Question

.    Jodha is offered two investment alternatives. If she chooses ALT 1, she will have to make an immediate outlay of $15,000. In return, she will receive $1200 at the end of every three months for the next ten years. If she chooses Alt 2, she will have to make an outlay of $7000 now and 7000 in two years. In return, she will receive $41,000 ten years from now. Interest is 12 % compounded semi-annually. Determine which investment should be accepted using the Net Present Value approach.show calculation by BAII plus Calculator.You are encouraged to draw the timelines for yourself to help you with setting up the logic of how to solve the problem.

Answer 1

We need to find the present value of both the investment. The investment with more NET PRESENT VALUE will be selected.

YEAR	PAYMENT	Received amount (1200*4)	PV FACTOR interest at 6%	PRESENT VALUE
0	15000		1
1		4800	0.943	4526.4
2		4800	0.89	4272
3		4800	0.84	4032
4		4800	0.792	3801.6
5		4800	0.747	3585.6
6		4800	0.705	3384
7		4800	0.665	3192
8		4800	0.627	3009.6
9		4800	0.592	2841.6
10		4800	0.558	2678.4
Total				35323.2

I have used the PV factor at 12% compounded semi annually so 12/2 which is 6%.

Also PV factor is taken from the PV table. The formula for calculating the pv factor is 1/(1+r)^n where r is interest rate and n is time.

Example to calculate PV factor at time 2 and interest rate 6%

1/(1+0.06)^2

=1/1.06^2

1/1.1236

=0.889

Present value is amount received * present value factor

Present value of amount received = $35323.2

Net present value = Present value of amount received - Amount invested

amount invested in alternative 1 is 15000

So net present value of alternative 1 is = $35323.2 - $15000 which is $20323.2

alternative 2

YEAR	PAYMENT	Received amount	PV FACTOR interest at 6%	PRESENT VALUE
0	7000		1
1			0.943
2	7000		0.89
3			0.84
4			0.792
5			0.747
6			0.705
7			0.665
8			0.627
9			0.592
10		41000	0.558	22878
Total				22878

Present value of payment at year 0 is 7000

Present value of payment at year 2 is 7000*0.89 which is $6230

present value of total amount invested = $7000 + $6230 which is $13230

present value of amount to be received in 10 years

4000 * 0.558 which is $22878

Net present value = amount received - amount invested

= $22878 - $13230

Net present value of alternative 2 is $9648

As net present value of Alternative 1 is more than net present value of alternative 2. Alternative 1 should be selected.

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GOOD LUCK!!