INTUITION: (i) The Presence of DEBT makes expected return on levered equity (Re) more variable relative to the return on UNLEVERED equity Ru (whose variability is always 50%)

Since people=investors dislike variability, the market will PRICE debt and equity (D, E respectively) in such a way that as the share of debt (D/D+E) increases, Re will increase as well.

ii) As debt reaches a CRITICAL threshold and becomes risky (in the sense that return becomes IFFY), the market will price debt and equity (D, E respectively) Rd will rise ABOVE the risk free rate Rf

Summary: in this illustration Risk free rate=0,05 Market Risk premium=Ru - Rf =0,10 Ru= return to UNLEVERED equity here 0,15 Risk free rate=0,05 1000=(0.5*1400 + 0.5*900)/1.15= 1150/1.15=1000 Market Risk=Ru - Rf =0,10

In this setup: Systematic Risk=Business Risk=Risk Borne by Unlevered Equity: 40%-(-10%) or 50%. The reward this business or systematic risk "deserves" is 10%

Thus total expected return to unlevered equity equals Rf+Risk Premium=0.15. SINCE debt increases the income variability borne by equity holders ABOVE 50%,

the way the rational people in the market price Debt (D) and Equity ( E), will RASE expected return to equity holders ABOVE 15%

The thing to be noted is: (i) as debt/equity mix varies D and E vary (ii) as share of debt in capital increases Re increases (iii) when debt becomes risky as well Rd rises above Rf=0.05 but

(D/D+E)*Rd + (E/D+E)*Re ALWAYS STAYS CONSTANT AT 0.15. Thus the deviation of Re from 15% is reward to shareholders for bearing for bearing financial risk

Question: If a new capital structure increases the risk to 75% for the owner of equity; (a) What is the theoretical forecast for reward in terms of E(R)? (b) If we test, is the predicted answer coming out?

Date 0 Date 1 Cash Flows Date 1 Returns As risk relative to Unle Initial Value Strong Weak Strong Weak E(R) 100 105 105 5% 5% 5% 1000 1400 900 40% -10% 15% 900 1295 795 43.89% -11.67% 16.11% Debt Unlevered Equity Levered Equity Debt Unlevered Equity Levered Equity 200 1000 800 210 1400 1190 210 900 690 5% 40% 48.75% 5% -10% -13.75% 5% 15% 17.50% 300 5% Debt Unlevered Equity Levered Equity 1000 700 315 1400 1085 315 900 585 40% 55.00% 5% - 10% -16.43% 5% 15% 19.29% Debt Unlevered Equity Levered Equity 400 1000 600 420 1400 980 420 900 480 5% 40% 63.33% 5% -10% -20.00% 5% 15% 21.67% Debt Unlevered Equity Levered Equity 500 1000 500 525 1400 875 525 900 375 5% 40% 75.00% 5% -10% -25.00% 5% 15% 25.00% Debt Unlevered Equity Levered Equity 600 1000 400 630 1400 770 630 900 270 5% 40% 92.50% 5% -10% -32.50% 5% 15% 30.00% 735 Debt Unlevered Equity Levered Equity 700 1000 300 735 900 165 5% 40% 1400 665 5% -10% -45.00% 5% 15% 38.33% 121.67% Debt Unlevered Equity Levered Equity 800 1000 200 840 1400 560 840 900 60 5% 40% 180.00% 5% - 10% -70.00% 5% 15% 55.00% 900 Debt Unlevered Equity Levered Equity 870 1000 130 945 1400 455 900 8.62% 3.45% 40% -10% 250.00% - 100.00% 6.03% 15% 75.00% 0 Date 0 Date 1 Cash Flows Date 1 Returns As risk relative to Unle Initial Value Strong Weak Strong Weak E(R) 100 105 105 5% 5% 5% 1000 1400 900 40% -10% 15% 900 1295 795 43.89% -11.67% 16.11% Debt Unlevered Equity Levered Equity Debt Unlevered Equity Levered Equity 200 1000 800 210 1400 1190 210 900 690 5% 40% 48.75% 5% -10% -13.75% 5% 15% 17.50% 300 5% Debt Unlevered Equity Levered Equity 1000 700 315 1400 1085 315 900 585 40% 55.00% 5% - 10% -16.43% 5% 15% 19.29% Debt Unlevered Equity Levered Equity 400 1000 600 420 1400 980 420 900 480 5% 40% 63.33% 5% -10% -20.00% 5% 15% 21.67% Debt Unlevered Equity Levered Equity 500 1000 500 525 1400 875 525 900 375 5% 40% 75.00% 5% -10% -25.00% 5% 15% 25.00% Debt Unlevered Equity Levered Equity 600 1000 400 630 1400 770 630 900 270 5% 40% 92.50% 5% -10% -32.50% 5% 15% 30.00% 735 Debt Unlevered Equity Levered Equity 700 1000 300 735 900 165 5% 40% 1400 665 5% -10% -45.00% 5% 15% 38.33% 121.67% Debt Unlevered Equity Levered Equity 800 1000 200 840 1400 560 840 900 60 5% 40% 180.00% 5% - 10% -70.00% 5% 15% 55.00% 900 Debt Unlevered Equity Levered Equity 870 1000 130 945 1400 455 900 8.62% 3.45% 40% -10% 250.00% - 100.00% 6.03% 15% 75.00% 0