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Posted on April 17th, 2014, by

Question A. Calculate the holding period return on a before-tax basis for each of these four investment vehicles.

1) Common stock

Overall, holding period return is calculated as follows: HPR = (Income + Ending value Beginning Value)/Beginning Value (Moyer et al., 2012). In the considered case, holding period is the past calendar year. For common stock, the holding period return is: HPR = (400*($.0.20+$0.20+$0.25+$0.25) + 400*18.75 400*$17.25))/ 400*$17.25 = (400*$0.9 + 400*$18.75 400*$17.25) / $6900 = ($360 + $7500 – $6,900) / $6,900 = $960 / $6,900 = 13.91%

2) Industrial bonds

HPR = (Income + Ending Value Starting Value ) / Starting Value = 8*($1,000*9.25%/100% + 96.375%*$1,000 / 100% – 97.000%*$1,000 / 100%) / 8*(97.000%*$1,000 / 100%) = 8*($92.50 + $963.75 – $970) / 8*$970 = 8*$86.25 / 8*$970 = 8.89%

3) Mutual fund shares

For mutual funds, HPR can be calculated as follows: HPR = (Income + Capital gain + NAV Ending NAV Beginning) / NAV Beginning. For the Stalchecks’ portfolio, HPR = (500*$0.60 + 500*$0.50 + 500*$20.02 500*$19.45) / 500*$19.45 = ($300 + $250 + $10,010 – $9,725) / $9,725 = $835 / $9,725 = 8.59%

4) Options

For options, HPR can be calculated as follows: HPR = (Total ending value of contracts Total beginning value of contracts) / Total beginning value of contracts = ($29,000 – $26,000) / $26,000 = $3,000 / $26,000 = 11.54%

Question B. Assuming that the Stalchecks’ ordinary income is currently being taxed at a combined (federal and state) tax rate of 38%, and that they would pay a 15% capital gains tax on dividends and capital gains for holding periods longer than 12 months, determine the after-tax HPR for each of their four investment vehicles.

1) Common stock

Income for common stock is taxable and will be taxed at 38% rate; change of stock value represents an unrealized capital gain and is not taxed (Moyer et al., 2012). After-tax value of stock income will be 400*($.0.20+$0.20+$0.25+$0.25)*(1-0.38) = $360*0.62 = $223.20. Therefore, after-tax HPR = ($223.20 + $7,500 – $6,900) / $6,900 = $823.20 / $6,900 = 11.93%

2) Industrial bonds

Income for industrial bonds is taxable and will be taxed at 38% rate; change of bond quote represents an unrealized capital gain and is not taxed. After-tax value of bond income will be 8*$1,000*0.0925*(1-0.38) = 8*$92.50*0.62=$458.8. Therefore, after-tax HPR = ($458.8 + 8*$963.75 8*$970) / (8*$970) = ($458.8 + $7,710 – $7,760) / $7,760 = $408.8 / $7,760 = 5.27%

3) Mutual fund shares

Income and capital gains for mutual funds are taxable and will be taxed at 38% rate; change of NAV represents an unrealized capital gain and is not taxed. After-tax value of income and capital gains for mutual fund will be 500*($0.50 + $0.60)*(1-0.38) = 500*$1.1*0.62 = $341. After-tax HPR = ($341 + $10,010 – $9,725) / $9,725 = $626 / $9,725 = $6.44%.

4) Options

The options were not exercised in the holding period, and therefore all changes of option value represent unrealized capital gains, and are not taxed. Therefore, after-tax HPR for options will be the same as before-tax HPR and equals to 11.54%.

Question C. Recognizing that all gains on the Stalchecks’ investments were unrealized, calculate the before-tax portfolio HPR for their four-vehicle portfolio during the past calendar year. Evaluate this return relative to its current income and capital gain components.

The return of the portfolio can be calculated as (Income + Ending Value Beginning Value) / Beginning Value. Before-tax income generated by all investments = Income from common stock + Bond income + Mutual fund dividends and gains = 400*($.0.20+$0.20+$0.25+$0.25) + 8*($1,000*0.0925) + (500*$0.60 + 500*$0.50) = $360 + $740 + $550 = $1,650.

Beginning value of the portfolio = $6,900 + $7,760 + $9,725 + $26,000 = $50,385.

Ending value of the portfolio = $7,500 + $7,710 + $10,010 + $29,000 = $54,220.

Unrealized capital gains during the past calendar year were $54,220 – $50,385 = $3,835. HPR of the portfolio = (Income + Capital Gains) / Beginning Value = ($1,650 + $3,835) / $50,385 = $5,485 / $50,385 = 10.89%. In this HPR, the current income component is $1,650 / $50,385 = 3.27%, and capital gains component is $3,835 / $50,385 = 7.61%. Overall, the capital gains component is by 2.32 times greater than the current income component of the HPR.

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