Present Value Discounting converts the value of future dollars into today's dollars through the interest rate. The present value (V) of a payment received one year from now is: * Def: V. = Payement 1 year from now 1 + Interest rate Where Interest rate = 10% * EX: $1 10 V = = $100.00 1.10 Present Value The present value of a future stream of incremental earnings and/or costs (E) is: E E, +... + E V = E. + (1 +i) (1+i) (1+i)" Costs are represented as negative values of E. E0 represents any income received immediately. E1 represents income received next year. N represents the individual's expected working life. N represents year before retirement. Present Value The present value of a future stream of incremental earnings or costs (E): E E, V. = E. + + (1 +i) (1+1) (1+i)" Decision Rule: An individual should make the investment if its net present value is greater than zero. Because then the present discounted value of the benefits exceeds the present discounted value of the costs.Present Value: Example Matthew graduated from high school. He is now deciding whether to enroll in a one-year intensive course in data processing. The direct costs of the course are $1000 and the opportunity cost is $5000. He is set to receive an inheritance and plans to work only three years and then retire permanently from the labor force. The incremental income he anticipates earning because of his data processing training is $2500, $3000, and $3500. The relevant interest rate is 10%. Is the decision to enroll in the data- processing course rational? Present Value: Example Direct Costs= $1000, Indirect Costs= $5000 Income1= 2500, Income2=3000, Income3=3500 Vo = En + E1 Es ( 1 + 1 ) + + (1 + 12 (1 + 0 Vo = -$6, 000 + $2,500 $3.000 $3,500 (1.10) + (1.10) (1.10)3 Vp = -$6, 000 + $2, 273 + $2, 479 + $2, 630 Vo = $1, 382 The net present value is greater than zero thus Matthew should enroll in the course. The present value of the benefits (incremental earnings) exceeds the present value of the costs by $1,382. Internal Rate of Return Internal rate of return (r) is the rate of discount at which the net present value of a human capital investment is zero. An alternative way to make an investment decision is to calculate the internal rate of return (r). We can compare the internal rate of return r to the interest rate i.Internal Rate of Return Suppose an individual has a stream of costs and earnings for n periods. The net present value formula for this stream of costs and earnings, assuming interest rate i would be: En Va = Eu+ + + + (1 + i) (1 + 1)- (1 + 1) (1 + 1) To calculate the internal rate of return r for this stream of costs and earnings, we use the following formula: E En V. = Fo + + + + . = 0 ( 1+r ) (1 + r)- (1 + r)" Internal Rate of Return Suppose an individual has a stream of costs and earnings for n periods. To calculate the internal rate of return r for this stream of costs and earnings, we use the following formula: EI En Vp = Eo + + + =0 (1 + r) (1 + p) (1 + r) The value of r that solves this equation is the internal rate of return r for this investment. The internal rate of return is the rate of return such that the individual breaks even from the investment. Internal Rate of Return If the internal rate of return r exceeds the market interest rate i, the investment is profitable and should be undertaken. If the internal rate of return r is less than the market interest rate i, the investment is unprofitable and should not be undertaken. Decision Rule: it will be profitable to invest in all human capital investment opportunities up to the point where r = i.Internal Rate of Return: Example Olivia graduated trom high school. She is now deciding whether to enroll in a oneyear intensive course in data processing. The direct costs of the course are $1000 and the opportunity cost is $5000. She is set to receive an inheritance and plans to work only one year and then retire permanently from the labor force. The incremental income she anticipates earning because of her data processing training is $8000. The relevant interest rate is 10%. is the decision to enroll in the data processing course rational? Internal Rate of Return : Example Direct Costs: $1000, indirect Costs: $5000 income 1: 8000 E _ _ E _ 1 t\" h\" _ [I +L-r') U _ E"+ (1+0 $9000 . u_ $['_ll[llll strum '1- p = St-. [till] -|- ' = S J 313 1 U + U U '10) 33000 D 33 F55. DI)\" '- The net present value is greater than zero thus Olivia should enroil' in the course. ris greater than i, 33% > 10% thus Olivia should enroll in the course. Human Capital Model: Generalizations The Human capital model leads to several generalizations. We will focus on 3 main ones: 1') Length of income Stream ; 2) Costs ; 3) Earnings Differentials 1) Length of income Stream: Other things being equal. the longer the stream of post investment incremental earnings. the more likely the net present value of an investment will be positive. . Example: Younger people are more likely to go to college (40 points) Sarah graduated from High School. She is now deciding whether to enroll in a 2-year intensive course in information technology. The direct costs and indirect costs of the course in year 0 (today) are $1731 and $1000 respectively. In year 1, these costs are $750 and $1250 respectively. Sarah has just recently won the lottery and has chosen to receive monthly payments which begin 4 years from today. She plans to work for two years after graduating from the intensive course and then retire permanently from the labor force. The incremental (yearly) income she anticipates earning because of her information technology training is $3000, and $4000, respectively. Answer the following questions: a. (15 points) The relevant interest rate is 10%. Is it rational to enroll in this course? Hint (Net Present Value) b. (15 points) Using the internal rate of return, is it rational to enroll in this course? (Hint: Using the internal rate of return, the discounted value of Sarah's costs in year 1 and earnings in year 2 are -$1,667 and $2083 respectively!!) 0. (5 points) Suppose the relevant interest rate is now 20%? Is it rational to enroll in this course? Explain? d. (5 points) Suppose the relevant interest rate is now 30%? Is it rational to enroll in this course? Explain