Question

Linda Clark received $225,000 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 $96,000. The stock paid no dividends, but it was sold for $165,000 at the end of three years b. Preferred stock was purchased at its par value of $51,000. 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 $37,000 c. Bonds were purchased at a cost of $78,000. The bonds paid annual interest of $4,500. After three years, the bonds were sold for $83,000. 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 ($165,000 $96,000) Preferred stock : Dividends paid (4% x $51, 000 x 3 years ) Loss on sale ($37,000 - $51, 000) Bonds: $ 69,000 6,120 (14,000) Interest paid ($4,500 3 years) Gain on sale ($83,000 $78,000) 13,500 5,000 $79,620 Net gain on all investments

Answer 1

1a.

Equity

Year	Cashflow	PV factor 11%	Discounted cashflow
0	-96000	1.0000	-96000
3	165000	0.731191	120646.6
		NPV	24646.58

Preference

Year	Cashflow	PV 11%	Discounted cashflow
0	-51000	1.00000	-51000.00
1	2040	0.900901	1837.84
2	2040	0.811622	1655.71
3	2040	0.731191	1491.63
3	37000	0.731191	27054.08
		NPV	-18960.74

Bonds

Year	cashflow	PV 11%	discounted cashflow
0	-78000	1.00000	-78000.00
1	4500	0.900901	4054.05
2	4500	0.811622	3652.30
3	4500	0.731191	3290.36
3	83000	0.731191	60688.88
			-6314.40

1b- From the above, its clear that Linda learned more than 11% from equity as it has positive NPV. However, the bonds and preference have negative NPV, so they earn lesser.

2. If the total NPV is zero or greater (ie positive), then Linda earns 11% or more. Accordingly, NPV = 24646.58 - 18960.74 - 6314.4 = -628.56. Since, the NPV is negative, Linda earns slightly lesser than the 11%.

3.

Linda wishes to receive 8% for 9 years after 3 years from today. So, we take into consideration PV @ 8% from Year 4 to Year 12. So, PV Factor for 9 Years is 4.959. So, PV of minumum cash inflow store should generate => 285000/4.959 = 57471.

(The above is solved assuming we are in Year 0 and cashflows from store generate from year 4 (ie after selling shares at end of year 3 and investing proceeds into retail stores. However if we assume that we are in year 3 and wish to invest the proceeds in retail stores, we get PV Factor @ 8% from year 1 to 9 = 6.247. accordingly Rent will be 285000/6.247 = 45622)

(please comment in case of any query regarding the solution)