Consumers and firms often need to move cash from one point in time to another. They do so by borrowing and lending.
For any interest-bearing account or loan, compounding of interest causes the account or loan balance to grow faster as time passes.
The PDV of a claim on future resources represents the price at which someone could buy or sell that claim today.
The longer the delay until payment and the higher the interest rate, the smaller the PDV of $1.
To find the PDV of a stream of payments, we take the PDV of each payment and then total them.
Interest rates differ because of variations in default risk, lender flexibility, and the timing of payments. When computing the PDV of some future payment, it's important to select an interest rate for an obligation with similar characteristics.
The real interest rate is approximately equal to the nominal interest rate minus the rate of inflation. This approximation works well when interest and inflation rates are low. When a bank or lender quotes an interest rate, it's usually a nominal rate.
Saving and borrowing
Saving reflects decisions about the timing of consumption. To analyze saving, we can apply the theory developed in Chapters 4 through 6, treating a good's "time of availability" as a physical characteristic. We use indifference curves to represent a consumer's preferences for consumption at different points in time, and a budget line to represent the available opportunities. In constructing the budget line, we use the price of each good from today's perspective—that is, the PDV of the future price.
Sufficiently patient consumers save and sufficiently impatient consumers borrow. Among savers, an increase in the interest rate can either raise or lower saving, because the income and substitution effects work in opposite directions. In contrast, among borrowers, an increase in the interest rate typically reduces borrowing, because the income and substitution effects usually work in the same direction.
The Life Cycle Hypothesis relies on two additional assumptions: first, that earnings tend to rise with experience, level off in middle age, and fall sharply at retirement; and second, that people like stability. The theory implies that people smooth consumption over their lifetimes, borrowing when they are young, saving during middle age, and spending down their wealth in retirement. The theory helps us to understand why saving rates differ from one country to another.
Investment
NPV is a measure of profitability—it is the difference between the value of a project's outputs and the value of its inputs, from today's perspective. An investment project is profitable when its NPV is positive and unprofitable when its NPV is negative.
By saving and borrowing, an investor can rearrange the timing of the project's cash flows so that he receives its NPV instantly if the NPV is positive, or pays its NPV instantly if the NPV is negative, and neither receives nor pays anything in the future. The project's NPV therefore tells us what it is worth in terms of instant cash.
When we compute the NPV of a project, we are netting out the opportunity cost of funds.
When faced with a choice between two or more mutually exclusive projects with positive NPVs, a company should choose the one with the highest NPV.
Every investment project excludes waiting as an alternative. Even when a project's NPV is positive, waiting may be better than starting the project immediately.
When interest rates rise, most potential projects become less profitable, and the general level of investment falls. Falling interest rates have the opposite effects.
As long as cash inflows occur before cash outflows, a project is profitable when the rate of interest is less than its internal rate of return (IRR), and unprofitable when the rate of interest is greater than its IRR. It is not usually appropriate to choose between mutually exclusive projects based on their IRRs, however.
The payback period is the amount of time required before a project's total inflows match its total outflows. In general, the payback period is not a reliable criterion for evaluating investment projects.
Human capital consists of marketable skills acquired through investments in education and training. Standard investment principles allow us to determine whether, in a particular instance, acquiring an education makes sense from a purely financial perspective.
