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# Calculating the future values and WACC

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1. Future Value and Annuity Payments Christy and Michael are trying to decide if they will have enough money to retire early in 15 years, at age 60. Their current assets include \$250,000 in retirement plans and \$100,000 in other investments. Together, they contribute \$30,000 per year to their retirement plans and another \$6,000 to other investments.

a. If their assets already in their retirement plans and other investments grow at 9 percent per year, how much money will they have when they turn 60?
b. After they retire, they will invest their wealth more conservatively and it will earn 6 percent per year. What will be the amount of money that they will be able to withdraw annually if they expect to live for 30 years in retirement?

2. Cost of Capital (WACC). Suppose your company has decided to use a divisional WACC approach to analyze projects. The firm currently has 2 divisions, A and B, with betas for each division of 0.5 and 1.5, respectively. If all current and future projects will be financed with half debt and half equity, and if the current cost of equity (based on an average firm beta of 1.0 and a current risk-free rate of 5%) is 18% and the after-tax yield on the company's bonds is 6%, what are the WACCs for divisions A and B?

Hint: First Solve for Market Risk Premium (MRP) using the avg. firm beta. MRP = (Km-Rf) Then plug this MRP into the other equations as needed to figure the following:

a. Division A WACC?
b. Division B WACC?

#### Solution Preview

1. Future Value and Annuity Payments Christy and Michael are trying to decide if they will have enough money to retire early in 15 years, at age 60. Their current assets include \$250,000 in retirement plans and \$100,000 in other investments. Together, they contribute \$30,000 per year to their retirement plans and another \$6,000 to other investments.

a. If their assets already in their retirement plans and other investments grow at 9 percent per year, how much money will they have when they turn 60?

Case 1: Assets already in retirement plans
Present accumulation=PV1=\$250,000
Annual contribution=R1=\$30,000
Growth rate=i=9%
Number of periods=n=15
Future Value =FV1=PV1*(1+i)^n+(R1/i)*((1+i)^n-1)
...

#### Solution Summary

The solutions depict the steps to estimate the annual withdrawal amount and WACC for individual divisions.

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