Linda Clark received $210,000 from her mother’s estate. She placed the funds into the hands of a broker, who purchased the following securities on Linda’s behalf:
a. Common stock was purchased at a cost of $91,000. The stock paid no dividends, but it was sold for $160,000 at the end of three years.
b. Preferred stock was purchased at its par value of $46,000. The stock paid a 4% dividend (based on par value) each year for three years. At the end of three years, the stock was sold for $32,000.
c. Bonds were purchased at a cost of $73,000. The bonds paid annual interest of $3,500. After three years, the bonds were sold for $75,000.
The securities were all sold at the end of three years so that Linda would have funds available to open a new business venture. The broker stated that the investments had earned more than a 11% return, and he gave Linda the following computations to support his statement:
1-a. Using a 11% discount rate, compute the net present value of each of the three investments.
1-b. On which investment(s) did Linda earn a 11% rate of return?
2. Considering all three investments together, did Linda earn a 11% rate of return?
3. Linda wants to use the $267,000 proceeds ($160,000 + $32,000 + $75,000 = $267,000) from sale of the securities to open a retail store under a 10-year franchise contract. What minimum annual net cash inflow must the store generate for Linda to earn a 8% return over the 10-year period?
Computation of NPV for each of three investment | ||||
Item | Now | 1 | 2 | 3 |
Common Stock: | ||||
Purchase of the stock | -91000 | |||
Sale of the stock | 160000 | |||
Total Cash Flows | -91000 | 160000 | ||
Discount factor | 1 | 0.9009 | 0.8116 | 0.7312 |
Present Value | -91000 | 0 | 0 | 116992 |
Net Present Value | 25992 | |||
Preferred Stock: | ||||
Purchase of the stock | -46000 | |||
Annual Cash Dividend | 1840 | 1840 | 1840 | |
Sale of the stock | 32000 | |||
Total Cash Flows | -46000 | 1840 | 1840 | 33840 |
Discount factor | 1 | 0.9009 | 0.8116 | 0.7312 |
Present Value | -46000 | 1657.656 | 1493.344 | 24743.808 |
Net Present Value | -18105.192 | |||
Bonds: | ||||
Purchase of the Bond | -73000 | |||
Annual Interest Income | 3500 | 3500 | 3500 | |
Sale of the bonds | 75000 | |||
Total Cash Flows | -73000 | 3500 | 3500 | 78500 |
Discount factor | 1 | 0.9009 | 0.8116 | 0.7312 |
Present Value | -73000 | 3153.15 | 2840.6 | 57399.2 |
Net Present Value | -9607.05 |
Solution 1b: | |||||
NPV of only common stock investment is positive. Therefore Linda earned 11% rate of return on common stock investment. |
Solution 2: | ||||
Overall NPV of three investment = $25992-$18105.192 - $9607.05 = -$1720.24 |
As combined NPV is negative therefore Linda did not earn 11% rate of return on all investment together. |
Solution 3: | |||||
Required annal cash inflows to earn 8% return = Investment required / cumualtive PV Factor for 10 year at 8% | |||||
"=267000/7.1389 = $37400.72 |
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