Linda Clark received 221000 from her mothers estate She plac

Linda Clark received $221,000 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 $110,000. The stock paid no dividends, but it was sold for $190,000 at the end of three years.

b. Preferred stock was purchased at its par value of $42,000. 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 $28,000.

c. Bonds were purchased at a cost of $69,000. The bonds paid annual interest of $3,000. After three years, the bonds were sold for $74,000.

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 12% return, and he gave Linda the following computations to support his statement:

   

Click here to view Exhibit 13B-1 and Exhibit 13B-2, to determine the appropriate discount factor(s) using tables.

Required:

1-a. Using a 12% discount rate, compute the net present value of each of the three investments.

1-b. On which investment(s) did Linda earn a 12% rate of return?

2. Considering all three investments together, did Linda earn a 12% rate of return?

3. Linda wants to use the $292,000 proceeds ($190,000 + $28,000 + $74,000 = $292,000) from sale of the securities to open a retail store under a 12-year franchise contract. What minimum annual net cash inflow must the store generate for Linda to earn a 9% return over the 12-year period?

Common stock:
Gain on sale ($190,000 – $110,000)	$	80,000
Preferred stock:
Dividends paid (4% × $42,000 × 3 years)		5,040
Loss on sale ($28,000 – $42,000)		(14,000	)
Bonds:
Interest paid ($3,000 × 3 years)		9,000
Gain on sale ($74,000 – $69,000)		5,000
Net gain on all investments	$	85,040

Solution

Stock Preferred stock Bonds Purchase price 110000 42000 69000 Interest (Annual) 4% 3000 Sale proceeds 190000 28000 74000 Holding period (i) Interest on Preferred stock = 42000 x 4% = 1680 Cash flows of the three securities = Year Stock Preferred stock Bonds PV Factor @ 12% PV of cash flows stock PV of cash flows Preferred stock PV of cash flows bonds 0 -110000 -42000 -69000 1 -110000 -42000 -69000 1 0 1680 3000 0.892857 0 1500 2678.571 2 0 1680 3000 0.797194 0 1339.286 2391.582 3 190000 29680 77000 0.71178 135238.2 21125.64 54807.08 NPV = 25238.25 -18035.1 -9122.77 (ii) Rate of return Stock Preferred stock Bonds NPV 25238.25 -18035.1 -9122.77 Purchase price 110000 42000 69000 Rate of return= NPV/Purchase price x 100 = 22.94% -42.94% -13.22% Only stocks earn 12% return and other have a negative return or a loss. (iii) Initial investment = 292000 time = 12 Years Discount rate= 12% Annual net cash flow = A At 12% return, NPV = 0 i.e. outflow = Inflow (Discounted at 12% return) 292000 = A x PVAF(12%,12) PVAF(12%,12) = 6.1944 (Present value annuity factor) 292000 = A x 6.1944 A = 292000/6.1944 A = 47139.55 She must have a annual cash flow of 47139.55 to earn a 12% return.