1. Explain Fisher's Separation Theorem and why it is important for both consumers and corporations. 2....

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1. Explain Fisher's Separation Theorem and why it is important for both consumers and corporations. 2. Given a set of productive opportunities, using a graph in co-c space, show the initial endowment (Y) of a consumer who will choose to disinvest in production and lend in the financial market. Be sure to label all the relevant components. 3. Suppose a consumer i faces a two-period lifespan and must choose a consumption plan, co and C1, in order to maximize his total utility, which is time separable of the form: U(Co, C) = U(Co) + SU (c), where 0 81 is the consumer's constant "time preference", or discount factor, for period 2 consumption. The consumer receives income of yo at the beginning of period 1 and y at the beginning of period 2. Finally, there is a capital market, so the present value of the consumer's lifetime consumption must equal the present value of the consumer's lifetime wealth, Wo. Thus: C1 Wo = co+ (1+r) Yo (1+r)* a. Use the constraint Wo co++ to form the Lagrangian [ function for the consumer's (1+r) inter-temporal utility maximization problem. b. If the consumer has log utility, U(c) = ln(c), show the first order conditions for L. c. Use the first order conditions to find expressions for the consumer's optimal consumption plan, co and c. d. Suppose consumer i has income in each period of y = y = 50,000 and 8 of 0.95. What will be his consumption choice in each period, co and c if the market interest rate, r, is 15%? e. What happens to consumption in each period if the consumer becomes more "patient", i.e., determine the signs (positive or negative) of ac and co. Interpret the results. f. Use the fact that Wo = y + (14+) to find how consumption will change in response to changes in the market interest rate, i.e., determine the signs of results. 4. Suppose an investment project has the following cash flows: aco r and Interpret the r Year 1 2 3 4 5 Cash Flow -125,000 75,000 55,000 25,000 10,000 -10,000 The firm's WACC is 10%. a. Compute the project's NPV. b. Compute the project's IRR. c. Compute the payback period. d. Compute MIRR if cash flows are reinvested at 10%. e. Will the project be accepted? Why? f. If the WACC is 15%, will the project be accepted? Why? 1. Explain Fisher's Separation Theorem and why it is important for both consumers and corporations. 2. Given a set of productive opportunities, using a graph in co-c space, show the initial endowment (Y) of a consumer who will choose to disinvest in production and lend in the financial market. Be sure to label all the relevant components. 3. Suppose a consumer i faces a two-period lifespan and must choose a consumption plan, co and C1, in order to maximize his total utility, which is time separable of the form: U(Co, C) = U(Co) + SU (c), where 0 81 is the consumer's constant "time preference", or discount factor, for period 2 consumption. The consumer receives income of yo at the beginning of period 1 and y at the beginning of period 2. Finally, there is a capital market, so the present value of the consumer's lifetime consumption must equal the present value of the consumer's lifetime wealth, Wo. Thus: C1 Wo = co+ (1+r) Yo (1+r)* a. Use the constraint Wo co++ to form the Lagrangian [ function for the consumer's (1+r) inter-temporal utility maximization problem. b. If the consumer has log utility, U(c) = ln(c), show the first order conditions for L. c. Use the first order conditions to find expressions for the consumer's optimal consumption plan, co and c. d. Suppose consumer i has income in each period of y = y = 50,000 and 8 of 0.95. What will be his consumption choice in each period, co and c if the market interest rate, r, is 15%? e. What happens to consumption in each period if the consumer becomes more "patient", i.e., determine the signs (positive or negative) of ac and co. Interpret the results. f. Use the fact that Wo = y + (14+) to find how consumption will change in response to changes in the market interest rate, i.e., determine the signs of results. 4. Suppose an investment project has the following cash flows: aco r and Interpret the r Year 1 2 3 4 5 Cash Flow -125,000 75,000 55,000 25,000 10,000 -10,000 The firm's WACC is 10%. a. Compute the project's NPV. b. Compute the project's IRR. c. Compute the payback period. d. Compute MIRR if cash flows are reinvested at 10%. e. Will the project be accepted? Why? f. If the WACC is 15%, will the project be accepted? Why?