and the Dallas Mavericks team agreed to a three-year contract worth US$41 million. The US$41 million value of the contract comes from simply adding up all the payments Green would receive over the three years of the contract - treating dollars received in three years as that same as dollars received today
Rule 2: Compounding
○ Suppose we have $1000 today, and we wish to determine the equivalent amount in one years’ time. If the current market interest rate is 10%,, we saw in the previous section that we can use that rate as an exchange rate, meaning the rate at which we exchange money today for money in one to move the cash flow forward in time. i.e. (1000 today) x (1.10 in one year/ 1 today) = 1100 today
○ In general, if the market interest rate for the year is r, then we multiply by the interest rate factor (1+r) to move the cash flow from the beginning to the end of the year. We multiply by (1 + r) because, at the end of the year, you will have (1 x your original investment) plus interest in the amount of (r x your original investment).
○ This process of moving forward along the timeline to determine a cash flow’s value in the future (its future value) is known as compound.
○ To calculate a cash flow’s future value, you must compound it
Rule of 72: Years to Double = 72/(interest in %)
Rule 3: Discounting
○ How to put a value today on a cash flow that comes in the future
○ That is, to move the cash flow back along the timeline, we divide it by the interest rate factor (1 + r), where r is the interest rate. This process of finding the equivalent today of a future cash flow is know as discounting.
○ Our third rule stipulates that to calculate the value of a future cash flow at an earlier point in time, we must discount it
Use Excel to calculate the future value and present value of a single cash flow.
- Rate = interest rate per period
- Nper = number of periods
- PMT = put “0” for single cash flow
- PV = present value of the cash flow (enter a negative number)
- Type = leave blank for single cash flow
- The = FV() function returns the future value of a single cash flow
