(a)

Question

   Find the holding-period return for a one-year investment period if the bond is selling at a yield to maturity of 6.1% by the end of the year Find the holding-period return for a one-year investment period if the bond is selling at a yield to maturity of 6.1% by the end of the year

Answer

   Holding-period return = 17.53%

Explanation

   determinate the value of the bond at yield of 7.1% and at yield of 6.1% which is the sum of the present value of the maturity and coupon payment:

Purchase price

C * 1-(1+r)^-time / rate = PV

Coupon payment = 1,000 x 0.041 = 41.00

time 15 years

rate 0.071

41 * 1-(1+0.071)^-15 = PV

PV $371.0773

Maturity / (1+rate)time = PV

Maturity 1,000.00

time 15.00

rate 0.071

1000 / (1+0.071)^15 = PV

PV 357.40

PV c $ 371.0773

PV m $ 357.4028

Total $ 728.4801

Selling Price

C * 1-(1+r)^-time / rate = PV

C 41.00

time 14 (one-year past so maturity is more closer)

rate 0.061

41 * 1-(1+0.061)^-14 / 0.061 = PV

PV $378.7456

Maturity / (1+rate)time = PV

Maturity 1,000.00

time 14.00

rate 0.061

1000 / (1+0.061)^14 = PV

PV 436.50

PV c $378.7456

PV m $436.5004

Total $815.2460

Holding period return:

return / investment - 1

(815.25 + 41) / 728.48 - 1 = 0.175387059 = 17.53%

Holding period return = 17.53%

.

(b)

Question

If you sell the bond after one year when its yield is 6.1%, 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

Answer

$41 x 40% = $ 16.40

815.25 - 728.48 = 86.77 capital gain x 30% = $ 26.03

Total: 26.03 + 16.40 = $ 42.43 income tax expense

Tax on interest income	$ 16.40
Tax on capital gain	$ 26.03
Total taxes	$ 42.43

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(c)

Question

What is the after-tax holding-period return on the bond?

Answer

After tax holding period return = (815.25 + 41 - 42.43) / 728.48 - 1 = 0.1171425 = 11.71%

After tax holding period return = 11.71%

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(d)

Question

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 6.1% at the end of the second year, and (iii) the coupon can be reinvested for one year at a 2.1% interest rate

Answer

we recalculate the price of the bond with 13 years left to maturity

Realized compound yield before taxes 26.94%

Explanation

we recalculate the price of the bond with 13 years left to maturity

C * 1-(1+r)^-time / rate = PV

C 41.00

time 14

rate 0.061

41 * 1-(1+0.061)^-14 / 0.061 = PV

PV $378.7456

Maturity / (1+rate)time = PV

Maturity 1,000.00

time 13.00

rate 0.061

1000 / (1+0.061)^13 = PV

PV 463.13

PV c $378.7456

PV m $463.1269

Total $841.8725

and redo the return, tax and after-tax return:

(841.87 + 41x1.021 + 41) /728.48 - 1 = 0.269401333

holding period return 26.94%

.

(e)

Question

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

Answer

tax expense:

(41x1.02 + 41) x 0.4 = 33.14

(841.87 - 728.48) x 0.3 = 34.02

tax expense: 67.16

after tax return:

(841.87 + 41x1.021 + 41 - 67.16) /728.48 - 1 = 0.177209379 = 17.72%

After tax two year realized compound yield = 17.72%