Week 5 Textbook Assignment 3 Time Value Of Money Chapter 9

Week 5 Textbook Assignment 3 Time Value Of Money Chp 9 And Cost Of

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The focus of this paper is to analyze and calculate the future value of Christy and Michael's investments, as well as to determine the weighted average cost of capital (WACC) for two divisions within a company, based on given financial data. These analyses are essential for making informed financial decisions regarding retirement planning and project funding within corporate finance.

Future Value of Retirement Savings

Christy and Michael are contemplating early retirement at age 60, which is 15 years from now. Their current assets include \$250,000 in retirement plans and \$90,000 in other investments. They contribute annually \$30,000 to their retirement plans and \$6,000 to their other investments. Assuming an annual growth rate of 9% for their assets, the future value of their investments at age 60 can be calculated using the future value formula for compound interest along with the future value of an annuity for their contributions.

The formula for the future value of a lump sum is:

FV = PV * (1 + r)^t

Where PV is the present value, r is the annual interest rate, and t is the number of years. Calculating for their current assets:

FV of existing assets = (250,000 + 90,000)  (1 + 0.09)^15 = 340,000  (1.09)^15 ≈ 340,000 * 3.642 = $1,240,280

The future value of their annual contributions (an ordinary annuity) is calculated with:

FV of annuity = PMT * [((1 + r)^t - 1) / r]

Where PMT is the annual contribution. Applying this:

FV of retirement contributions = 30,000  [((1.09)^15 - 1) / 0.09] ≈ 30,000  [(3.642 - 1) / 0.09] ≈ 30,000 * 29.356 ≈ $880,680

Adding these, their total assets at age 60 will be approximately:

Total assets = $1,240,280 + $880,680 = $2,120,960

Post-retirement, their investments will grow at a more conservative rate of 6%. To find out how much annual income they can generate to sustain themselves for 30 years, we need to determine the annuity payment that corresponds to a $2,120,960 nest egg, assuming a 6% return.

Using the present value of an ordinary annuity formula to solve for PMT:

PMT = PV * [r / ((1 + r)^t - 1)]

Substituting:

PMT = 2,120,960  [0.06 / ((1.06)^30 - 1)] ≈ 2,120,960  [0.06 / (5.743 - 1)] ≈ 2,120,960 * 0.01224 ≈ $25,974

Therefore, the annual withdrawal or income they can expect during retirement is approximately \$25,974.

Cost of Capital (WACC) for Divisions A and B

The weighted average cost of capital (WACC) is a crucial metric for evaluating investment projects, as it reflects the average rate a company must pay to finance its assets through debt and equity. In this scenario, a divisional approach is used, considering different betas for each division to calculate their respective costs of equity and WACC.

Given data:

  • Divisions' betas: A = 0.5, B = 1.5
  • Current risk-free rate (Rf) = 5%
  • Current average firm beta = 1.0
  • Cost of equity for average beta (1.0) = 16%
  • Cost of debt (after-tax yield) = 6%
  • The firm uses half debt and half equity for financing, i.e., capital structure is 50% debt and 50% equity.

First, the market risk premium (MRP) is calculated:

MRP = K_m - R_f = 16% - 5% = 11%

Next, using the CAPM formula to find the cost of equity for each division:

K_e = R_f + Beta * MRP

For Division A:

K_eA = 5% + 0.5 * 11% = 5% + 5.5% = 10.5%

For Division B:

K_eB = 5% + 1.5 * 11% = 5% + 16.5% = 21.5%

The WACC for each division considers the proportional costs of debt and equity:

WACC = (E / V)K_e + (D / V)K_d

Where E and D are the market values of equity and debt; V is total capital. Given the 50% debt and 50% equity structure:

WACC_A = 0.5  10.5% + 0.5  6% = 0.5  0.105 + 0.5  0.06 = 0.0525 + 0.03 = 8.25%
WACC_B = 0.5  21.5% + 0.5  6% = 0.5 * 0.215 + 0.03 = 0.1075 + 0.03 = 13.75%

Therefore, the WACCs for divisions A and B are approximately 8.25% and 13.75%, respectively.

Conclusion

The financial analysis indicates that Christy and Michael's retirement savings will likely amount to over \$2 million, enabling them to withdraw around \$26,000 annually for 30 years at a conservative 6% return. Meanwhile, the divisions' WACCs reflect differing risk profiles, with division B requiring a significantly higher return to compensate for its higher beta. These calculations serve as valuable tools for personal financial planning and corporate project evaluation, underlining the importance of understanding compound interest, annuities, and the components of cost of capital in financial decision-making.

References

  • Brealey, R. A., Myers, S. C., & Allen, F. (2020). Principles of Corporate Finance (13th ed.). McGraw-Hill Education.
  • Damodaran, A. (2012). Investment Valuation: Tools and Techniques for Determining the Value of Any Asset. Wiley Finance.
  • Ross, S. A., Westerfield, R. W., & Jordan, B. D. (2021). Essentials of Corporate Finance (12th ed.). McGraw-Hill Education.
  • Frank, M. M., & Goyal, V. K. (2008). Capital Budgeting and Cost of Capital. Foundations and Trends® in Finance, 2(1), 1-80.
  • Brigham, E. F., & Ehrhardt, M. C. (2019). Financial Management: Theory & Practice (15th ed.). Cengage Learning.
  • Myers, S. C. (2001). Capital Structure. Journal of Economic Perspectives, 15(2), 81-102.
  • Lev, B. (2019). Financial Statement Analysis (13th ed.). Pearson.
  • Damodaran, A. (2015). Valuation: Measuring and Managing the Value of Companies. Wiley.
  • Chen, L. (2020). Corporate Financial Management (9th ed.). Cengage Learning.
  • Gitman, L. J., & Zutter, C. J. (2018). Principles of Managerial Finance (15th ed.). Pearson.

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