Consider a firm that lasts 5 years and earns revenues of $1000K per year (years

Question

Consider a firm that lasts 5 years and earns revenues of $1000K per year (years 1-5) after an initial investment of $1500K in year 0. The firm faces a tax rate of 10% per year.

a) Assume that the firm carries no debt, and faces a cost of equity of 12%. What is the unlevered value of the firm?

b) Assume that the firm issues 5-year debt with face value $1000K. If the coupon rate is 5% and yield to maturity is 5%, what is the market value of debt?

c) Find the present value of the interest tax shield.

d) Use the information in b) and c) to find the value of the levered firm and the implied market value of equity.

Explanation / Answer

a) in Thousands Year Cash flow Tax Rate 10% After Tax Cash Flow PV @12% Present Value 0 -$1,500 0 -$1,500 1 -$1,500 1 $1,000 $100 $900 0.893 $803.57 2 $1,000 $100 $900 0.797 $717.47 3 $1,000 $100 $900 0.712 $640.6 4 $1,000 $100 $900 0.636 $571.97 5 $1,000 $100 $900 0.567 $510.68 Value of unlevered firm $1,744.3 b) Coupon Rate 5.00% Face Value (FV) 1000 k Coupon Payment (PMT ) $50 Rate 5.00% Nper 5 market value of debt(PV(5%,5,-50,-1000) $1,000 k c) Interest Tax Shield Year Interest Tax Shield= $50*10% PV @12% Present Value of Interest Shield 1 $50 $5 0.8929 $4.46 2 $50 $5 0.7972 $3.99 3 $50 $5 0.7118 $3.56 4 $50 $5 0.6355 $3.18 5 $50 $5 0.5674 $2.84 Total $18.02 d) Value of levered firm = Value of unlettered + debt Value of levered firm = $1744.3+$1000 $2,744.3 k

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