Question: A newly issued bond pays its coupons once a year. Its coupon rate is 5%, its maturity is 20 years, and its yield to maturity is 8%.
a. Find the holding-period return for a one-year investment period if the bond is selling at a yield to maturity of 7% by the end of the year.
b. If you sell the bond after one year when its yield is 7%, what taxes will you owe if the tax rate on interest income is 40% and the tax rate on capital gains income is 30%? The bond is subject to original-issue discount (OID) tax treatment.
c. What is the after-tax holding-period return on the bond?
d. Find the realized compound yield before taxes for a two-year holding period, assuming that (i) you sell the bond after two years, (ii) the bond yield is 7% at the end of the second year, and (iii) the coupon can be reinvested for one year at a 3% interest rate.
e. Use the tax rates in part ( b ) to compute the after-tax two-year realized compound yield. Remember to take account of OID tax rules.
Given, n = 20; PMT = 50; FV = 1,000; i = 8
Initial price p0 =705.46
Next year's price, P1 = 793.29 (n = 19; PMT = 50; FV = 1000; i = 7)
Formulae for HPR = (Income + Value at the end of the holding period - Value at the start of the holding period) / Value at the start of the holding period
HPR = $ 50 + ($ 793.29 - $705.46) / $705.46
As per OCD rules, the cost basis and imputed interest under the constant yield method are obtained by discounting bond payments at the original 8% yield to maturity, and simply reducing maturity by one year at a time:
P0 = $705.46
P1 = $711.89 so implicit interest over first year = $711.89 - $705.46 = $6.43
P2 = $718.84 so implicit interest over second year = $718.84 - $711.89 = $6.95
Coupon received and imputed taxable interest over the first year is treated as ordinary income = 40% x ($50 + $6.43) = $22.57
Capital gain = Actual price at 7% YTM – Constant yield price
= $793.29 - $711.89
Tax on capital gain at 30% = 30% x $81.40 = $24.42
Total taxes = $22.57 + $24.42 = $46.99
Formulae for HPR = (Income + Value at the end of the holding period - Value at the start of the holding period) – Total taxes / Value at the start of the holding period
HPR = $ 50 + ($ 793.29 - $705.46) – $46.99 / $705.46
Value of bond after two years = $798.82 where n = 18; i = 7
Total income from the two coupons, including reinvestment income: ($50 x 1.03) + $50 = $101.50
Total funds after two years: $798.82 + $101.50 = $900.32
Therefore, the fund after two years = $900.32.
Þ705.46 (1 + r)2 = 900.32
r = 0.1297 = 12.97%
Coupon received in first year: $50.00
Tax on coupon @ 40% = – 20.00
Tax on imputed interest (0.40 x $6.43) = – 2.57
Net cash flow in first year = $27.43
If you invest the year-1 cash flow at an after-tax rate of: 3% x (1 – 0.40) = 1.8%
Then, by year 2, it will grow to: $ 27.43 x 1.018 = $27.92
You sell the bond in the second year for: $798.82
Tax on imputed interest in second year: – 2.78 [0.40 x $6.95]
Coupon received in second year, net of tax: + 30.00 [$50 x (1 – 0.40)]
Capital gains tax on sales price using constant yield value: – 23.99 [0.30 x ($798.82 – $718.84)]
CF from first year's coupon (reinvested): + 27.92 [from above]
Therefore, after two years, fund grows to $829.97.
If the plan in the previous problem wants to fund and immunize its position fully, how much of its portfolio should it allocate to one-year zero-coupon bonds and perpetuities, respectively, if these are the only two assets? Funding the plan?.
“A pension plan is obligated to make disbursements of $1 million, $2 million, and $1 million at the end of the next three years, respectively.”
A 30-year maturity bond has a 7% coupon rate, paid annually. It sells today for $867.42. A 20-year maturity bond has a 6.5% coupon rate, also paid annually. It sells today for$879.50. A bond market analyst forecasts that in five years, 25-year maturity bonds will sell at yields to maturity of 8% and that 15-year maturity bonds will sell at yields of 7.5%. Because the yield curve is upward-sloping, the analyst believes that coupons will be invested in short-term securities at a rate of 6%. Which bond offers the higher expected rate of return over the five-year period?
Bonds of Zello Corporation with a par value of $1,000 sell for $960, mature in five years, and have a 7% annual coupon rate paid semi-annually.
a. Calculate the:
(1) Current yield.
(2) Yield to maturity.
(3) Horizon yield (also called realized compound return) for an investor with a three year holding period and a reinvestment rate of 6% over the period. At the end of three years the 7% coupon bonds with two years remaining will sell to yield 7%.
b. Cite one major shortcoming for each of the following fixed-income yield measures:
(1) Current yield.
(2) Yield to maturity.
(3) Horizon yield (also called realized compound return).
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