Compute the PV of the interest tax shields generated by the following three debt issues. In each case the debt is risk free while the corporate tax rate is 35%. a) A $1,000 one-year loan at the risk-free rate of 8%. b) A five-year loan of $1,000 at the risk-free rate of 8%. Assume interest is paid annually while the principal is paid back at maturity. c) A $1,000 debt perpetuity at the risk-free rate of 7%.

a. Present value of tax shield = $25.93

b. Present value of tax shield = $111.80

c. Tax shield = $350

Explanation:

a. Tax shield =  Loan * rate * tax rate

Tax shield = 1,000 * 8% * 35%

Tax shield = $28

Present value of tax shield = 28 / (1+8%)

Present value of tax shield = 28 / 1.08

Present value of tax shield = 25.92592593

Present value of tax shield = $25.93

b. Tax shield each year = 28

Present value of tax shield = 28 / (1+8%)^1 + 28 / (1+8%)^2 + 28 / (1+8%)^3 + 28 / (1+8%)^4 + 28 / (1+8%)^5

Present value of tax shield = 28/1.08  + 28/1.1664 + 28/1.25971 + 28/1.36049 + 28/1.46933

Present value of tax shield = 111.795875652

Present value of tax shield = $111.80

c. Tax shield = Perpetuity * tax rate

Tax shield = 1000 * 35%

Tax shield = $350

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explanation:

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