Corporate Finance, Final Exam, Practice Problems: Tax Shields
(The attached PDF file has better formatting.)
*Question 1.1: Debt Tax Shields
A firm has $100,000 (par value) of 6% annual coupon perpetual debt. The yield to maturity of the debt is 5% and its market value is $120,000. The corporate tax rate is 35%. What is the present value of all future debt tax shields, assuming the amount of debt is fixed and does not vary with the value of the firm? (The $120,000 market value is $100,000 × 6% / 5%.)
$100,000 × 35% / (1 – 35%) = $53,846
$120,000 × 35% / (1 – 35%) = $64,615
$120,000 × 5% / 35% = $171,429
$100,000 × 35% = $35,000
$120,000 × 35% = $42,000
Answer 1.1: E
With perpetual debt that does not vary, the present value of the tax shields is the corporate tax rate times the market value of the debt.
*Question 1.2: Tax Shields
A firm has perpetual debt at a fixed coupon rate, and it does not intend to vary the amount of the debt. If the corporate tax rate is 35% and the present value of the tax shields from the debt is $77,000, what is market value of the perpetual debt?
$77,000
$77,000 / (1 – 35%) = $118,462
$77,000 / 35% = $220,000
$77,000 × 35% = $26,950
$77,000 × (1 – 35%) = $50,050
Answer 1.2: C
The tax shield of perpetual debt is the market value of the debt times the tax rate, so the market value is the tax shield divided by the tax rate: $77,000 / 35% = $220,000.
*Question 1.3: Debt Tax Shields and Corporate Tax Rate
A firm has $100,000 (par value) of 8% annual coupon perpetual debt. Because of hostilities in South-East Asia, the yield to maturity of the debt rises to 10% per annum, and its market value falls to $80,000. (The $80,000 market value is $100,000 × 8% / 10%.)
To pay for higher military spending, the government raises the corporate tax rate from 35% to 40%. What is the change in the present value of all future debt tax shields, assuming the amount of debt is fixed and does not vary with the value of the firm?
An increase of $8,000
An increase of $4,000
No change
A decrease of $4,000
A decrease of $8,000
Answer 1.3: B
The old present value of the tax shields is 35% × $80,000 = $28,000.
The new present value of the tax shields is 40% × $80,000 = $32,000.
The increase is $32,000 – $28,000 = $4,000.