Chapter 9: Investments in Human Capital: Education and Training
PROBLEMS
The Benefits and Costs of Educational Investments: The Present Value Method
1. Consider an individual who currently earns $20,000 as an unskilled laborer. Suppose that by taking courses full-time at a community college for one year, the person can qualify for a more skilled job paying $23,000 that is guaranteed to last for 10 years (after which the person would retire). Assume the cost of tuition and books at the community college for one year is $2,000 and that the current interest rate is 6 percent. Is this a good investment?
The Benefits and Costs of an Educational Investment: The Internal Rate of Return Method
2. Consider a worker who is offered a salary bonus of $2,000 for each of the next two years if he or she enrolls in a job training program this year. The total cost to the worker, including any forgone earnings, is $3,500.
2a. What is the internal rate of return on this investment?
2b. Would this be a good investment for someone with a discount rate of 6%?
2c. What is the highest discount rate a person could have and still find this investment attractive? Is it possible for a person to have a higher discount rate than the market interest rate?
2d. Why are older workers less likely to seek out, or be offered, on-the-job training opportunities? How does this affect the shape of the typical age-earnings profile?
The Relationship Between Expected Inflation and the Discounting of Future Benefits from Education
3. In evaluating educational investments in which costs are incurred in the current year (year 0), but benefits accrue over future years (years 1 through T), it is important that the future benefits be discounted. Dollars accessible today are more valuable since they can be consumed with certainty today or invested at a certain rate of interest. Therefore, dollars received in the future must first be discounted if they are to be fairly compared with current dollars. However, dollars received in the future may also be less valuable than dollars today if inflation occurs, which raises the general level of prices and reduces the purchasing power of future dollars.
In Chapter 2, adjustments for inflation were discussed in the context of converting nominal wages to real wages. To adjust nominal values to real values, one simply divides the nominal dollar values by the price index and then multiplies the result by 100. The result is a measure that can be compared to dollar values in the base year of the price index.
When inflation is anticipated, it is also important to note that anyone loaning (investing) money will typically require that a premium for expected inflation be built into the interest rate payable on the investment to assure a certain real rate of return after accounting for inflation. The nominal (market) interest rate is converted to the real interest rate by the formula:
where i is the real interest rate, r is the market interest rate (expressed as a fraction), and p is the expected rate of inflation (also expressed as a fraction). When expected inflation is small, the above formula is often approximated by the simple formula i = r-p.
Table 9-1 lists the costs and benefits associated with an educational investment. The price indices presented in the table reflect the expectation that, in each of the two years following the investment, inflation will be 4 percent. The market interest rate throughout the period is assumed to be constant at 6 percent per year.
Table 9-1.
|
Year
|
Price Index
|
Costs
|
Benefits
|
|
Year 0
|
100
|
$10,000
|
$0
|
|
Year 1
|
104
|
$0
|
$6,000
|
|
Year 2
|
108.16
|
$0
|
$6,000
|
3a. Using the market interest rate as the discount rate, convert the nominal values of the costs and benefits to present values. Does the present value of the benefits exceed the present value of the costs? If so, by how much?
3b. Compute the real rate of interest expected in each year to five decimal places.
3c. Using the expected price indices, convert the nominal values of the costs and benefits to real values.
3d. Using the real interest rate as the discount rate, convert the real values of the costs and benefits to present values. Does the present value of the benefits exceed the present value of the costs? If so, by how much?
3e. Compare your answers to 3a and 3d. Is it necessary to convert all nominal values to real values to accurately assess the costs and benefits of educational investments?
Measuring the Rate of Return to Educational Investments
4. According to studies cited in the text, estimates of the individual rate of return on educational investments range (in real terms) from 5 percent to 15 percent.
4a. If you knew that these studies suffered from selection bias, would you be more inclined to believe the upper or lower range of these estimates?
4b. What similarities do you see between the notions of selection bias and ability bias?