Suppose your grandmother is working on a financial plan for the last (what she b
ID: 2736239 • Letter: S
Question
Suppose your grandmother is working on a financial plan for the last (what she believes is) the last 20 years of her life. So far, she has committed to the following:
2,000 shares of preferred stock ABC that pays a 3.0% dividend on a $50 face value The required rate of return is 3.8%.
1,000 shares of common stock XYZ that pays no dividend, but is currently selling for $48.10 per share.
Her first concern is making sure she gets enough ongoing income from her portfolio. She needs to get $10,000 in annual income in total from dividends and coupons. So, she has to get the remainder of the income needed from the coupons from coupon bonds, which have the characteristics below.
7.0% coupon rate, $1000 face value, 7.2% YTM, 20 years left until maturity, and compounded semiannually.
Given all this, how much will she have to pay in total for her total portfolio?
Explanation / Answer
Preferred stock dividend=Rate of Dividend*Face Value= 3%*$50=$1.5
Preferred stock price per share=Dividend/Rate ofreturn=$1.5/3.8%=$1.5/0.038=$39.47
Total preferred stock dividend=2,000*$1.5=$3,000
Common stock price=$48.10
Annual income in total from dividends and coupons needs to get=$10,000
so the amount to be get from Coupons=$10,000-$3,000=$7,000
Coupon amount per bond=$1,000*7%=$70
so no of bonds=$7,000/$70=100
Price of the bond:=$1,090.98(Working note1)
total for her total portfolio=2,000*$39.47+1,000*$48.10+100*$1090.98=$236,138
Working note1:
Price of the bond:
Year Cash flow PV@3.1% PV 0.5 35 0.9699 33.95 1 35 0.9408 32.93 1.5 35 0.9125 31.94 2 35 0.8850 30.98 2.5 35 0.8584 30.05 3 35 0.8326 29.14 3.5 35 0.8076 28.27 4 35 0.7833 27.42 4.5 35 0.7598 26.59 5 35 0.7369 25.79 5.5 35 0.7148 25.02 6 35 0.6933 24.26 6.5 35 0.6724 23.53 7 35 0.6522 22.83 7.5 35 0.6326 22.14 8 35 0.6136 21.47 8.5 35 0.5951 20.83 9 35 0.5772 20.20 9.5 35 0.5599 19.60 10 35 0.5430 19.01 10.5 35 0.5267 18.43 11 35 0.5109 17.88 11.5 35 0.4955 17.34 12 35 0.4806 16.82 12.5 35 0.4662 16.32 13 35 0.4521 15.82 13.5 35 0.4385 15.35 14 35 0.4254 14.89 14.5 35 0.4126 14.44 15 35 0.4002 14.01 15.5 35 0.3881 13.58 16 35 0.3765 13.18 16.5 35 0.3651 12.78 17 35 0.3542 12.40 17.5 35 0.3435 12.02 18 35 0.3332 11.66 18.5 35 0.3232 11.31 19 35 0.3135 10.97 19.5 35 0.3040 10.64 20 35 0.2949 10.32 20 1000 0.2949 294.89 1,090.98Related Questions
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