Retirement Planning, Cash Flows, Investment Decisions, Sensitivity Analysis, Asset Pricing

Retirement annuity calculation

You plan to retire in exactly 30 years. Your goal is to create a fund that will allow you to receive $24 000 at the end of each year for 20 years. You know that you will be able to earn 10% per year during the 20-year retirement period.
a. How large a fund will you need when you retire in 30 years to provide the 20-year, $24,000 retirement annuity?
b. How much will you need today as a single amount to provide the fund calculated in part a if you earn only 9% per year during the 30 years proceeding retirement?
c. You plan to make end of year annuity deposits during the 30 years proceeding retirement to fund the 20-year, $24 000 retirement annuity. How much will you need to deposit at the end of each year if you earn 9% per year during the 30 years period preceding retirement? 5 marks

a. For the given mixed stream of cash flows below, determine the future value at the end of fifth year if the deposits are made into an account paying annual interest of 12%, assuming that no withdrawals are made during the period and that the deposits are made.
b. For the given mixed stream of cash flows below, determine the future value at the end of final year if the deposits are made into an account paying annual interest of 10%, assuming that no withdrawals are made during the period and that the deposits are made.
c. Determine the present value for each of the mixed streams provided in part a and b.

Calculate the Payback, NPV and IRR for each of independent projects shown in the following table, and indicate whether each is acceptable. Assume that the firm’s cost of capital is 12% and the firm’s maximum acceptable payback is 6 years.Project A Project
Year (t) Cash Inflows (CFt)
Initial investment (CF0) -$30,000 -$600,000 -$950,000 -$100,000
1 $4,500 $100,000 $230,000 $0
2 $4,500 $120,000 $230,000 $0
3 $4,500 $140,000 $230,000 $0
4 $4,500 $160,000 $230,000 $20,000
5 $4,500 $180,000 $230,000 $30,000
6 $4,500 $200,000 $230,000 $0
7 $4,500 $220,000 $230,000 $50,000
8 $4,500 $60,000
9 $4,500
10 $4,500

Critical factors influencing investment decisions – capital rationing vs. unlimited funds, and independent vs. mutually exclusive projects  8 marks A Company has the following investment options with costs, net cash flows and IRR of each project as shown below.
a. If the company requires a rate of return (cost of capital) of at least 15% from every new project, which projects will you choose in case of unlimited funds? Discuss your decision.
b. Explain the relationship between the proposed projects in part a in terms of whether they are independent or mutually exclusive.
c. Will the relationship between the proposed projects change if the company has a budget of $12 million? Justify your answer with proper reasoning.
d. If the company requires a rate of return (cost of capital) of at least 15% from every new project, which projects will you choose if capital is rationed to a maximum of $35 million? Assume IRR approach is preferable in selecting the best group of projects for the Company.

a. Compute NPV for each states of nature for each machine
b. Calculate the range for the NPV between the pessimistic and optimistic states.
c. Discuss the result of sensitivity analysis.
a. Calculate the required return for an asset with a beta of 0.90 when risk-free rate and market required return are 8% and 12%, respectively.
b. Calculate the risk-free rate for a firm with a required return of 15% and a beta of 1.25 when the market return is 14%.
c. Calculate the market return for an asset with a required return of 16% and a beta of 1.10 when the risk-free rate is 9%.
d. Calculate the beta for an asset with a required return of 15% when risk-free rate and market return are 10% and 12.5%, respectively.