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Inflation and savings

Old Alfred Road, who is well-known to drivers on the Maine Turnpike, has reached his seventieth birthday and is ready to retire. Mr. Road has no formal training in finance but has saved his money and invested carefully. Mr. Road owns his home the mortgage is paid off and does not want to move. He is a widower, and he wants to bequeath the house and any remaining assets to his daughter. He has accumulated savings of $180,000, conservatively invested. The investments are yielding 9 percent interest. Mr. Road also has $12,000 in a savings account at 5 percent interest. He wants to keep the savings account intact for unexpected expenses or emergencies.

Mr. Road`s basic living expenses now average about $1,500 per month, and he plans to spend $500 per month on travel and hobbies. To maintain this planned standard of living, he will have to rely on his investment portfolio. The interest from the portfolio is $16,200 per year (9 percent of $180,000), or $1,350 per month. Mr. Road will also receive $750 per month in social security payments for the rest of his life. These payments are indexed for inflation. That is, they will be automatically increased in proportion to changes in the consumer price index.

Mr. Road`s main concern is with inflation. The inflation rate has been below 3 percent recently, but a 3 percent rate is unusually low by historical standards. His social security payments will increase with inflation, but the interest on his investment portfolio will not.

What advice do you have for Mr. Road? Can he safely spend all the interest from his investment portfolio? How much could he withdraw at year-end from that portfolio if he wants to keep its real value intact?

Suppose Mr. Road will live for 20 more years and is willing to use up all of his investment portfolio over that period. He also wants his monthly spending to increase along with inflation over that period. In other words, he wants his monthly spending to stay the same in real terms. How much can he afford to spend per month?

Assume that the investment portfolio continues to yield a 9 percent rate of return and that the inflation rate is 4 percent.

Summary

To what future value will money invested at a given interest rate grow after a given period of time?

An investment of $1 earning an interest rate of r will increase in value each period by the factor (1 + r). After t periods its value will grow to $(1 + r)t. This is the future value of the $1 investment with compound interest.

What is the present value of a cash flow to be received in the future?

The present value of a future cash payment is the amount that you would need to invest today to match that future payment. To calculate present value we divide the cash payment by (1 + r)t or, equivalently, multiply by the discount factor 1/(1 + r)t. The discount factor measures the value today of $1 received in period t.

How can we calculate present and future values of streams of cash payments?

A level stream of cash payments that continues indefinitely is known as a perpetuity; one that continues for a limited number of years is called an annuity. The present value of a stream of cash flows is simply the sum of the present value of each individual cash flow. Similarly, the future value of an annuity is the sum of the future value of each individual cash flow. Shortcut formulas make the calculations for perpetuities and annuities easy.

What is the difference between real and nominal cash flows and between real and nominal interest rates?

A dollar is a dollar but the amount of goods that a dollar can buy is eroded by inflation. If prices double, the real value of a dollar halves. Financial managers and economists often find it helpful to reexpress future cash flows in terms of real dollars that is, dollars of constant purchasing power.

Be careful to distinguish the nominal interest rate and the real interest rate that is, the rate at which the real value of the investment grows. Discount nominal cash flows (that is, cash flows measured in current dollars) at nominal interest rates. Discount real cash flows (cash flows measured in constant dollars) at real interest rates. Never mix and match nominal and real.

How should we compare interest rates quoted over different time intervals for example, monthly versus annual rates?

Interest rates for short time periods are often quoted as annual rates by multiplying the perperiod rate by the number of periods in a year. These annual percentage rates (APRs) do not recognize the effect of compound interest, that is, they annualize assuming simple interest. The effective annual rate annualizes using compound interest. It equals the rate of interest per period compounded for the number of periods in a year.