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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.

\$2.19

## Present Value, Price of stock, WACC

1. Janice Smith wishes to accumulate \$8,000 by the end of 5 years by making equal annual end-of-year deposits over the next five years. If Janice can earn 7 percent on her investments, how much must she deposit at the end of each year to meet this goal?

2. J& J just issued a bond with a \$1,000 face value and a coupon rate of 7%. If the bond has a life of 30 years, pays annual coupons and the yield to maturity (YTM) is 6.8%, what will be the bond sell for?

3. Biogenetics, Inc plans to retain and reinvest all of their earnings for the next 30 years. Beginning in year 31, the firm will begin to pay a \$12.00 per share dividend. The dividend will not subsequently change. Given a required return of 15%, what should the stock sell for today?

4. What is the NPV of a project that is expected to pay \$10,000 a year for 7 years if the initial investment is \$40,000 and the required return is 15%?

5. A firm has 2,000,000 shares of common stock outstanding with a market price of \$2.00 per share. It has 2,000 bonds outstanding, each selling for \$1,200. The bonds mature in 15 years, have a coupon rate of 10% and pay coupons annually. The firm's beta is 1.2, the risk free rate is 5%, and the market risk premium is 7%. The tax rate is 34%. Calculate the WACC?

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