Compute the present value of interest tax shields generated

Compute the present value of interest tax shields generated by these three debt issues. Consider corporate taxes only. The marginal tax rate is Tc = .35. a. A $1,800, one-year loan at 10%. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Present value $ 57.27 b. A four-year loan of $1,800 at 10%. Assume no principal is repaid until maturity. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Present value $ c. A $1,800 perpetuity at 9%. Present value

Solution

a)

Present value of tax shield = [tax ( rate * debt)] / 1 + r

Present value of tax shield = [ 0.35 ( 0.1 * 18,00)] / 1 + 0.1

Present value of tax shield = 63 / 1.1

Present value of tax shield = $57.27

b)

Tax shield per year = 0.35 * ( 0.1 * 1,800)

Tax shield per year = 63

Number of years = 4

discount rate = 10%

Present value of annuity = Annuity * [ 1 - 1 / ( 1 + R)ⁿ] / R

Present value of annuity = 63 * [ 1 - 1 / ( 1 + 0.1)⁴] / 0.1

Present value of annuity = 63 * 3.169865

Present value of annuity = $199.70

You can also find this using a financial calculator: PMT = -63, I/Y = 10, N = 4, CPT PV

c)

Present value = Tax * debt

Present value = 0.35 * 1800

Present value = $630