Simon Software Co. is trying to estimate its optimal capital structure. Right now, Simon has a capital structure that consists of 20% debt and 80% equity, based on market values. (Its D/S ratio is 0.25.) The risk-free rate is 6% and the market risk premium, rM – rRF, is 5%. Currently the company’s cost of equity, which is based on the CAPM, is 12% and its tax rate is 40%. What would be Simon’s estimated cost of equity if it were to change its capital structure to 50% debt and 50% equity?

Simons estimated cost of equity is going to be 14.35 percent

To solve this problem, we have to make use of the formula below

rs = rRF + RPM(b)

Where rs = 12%

rRF = 6%

RPM = 5%

When we put these values into the formula we have;

12% = 6% + 5%b

We take like terms

5%b = 12%-6%

5%b = 6%

0.05b = 0.06

b = 0.06/0.05

= 1.2

The formula for b

b = bU[1 + (1 - T)(D/E)]

where 1-t = 0.6

D/E = 0.25

1.2 = bU[1 + 0.6*0.25]

1.2 = bU[1+0.15]

1.2 = 1.15bU

Divide through by 1.15

bU = 1.2/1.15

= 1.044

b = bU[1 + (1 - T)(D/E)]

We have to put in the value of bU into the formula above

b = 1.044[1 + 0.6]

b= 1.67

We have to put the value of b into the first equation

rs = 0.06+0.05(1.67)

= 0.06+0.0835

= 0.1435 * 100

= 14.35%

Simons estimated cost of equity is going to be 14.35 percent

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