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Economic Problem. Evaluating Future Benefits. Income or earnings accrue in the future What are those benefits worth to us today Investing in a college or a master’s degree Situation of wrongful termination Discrimination case Value of lost future earnings. A Dollar Today or Tomorrow?.
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Evaluating Future Benefits • Income or earnings accrue in the future • What are those benefits worth to us today • Investing in a college or a master’s degree • Situation of wrongful termination • Discrimination case • Value of lost future earnings Prof. Leighton
A Dollar Today or Tomorrow? • A dollar received in the future is worth less to us than a dollar received in the present Prof. Leighton
A Dollar Today or Tomorrow? • A dollar held today can be invested at some market rate of interest so that by the next period it will be worth more than a dollar • $1.00(1.05) = $1.05 Today’s dollar invested at 5% grows to $1.05 tomorrow Prof. Leighton
Investing at a Rate of r • How much money will you have in the next period if you invest B0 today at a rate of interest r ? B0 + r B0 = B0(1+r ) = B1 • B1 next period and B0 now are equivalent values • Assuming you are neither present nor future oriented Prof. Leighton
Discounted Value of B1: What Is B1 Worth Today? • Work the simple problem backwards B0(1 + r ) = B1 • B1 received in the future is worth B0 today; solve for B0 B0= B1/(1 + r ) • B0is the discounted value of B1 Prof. Leighton
Present Value • Value now of an entire stream of future benefits or costs • Receive benefits of B0, B1, B2,…,Bn over the current and next n periods • Face the same interest rate, r, in each period • The present value of benefits is given by:PVB = B0 + B1/(1 + r) + B2/(1 + r)2 + B3/(1 + r)3 +…..+ Bn/(1 + r)n Prof. Leighton
Is a Master’s Degree a Sound Financial Investment? • If the PVB > PVC, invest in master’s degree • If the PVB < = PVC, do not invest Prof. Leighton
Planning the Worksheet • Need information on • The direct costs of graduate school • The earnings foregone while in graduate school • The earnings stream of workers with a college education • The earnings stream of workers with a master’s degree • The appropriate rate of interest Prof. Leighton
Ideal vs. Available Data • Longitudinal data collected each year • Same individuals are surveyed each year • Some have college degree; some have master’s degree • Follow worker over his/her work life • Data sets tend to be small • Synthetic Cohort • Look at a cross-section, say 1991 • Look at the average earnings for each age level • Assume hypothetical student will follow same earnings path as the different workers in the sample did at each age Prof. Leighton
Benefits Indirect costs Synthetic Cohort Prof. Leighton
Needed Formulas • Difference between earnings of college graduate and master’s graduate at each age • Discounted value of that difference at each age • Sum of the discounted values = PVB • IF function to decide whether or not to invest Prof. Leighton