Linda Clark received 229000 from her mothers estate She plac

Linda Clark received $229,000 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 $125,000. The stock paid no dividends, but it was sold for $210,000 at the end of three years b. Preferred stock was purchased at its par value of $49,000. The stock paid a 7% dividend (based on par value) each year for three years. At the end of three years, the stock was sold for $35,000 c. Bonds were purchased at a cost of $55,000. The bonds paid annual interest of $1,000. After three years, the bonds were sold for $81,000 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 16% return, and he gave Linda the following computations to support his statement: Common stock: Gain on sale ($210,000 $125,000) $ 85,000 Preferred stock: Dividends paid (7% x $49,000 x 3 years) Loss on sale ($35,000 - $49,000) 10,290 (14,000) Bonds: Interest paid ($1,000 x 3 years) Gain on sale ($81,000 - $55,000) 3,000 26,000 $110,290 Net gain on all investments $119,290 3 years $229,000 -16.10 % 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 16% discount rate, compute the net present value of each of the three investments. 1-b On which investment(s) did Linda earn a 16% rate of return? 2. Considering all three investments together, did Linda earn a 16% rate of return? 3. Linda wants to use the $326,000 proceeds ($210,000 + $35,000 + $81,000 = $326,000) from sale of the securities to open a retail store under a 7-year franchise contract. What minimum annual net cash inflow must the store generate for Linda to earn a 11% return over the 7-year period? Complete this question by entering your answers in the tabs below Req 1A Req 1B Req 2 Req 3

Solution

(1a) Common Stock:

Discount Rate = 16 % per annum

Initial Investment = $ 125000 and Final Cash Flow = $ 21000

Investment Tenure = 3 years

PV of Final Cash Flow = 210000 / 1.16^(3) = $ 134538.11

NPV = 134538.11 - 125000 = $ 9538.11

Preferred Stock:

Preferred Stock Face Value = $ 49000, Dividend Rate = 7 % of Par Value

Annual Dividend = 0.07 x 49000 = $ 3430

Discount Rate = 16 % per annum and Investment Tenure = 3 years

Stock Sale Proceed = $ 35000

PV of Annual Cash Flows = 3430 / 1.16 + 3430 / (1.16)^(2) + 3430 / (1.16)^(3) + 35000 / (1.16)^(3) = $ 30126.42

NPV = 30126.42 - 49000 = - $ 18873.58

Bonds:

Annual Interests = $ 1000, Sale Proceeds = $ 81000 and Purchase Price = $ 55000

Investment Tenure = 3 years and Discount Rate = 16 % per annum

PV of Annual Cashflows = 1000 / 1.16 + 1000 / (1.16)^(2) + 1000 / (1.16)^(3) + 81000 / (1.16)^(3) = $ 54139.16

NPV = 54139.16 - 55000 = - $ 860.84

(1b) Any investment that provides a rate of return of 16 % implies that a discount rate equal to the rate of return would equalize the investment\'s future cash flows to the initial investment outlay. In other words a rate of return of 16 % implies an IRR(internal rate of return) of 16%.

As two of the three investments (preferred stock and bond) have a negative NPV, it implies that the negative NPV investments have IRRs less than 16 % per annum (the discount rate). Hence, these two investments have rates of return less than the stated discount rate of 16 % per annum.

The common stock investment possesses a positive NPV which implies a rate of return (IRR) greater than the discount rate of 16 %.

Hence, although none of the investments earns an exact return of 16 % the first one has returned greater than the same and the latter two have rates of return less than 16 %.

(2) Combined Initial Investment = $ 229000

Combined PV of Cash Flows = 134538.11 + 30126.42 + 54139.16 = $ 218803.69

NPV = 218803.69 - 229000 = - $ 10196.31

As the combined NPV is negative the IRR is less than the discount rate of 16 %. Hence, the combined investment does not earn a rate of return of 16 % and in fact has a return rate lesser than the same.

(3) Required Rate of Return =11 % per annum, Franchise Contract Tenure = Cash Flow Tenure = 7 years, Initial Investment = $ 326000

Let the minimum annual cash flow be $ K

If the return rate is 11 %, the same as the discount rate would equalize the combined PV of the minimum annual cash flows to the initial investment.

Therefore, 326000 = K x (1/0.11) x [1/{1/(1.11)^(7)}]

K = $ 69182.18 approximately.