White Pension Fund Required Rates

7/30/2019 White Pension Fund Required Rates

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Risk-Adjusted Rates of ReturnCorporate Finance 101

Alan White

Rotman School of Management

University of Toronto


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Overview

What does corporate finance tell us about required

rates of return? Weighted average cost of capital

Capital structure theory Modigliani and Miller

Application to pension plans

Defined benefit plan Defined contribution plan


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Corporate Model

AssetsEarn rate k

DebtInterest rate r

EquityCost of equity ke

A market value balance sheet

Assets = Debt + Equity

Assume no taxes


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Investment Rule - WACC

Borrow $60 (D) at 5% interest (r) Annual cost is $3 (D r)

Raise $40 equity (E) Investors require a 10%return (ke) Annual cost is $4 (E ke)

Invest the assets (A = $100 = D + E) at rate k Annual income is $100 k

Investment rule is income should exceed costs

A k D kd + E r

0.6 5% 0.4 10% 7%e

D Ek r k

D E D E + = + =

+ +


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Levering Up Traditional View

Lower WACC implies makes it easier to attain our

objective Debt is cheap so use more debt. For example, use

90% debt financing

If assets earn 7% ($7 per year) we earn enough topay interest ($4) plus shareholders required return

($2) and have $1 residual The residual accrues to the shareholders

increasing the stock price

WACC 0.8 5% 0.2 10% 6%= + =


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Leverage and the Cost of Capital -Traditional View

WACC

Traditional View

0%

2%

4%

6%

8%

10%

12%

0% 20% 40% 60% 80% 100%

Debt / Debt + Equity

WACC r ke


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Changing Capital StructureModigliani and Miller

Procedure:

Start with our $60 debt, $40 equity firm Borrow an additional $20 (D*)

Repurchase $20 of equity or pay a $20 dividend

Result:

Debt is now worth $80 (D + D*)

Equity is now E* Shareholders have $20 in cash


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Are Shareholders Better Off? part 1

Formerly earned

100 k 60 r Now earn

100 k 80 r and have $20

If shareholders invest the cash in bonds theywould earn

(100 k 80 r) + (20 r) = 100 k 60 r


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Are Shareholders Better Off? part 2

Now earn

100 k 80 r and have $20 in cash

Before the capital structure change shareholderscould have borrowed $20.

In this case they would earn

(100 k 60 r) 20 r = 100 k 80 r

and have $20 in cash


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MM Conclusion

Capital structure changes can be replicated or

undone by homemade leverage As a result there is no value to a capital structure

change

Value of equity after the change plus the cash(E* + cash) equals the value of equity before the

change (E) In our example E = $40, cash = $20 so E* = $20


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MM: Implications for Cost of Equity

If assets earn 7% ($7 per year) we earn enough to

pay interest ($4 = 5% of $80) and to pay theshareholders $3

The equity value is $20 (E*)

Shareholders require and earn a rate of returnof 15%

As the firm levers up from 60% debt to 80% debtshareholders increase their required rate of returnfrom 10% to 15%


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MM: Implications for Cost of Capital

Cost of capital is independent of capital structure

Cost of debt is assumed constant Cost of equity rises as we lever up

where keU

is the cost of equity when there is nodebt, in our example 7%

( )U Ue e eD

k k k r A D

= +


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Leverage and the Cost of Capital -MM View

WACC

MM View

0%

5%

10%

15%

20%

0% 20% 40% 60% 80% 100%

Debt / Debt + Equity

WACC r ke


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MM: Implications for Equity Risk

Cost of equity rises as we lever up

Similar relation holds for both systematic and firmspecific risk measures. If debt is riskless

( )U Ue e eDk k k r A D

= +

ande A e A

A A

A D A D = =


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Application to DB Plan

The balance sheet of a DB plan looks quite a bit

like a corporate balance sheet Assets are a portfolio of 60% equity, 40% debt

Asset beta is about 0.6, asset volatility is about 12%

Pension liabilities are lot like debt

What are the characteristics of the surplus?

Translating this into the corporate modelsurplus = A D


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Risk of Surplus

Surplus Risk

Typical DB Plan

0

10

20

30

40

50

60

0% 5% 10% 15% 20% 25%

Surplus / Assets

Beta

Volatility


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Required Return on Surplus(Riskfree rate 4%, Risk Premium 4%)

Required Return on Surplus

Typical DB Plan

0%

50%

100%

150%

200%

250%

0% 5% 10% 15% 20% 25%

Surplus / Assets


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DB Plan

The risks of the surplus are substantial

Betas and volatilities apply to rates of return The dollar volume of risk is the return based risk

measure times the size of the surplus

Are these the types of risks that a corporationwants on its balance sheet?

$ $or 0.12AA A = =


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Impact on Corporate Balance Sheet(Assume no taxes, Risk premium = 4%)

6.0%6.0%6.0%6.0%WACC

8.4%6.7%6.3%6.8%ke4.0%4.0%4.0%4.0%kd

1.100.690.580.70Equity beta

0.500.500.500.50Asset beta

5.98.642.630.9Equity

7.13.26.812.3Debt1311.849.443.2Assets

TextronKodakDupontBoeing


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Impact on Corporate Balance Sheet(continued part 2)

0.60.5-0.91.1Surplus

3.97.418.832.7Liabilities

4.57.917.933.8Assets

Pension

5.98.642.630.9Equity

7.13.26.812.3Debt1311.849.443.2Assets



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Impact on Corporate Balance Sheet(continued part 3)

6.1%6.2%6.1%6.2%WACC

9.7%8.7%7.4%9.2%ke4.0%4.0%4.0%4.0%kd

1.421.170.851.31Equity beta

0.530.540.530.54Asset beta

6.59.141.732Equity

1110.625.645Debt17.519.767.377Assets



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Application to DC Plan

The balance sheet of a DC plan is different from a

corporate balance sheet Assets are a portfolio of 60% equity, 40% debt

Asset beta is about 0.6, asset volatility is about 12%

There is no surplus

Pension liabilities act like equity absorbing all risks

and returns This is like an all equity firm


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DC Plan Pension Risk

Pension risks are the same as the asset risks

The value of pension assets has an annual

volatility of about 12% Over a 25-year horizon the standard deviation of

asset returns and the standard deviation of

pension values is about 60% Are these the risks that pensioners are likely to

prefer?

pension pension0.6 and 12%A A = = = =


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Conclusions

Pensions that invest in risky assets create great

risk for the sponsor For DB plans the shareholders absorb a high level

of risk

For DC plans the pensioners absorb the risk

White Pension Fund Required Rates

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