Question

Avicorp has a $15.5 million debt issue outstanding, with a 6.3% coupon rate. The debt has semi-annual coupons, the next coupon is due in six months, and the debt matures in five years. It is currently priced at 92% of par value. a. What is Avicorp's pre-tax cost of debt? Note: Compute the effective annual return. (Another note: The pre-tax cost of debt is the yield to maturity (YTM) on the outstanding debt issue. We solve for the 6-month YTM on the bond: (This is what I have so far... not sure how they got $920 here:) ** $920 = (31.50/(1+YTM)) + (31.50/(1+YTM)^2)) + (31.50/(1+YTM)^9)) + (31.50 + 1,000)/(1+YTM)^10) Therefore, YTM = 4.1434% Then compute the effective annual return (EAR) as: EAR = (1 + 0.041434)^2 -1 = 0.084585 The pre-tax cost of debt is 4.1434% every 6 months, or 8.4585% per year. b. If Avicorp faces a 40% tax rate, what is its after-tax cost of debt? After-tax cost of debt = EAR x (1-TC) where Tc is Avicorp's tax rate. Then, After- tax cost of debt = 0.084585 x (1-0.4) = 0.050751 If Avicorps faces a 40% tax rate, the after-tax cost of debt is 5.0751%.

Answer 1

Answer:

a) Pre-tax cost of debt is 8.45%

b) After tax cost of debt is 5.07%

Explanation:

a) Given:

Debt issue outstanding = $15.5 million

Semi-annual coupon rate = 0.063 / 2 = 0.0315

Assumed par value (FV) = $1,000

Coupon payment (pmt) = 0.0315 × 1000 = $31.5

Current bond price (PV) = 92% of $1,000 = $920

Time period (nper) = 5 × 2 = 10 periods

Calculate semi-annual rate using  spreadsheet function =Rate(nper,pmt,PV,FV)

Semi-annual rate = 4.14%

Pmt and FV are negative as they are cash outflows.

YTM = 4.14 × 2 = 8.28%

Effective annual rate = $(1+\frac{Rate}{compounding\ periods}) ^{2} -1$

                                   = $(1+\frac{0.0828}{2}) ^{2} -1$

                                   = 0.0845 or 8.45%

b) Tax rate is 40%

After tax cost of debt = Pre tax cost of debt × (1 - 0.4)

                                    = 0.0845 × 0.6

                                    = 0.0507 or 5.07%