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Growth and Terminal Value

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Walgreen Company reported the following earnings per share from 1989 to 1994.

Year
1989
1990
1991
1992
1993
1994

a. Estimate the arithmetic average and geometric average growth rate in earnings per share between 1989 and 1994. Why are they different? Which is more reliable?
b. Estimate the growth rate using a linear growth model.
c. Estimate the growth rate using a log-linear growth model.

Recalculate the Genoa Pasta problem when:

EBIT is \$130 million.
The initial less-stable, fast growth period is 10 years.
The first, fast period growth rate is 15%.
The cost of capital during the slower, stable second period is 12%.

Genoa Pasta manufactures Italian food products and currently earns \$80 million in earnings before interest and taxes. You expect the firm's earnings to grow 20 percent a year for the next six years and 5% thereafter. The firm's current after-tax return on capital is 28%, but you expect it to be halved after the sixth year. If the cost of capital for the firm is expected to be 10% in perpetuity, estimate the terminal value for the firm. (The tax rate for the firm is 40%).

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QUESTION
Year Dividends per share
2005 0.22
2006 0.27
2007 0.33
2008 0.4
2009 0.48

a. Estimate the arithmetic average and geometric average growth rate in earnings per share between 2005 and 2009. Why are they different? Which is more reliable?
Prediction
Arithmetic average Geometric Average
Year Dividends per share Yearly growth rate Value Difference Base value Geometric average rate Value Difference
2005 \$0.22 \$0.22 0.00 \$0.22 1.00 =(1+21.5%)^1 \$0.22 =base value * 1.00 0.00 =0.22 - 0.22
2006 \$0.27 22.7% =(0.27 - 0.22)/0.22 0.27 =0.22 * (1+21.5%)^1 0.00 0.22 1.22 =(1+21.5%)^2 \$0.27 0.00
2007 \$0.33 22.2% 0.32 =0.22 * (1+21.5%)^2 0.01 0.22 1.48 \$0.32 0.01
2008 \$0.40 21.2% 0.39 0.01 0.22 1.80 \$0.39 0.01
2009 \$0.48 20.0% 0.48 0.00 0.22 2.18 \$0.48 ...

Solution Summary

Growth and terminal values are examined in the solution.

\$2.19

Growth, terminal value, annual withdrawals, tax impact

This problem uses a tax deferred 401(k) pension plan as the basis for considering the choice among different types of mutual funds.

1. This first question illustrates the large amount to which a modest amount will grow over an extended time period.

Bozena's contribution \$1,600
Company's match 800
_______
Total contribution \$2,400

PMT = -2400; N = 45; I = 10; PV = 0;
FV = ? = ________(Qs 1)
This is the terminal value.

The interest table for the future value of an annuity does not have 45 years. An alternative means to solve the problem is to compute the interest factor.
FVAIF = (1 + i)^n - 1 = (1 + .1)^45 - 1
--------------- -------------------
i 0.1
= 718.905
The next step is \$2,400 X 718.905 = ?

2. If Bozena does not participate in the 401(k) but saves \$1,600 annually, she will have considerably less because (1) she does not get the matching funds and (2) her earnings are taxed. Unless she pays the tax obligation from another source of funds, she nets only 8 percent annually. The terminal value is reduced to ___________(Qs 2).
(PMT = -1600; N = 45; I = 8; PV = 0; FV = ?_______) or
FVAIF =(1 + i)^n - 1 = (1 + .08)^45 - 1
---------------- ---------------------
i .08

= 386.506

and \$1,600 x 386.506 = ?.

3. In this question Bozena withdraws the funds from the accounts. In the case of the 401(k), the annual withdrawal is

\$1,725,372 = X (Interest factor for the present value of an annuity at 10 percent for twenty years)
= X (8.514)
X = ?_______(Qs 3)

(N = 20; I = 10; FV = 0; PV = 1725372; PMT = ?________)

After taxes of \$40,530, she nets X - 40,530 = \$162,121.

In the case of the funds outside the 401(k) she withdraws less because she has accumulated less and she continues to earn less even after adjusting for taxes. The annual withdrawal is

\$618,409 = X (Interest factor for the present value of an annuity at 8 percent for twenty years)
= X(9.818)
X = ?_______(Qs4)

She nets the entire ?________ because the taxes have already been paid. The difference between the two withdrawals is about \$100,000 annually.

4. If her salary grows, the amount in the account will also grow. The easiest way to work this problem may be to set up the following spreadsheet using a financial calculator.

Years 1-5 6-10 11-15 16-20 21-25
Salary \$32,000 37,000 42,000 47,000 52,000
Contribution \$2,400 2,775 3,150 3,525 3,525
N = 5 5 5 5 5
I = 10 10 10 10 10
PV = 0 -14652 -40539 -84520 -157641
PMT = -2400 -2775 -3150 -3150 -3525
FV = 14652 40539 84520 157641 277692

Years 26-30 31-35 36-40 41-45
Salary \$57,000 62,000 67,000 72,000
Contribution \$4,272 4,650 5,025 5,400
N = 5 5 5 5
I = 10 10 10 10
PV = -277692 -473325 -790683 -1304081
PMT = -4272 -4650 -5025 -5400
FV = 473325 790683 1303081 2133203

The amount in the account now exceeds ___________(Qs 5) million.