Question

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%.

Answer 1

Answer:

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