Question

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:

Common stock: Gain on sale ($160,000 - $91,000) $ 69,000 Preferred stock: Dividends paid (4% x $46,000 x 3 years) Loss on sale ($32,000- 46,000) 5,520 (14,000) Bonds: Interest paid ($3,500 x 3 years) Gain on sale ($75,000 73,000) 10,500 2,000 $ 73,020 Net gain on all investments

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?

Answer 1

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