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# Present Value, Economic Cost Determination

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1. A firm is expected to earn \$10,000, \$25,000, \$48,000, and \$75,000 during the next four years, after which it will be dissolved. What is the present value of the firm if the discount rate is 8%?

2. Jane has compiled the following list of expenses after completing one year of college. Assume that Jane would be living with her parents and working if she weren't attending college. Use this information to calculate Jane's economic cost of attending college for one year.

Tuition \$ 8,000
Dormitory room 4,000
Books and supplies 1,000
Food plan 3,000
Foregone income 19,000
Entertainment expenses 1,000
Clothing 2,000
Health insurance 1,000

3. A firm's demand function is defined as Q = 30 - P. Use this function to calculate total revenue when price is equal to 5 and when price is equal to 6. What is marginal revenue equal to between P=5 and P=6. (Hint: total revenue = P x Q and marginal revenue = change in total revenue / change in quantity)

4. Use the demand schedule that is presented in the table below to determine the optimal rate of production and price when the firm has the following marginal cost function: MC = 1 + Q. (Hint: the firm should produce the product as long as MR is greater than or equal to MC)

Quantity 1 2 3 4 5 6 7 8 9 10
Price 80 60 48 40 34 29 25 20 15 10

#### Solution Preview

1. A firm is expected to earn \$10,000, \$25,000, \$48,000, and \$75,000 during the next four years, after which it will be dissolved. What is the present value of the firm if the discount rate is 8%?

You need to find the present value for cash flow for each year in the next four years by using the present value formula as follows:-

PV = FVn where PV is the present value
(1 + i)n FV is the future value in that particular year
i is the discount rate
n is the period.

Year 0 1 2 3 4
10,000 25,000 48,000 75,000

PV = 10,000 + 25,000 + 48,000 + 75,000
(1 + 0.08)1 (1 + 0.08)2 (1 + 0.08)3 (1 + 0.08)4

PV = 10,000(0.9259) + 25,000(0.8573) + 48,000(0.7938) + 75,000(0.7350)
PV = 123,918.90

2. Jane has compiled the following list of expenses after completing one ...

#### Solution Summary

This solution is comprised of a detailed explanation to answer what is the present value of the firm if the discount rate is 8%, calculate Jane's economic cost of attending college for one year, what is marginal revenue equal to between P=5 and P=6, and determine the optimal rate of production and price when the firm has the following marginal cost function: MC = 1 + Q.

\$2.19