Question

5. Monicaclinton Ltd., a wholesale importer, is in the process of issuing $6,000,000 of 12% coupon debt with a maturity of 5 years. A sinking fund must be established to retire 60% of the issue prior to maturity. Assuming the bonds are retired at par and the tax rate is 35%, how large must the annual sinking fund payments be if the firm wishes to retire the bonds in equal installments over 4 years starting one year from now? What will be the annual after-tax cash outflow for each of the 5 years?

Answer 1

Bond Tenure = 5 years, Par Value = $ 6 million, Coupon = 12 %, If the bonds are to be retired at par then the bond's yield to maturity (YTM) should equal its coupon rate of 12%, Sinking Fund should retire 60% of the issue prior to maturity, Entire bond will be retired by means of equal annual installments over 4 years beginning 1 year post maturity.Tax Rate = 35%,

Let the required annual sinking fund payments be $ p

Further, Value of Issue to be retired using sinking fund = 60% of Par Value = 0.6 x 6 = $ 3.6 million, Sinking Fund Amount used per annum = 3.6 / 4 = $ 0.9 million

Equal Annual Installments = $ 6000000 / 4 = $ 1500000 or $ 1.5 million of which $ 0.9 million comes from sinking funds.

Therefore, p x (1.12)^(4) +..............+ p = 1.5 x (1.12)^(3) + ..............+ 1.5

p x [{(1.12)^(5)-1}/{(1.12)-1}] = 1.5 x [{(1.5)^(4)-1}/{(1.5)-1}]

p x 6.352847 = 7.168992

p = $ 1.128469 million ~ $ 1.1285 million

After-Tax Annual Bond Coupon = 0.12 x 6000000 x (1-0.35) = $ 0.468 million

From the Bond Issuer's Perspective:

Year 1 After-Tax Cash Flow = 1.1285 + 0.468 = $ 1.5965 million

Year 2 After-Tax Cash Flow = 1.1285 + 0.468 + 1.5 = $ 3.0965 million

Year 3 After-Tax Cash Flow = 1.1285 + 0.468 + 1.5 = $ 3.0965 million

Year 4 After-Tax Cash Flow = 1.1285 + 0.468 + 1.5 = $ 3.0965 million

Year 5 After-Tax Cash Flow = 1.1285 + 0.468 + 1.5 = $ 3.0965 million