Question

Linda Clark received $236,000 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 $100,000. The stock paid no dividends, but it was sold for $171,000 at the end of three years.

b. Preferred stock was purchased at its par value of $55,000. 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 $40,000.

c. Bonds were purchased at a cost of $81,000. The bonds paid annual interest of $4,500. After three years, the bonds were sold for $89,000.

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:

   

Common stock:
Gain on sale ($171,000 – $100,000)	$	71,000
Preferred stock:
Dividends paid (7% × $55,000 × 3 years)		11,550
Loss on sale ($40,000 – $55,000)		(15,000	)
Bonds:
Interest paid ($4,500 × 3 years)		13,500
Gain on sale ($89,000 – $81,000)		8,000
Net gain on all investments	$	89,050

$89,050 ÷ 3 years	= 12.60 %
$236,000

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 $300,000 proceeds ($171,000 + $40,000 + $89,000 = $300,000) 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 11% return over the 12-year period?

Answer 1

	1a	CALCULATION OF NET PRESENT VALUE(NPV)
		Present Value(PV) of cash flow
		Cashflow)/((1+i)^N)
		i=discount rate =12%=0.12
		N=Year of Cash Flow
		a. INVESTMENT IN COMMON STOCK
			N	CF	PV=CF/(1.12^N)
			Year	Cash flow	Present Value
			0	($100,000)	($100,000)
			1	$0	$0
			2	$0	$0
			3	$171,000	$121,714
				SUM	$21,714
		Net Present Value(NPV)=Sum of PVs=	$21,714
		b. INVESTMENT IN PREFERRED STOCK
			N	CF	PV=CF/(1.12^N)
			Year	Cash flow	Present Value
			0	($55,000)	($55,000)
		(55000*7%)=3850	1	$3,850	$3,438
			2	$3,850	$3,069
		3850+40000=43850	3	$43,850	$31,212
				SUM	($17,282)
		Net Present Value(NPV)=Sum of PVs=	($17,282)
		c. INVESTMENT IN BONDS
			N	CF	PV=CF/(1.12^N)
			Year	Cash flow	Present Value
			0	($81,000)	($81,000)
			1	$4,500	$4,018
			2	$4,500	$3,587
		4500+89000=93500	3	$93,500	$66,551
				SUM	($6,843)
		Net Present Value(NPV)=Sum of PVs=	($6,843)
	1b	INVESTMENT in COMMON STOCK has Positive NPV
		Comon stock gave return higher than 12%
		Other investments have negative NPVs
		They gave less than 12% return
	2	Cash Flow taking all investments together
			N	CF	PV=CF/(1.12^N)
			Year	Cash flow	Present Value
			0	($236,000)	($236,000)
			1	$8,350	$7,455
			2	$8,350	$6,657
			3	$308,350	$219,477
				SUM	($2,411)
		Net Present Value(NPV)=Sum of PVs=	($2,411)
		NPV is negative.
		Earnings was less than 12%
		Using IRR function of excel, IRR	11.605%
		(Internal Rate of Return)
	3
	Pv	Initial Investment	$300,000
	Rate	Required Return	11%
	Nper	Number of years	12
	PMT	Minimum Annual net Cash Flow	$46,208.19
		(Using PMT function of excel)