comhmtps0020264206003493768 153146315344 newly issued bond p

com/hm.tps?0.020264206003493768 153146315344 newly issued bond pays its coupons once a year. Its coupon rate is 43%, its maturity is 10 years, and its yield to maturity is 7.3%. ing at a yield to matrty of 6.3% by the end ofthe year (00 . Find the holding-period return for a one-year investment ot round intermediate calculations. Round your answer to 2 decimal places.) 1471% Holding-perlod retun re is 40% ard the tax rate on b.If you selthe bond after one year when its yield is 6.3%, what taxes wil you awe if the capital gains i Round your answers to 2 decimal places.) tax rate on interest ncre is 30%? The bond is subject to ongna-issue discount (00) tax treatment (Do not round intermediate calculations. Tax on interest icome Tax on captal gan Total tavin c. What is the after-ax hoiding-period return on the bond? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Alfter-tax holding-period return d. Find the realized compound yield before taxes for a two-year holding period, assuming that () you sell the bond after two years, (i) the bond jed is 63% atthe end of te second year, and (i) t e coupon can be reinvested for one yearata 23% irterest rate. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Realized compound yield before taxes ?Use he tax rates i, pa te tocompute the ater-tax two year realtzed compound yield. Remember to take acout of OID tax rules. Do not round intermediate calculations. Round your answer to 2 decimal places.) Atter-jax wo-year reakized compound yed References eBook & Resources earning Objective: 10-06 pe here to search

Solution

Part 1: At 7.3%, ytm the price of the bond will be the future cash flows (coupon & maturity proceeds) discounted at ytm of 7.3%. Assuming face value of $100, the price will be :

Purchase Price = 4.3/(1+7.3%) + 4.3/(1+7.3%)² + ... + (4.3 + 100)/(1+7.3%)¹⁰ = 79.22

After 1 year, the ytm will be 6.3% and residual maturity is only 9 years, hence the sale price will be:

Sale price = 4.3/(1+6.3%) + 4.3/(1+6.3%)² + ... + (4.3 + 100)/(1+6.3%)⁹ = 86.57

Hence the holding period return = [(86.57 - 79.22) + 4.3]/79.22 = 14.71%

Part 2. Before we arrive at taxes, we need to segregate the portion of discount in bond price at the time of purchase into taxable as interest income and taxable as capital gains. SInce the bond was purchase (sold) at ytm of 7.3% at a price of 79.22 compared to face value (redemption value) of 100, we will calculate the price of bond at same yield after 1 year (constant yield price) - the difference between the purchase price and price after 1 year at constant yield is also considered as imputed interest income - it is a way of anortising the discount over the life of the bond. So the price of bond at 7.3% yield after 1 year will be :

Constant yield price = 4.3/(1+7.3%) + 4.3/(1+7.3%)² + ... + (4.3 + 100)/(1+7.3%)⁹ = 80.70

Hence imputed interest income = (80.70 - 79.22) = 1.48

Thus total income taxable as interest income = (4.3+1.48) = 5.78 and taxes there on = (5.78 * 40%) = 2.31

Capital gains will be = (86.57 - 79.22 - 1.48) = 5.87 and taxes there on = (5.87 * 30%) = 1.76

Total taxes = (2.31+1.76) = 4.07

Part 3. After tax holding period return = [(86.57 - 79.22) + 4.3 - 2.31 - 1.76]/79.22 = 9.57%

Part 4. In 2 years the cash flows will be as below:

Purchase price = 79.22

Coupon Year 1 = 4.3; reinvested at 2.3% we get at end of Year 2 = 4.3 * (1+2.3%) = 4.40

Coupon Year 2 = 4.3

Sale price = 4.3/(1+6.3%) + 4.3/(1+6.3%)² + ... + (4.3 + 100)/(1+6.3%)⁸ = 87.73

Hence total cash flows at end of Year 2 = 87.73 + 4.3 + 4.40 = 96.43

Hence the 2 year compounded return : 79.22 * (1+r)² = 96.43 where r is the 2 year compounded holding period annualised return. SOlving for r, we get r = 10.33%

Part 5. We will first calculate the constant yield price for the bond at end of year 2 at 7.3% ytm:

Constant yield price = 4.3/(1+7.3%) + 4.3/(1+7.3%)² + ... + (4.3 + 100)/(1+7.3%)⁸ = 82.29

Now the Interest component and tax there on will be as below:

Year 1 coupon = 4.3 and imputed interest is 1.48 and the tax there on is 2.31, hence net available for reinvestment is (4.3 + 1.48 - 2.31) = 3.47; at reinvestmen rate of 2.3%, it will become = 3.47*(1+2.3%) = 3.55 and taxes will be (3.55-3.47) * 40% = 0.03 and net of tax = 3.52

Year 2 coupon = 4.3 and imputed interest income will be (82.29 - 80.70) = 1.59 ; total = 5.89 and net of tax will be 3.53

Capital gains = (87.73 - 79.22 - 1.48 - 1.59) = 5.44 and net of tax will 3.81

Hence net of tax cash flows at the end of year 2 = 3.52 + 3.53 + (79.22+3.81) = 90.08

Hence the 2 year compounded return : 79.22 * (1+r)² = 90.08 where r is the 2 year compounded holding period annualised return. SOlving for r, we get r = 6.63%