Question

Use present worth analysis to determine whether the following proposal seems to be justified, if an annual rate of return of 16%, compounded semi-annually, is desired:

Investments would be $50,000 on January 1, 1995 and $70,000 on July 1, 1995. Income would be quite irregular, starting at $10,000 each six months beginning January 1, 1996 until, and including, January 1, 1998. There would be no income after that until July 1, 1999, when $35,000 would be received. Then, there would be income of $25,000 on January 1, 2000; $50,000 on July 1, 2000; and $25,000 on January 1, 2001. a) 78,347 b) 92,090 c) -17,385 d) -439 (almost zero)

Answer 1

Option C is correct

The table below schedules the cash flow for each half year. The income is received every half year and interest rate is also compounded every half year so we take R = 16%/2 = 8%. The present value factor is (1+R)^(-N). The net present value is turned out to be c) -17,385

N(a half year)		Present value	P/F = (1+R%)^-N	Half years
0	-50000	-50000.00	1.0000	Jan-95
1	-70000	-64814.81	0.9259	Jul-95
2	10000	8573.39	0.8573	Jan-96
3	10000	7938.32	0.7938	Jul-96
4	10000	7350.30	0.7350	Jan-97
5	10000	6805.83	0.6806	Jul-97
6	10000	6301.70	0.6302	Jan-98
7	0	0.00	0.5835	Jul-98
8	0	0.00	0.5403	Jan-99
9	35000	17508.71	0.5002	Jul-99
10	25000	11579.84	0.4632	Jan-00
11	50000	21444.14	0.4289	Jul-00
12	25000	9927.84	0.3971	Jan-01
NPV		-17384.7394