Chapter 5, Problem 101P

To determine

(a)

When the higher payments catch up in total dollars received with the lower payment that begins earlier.

Answer to Problem 101P

The higher payments catch up in total dollars received with the lower payment that begins earlier in the 18 Year in case of higher payments collected.

Explanation of Solution

Given information:

Option A: Receive $2,000 per month from age 66 − 85 i.e. 19 Years

Option B: Receive $1,500 per month from age 62 − 85 i.e. 23 Years.

Based on the above information, the following tables express the total cumulative dollars received.

Annual Receipts (Option 1) = $2,000 × 12 = $24,000

Annual Receipts (Option 2) = $1,500 × 12 = $18,000

Option 1: $2,000 from Age 66 - 85			Option 2: $1,500 from Age 62 - 85
Age	Annual Receipt	Cumulative Receipt	Age	Annual Receipt	Cumulative Receipt
66	$24,000.00	$24,000.00	62	$18,000.00	$18,000.00
67	$24,000.00	$48,000.00	63	$18,000.00	$36,000.00
68	$24,000.00	$72,000.00	64	$18,000.00	$54,000.00
69	$24,000.00	$96,000.00	65	$18,000.00	$72,000.00
70	$24,000.00	$120,000.00	66	$18,000.00	$90,000.00
71	$24,000.00	$144,000.00	67	$18,000.00	$108,000.00
72	$24,000.00	$168,000.00	68	$18,000.00	$126,000.00
73	$24,000.00	$192,000.00	69	$18,000.00	$144,000.00
74	$24,000.00	$216,000.00	70	$18,000.00	$162,000.00
75	$24,000.00	$240,000.00	71	$18,000.00	$180,000.00
76	$24,000.00	$264,000.00	72	$18,000.00	$198,000.00
77	$24,000.00	$288,000.00	73	$18,000.00	$216,000.00
78	$24,000.00	$312,000.00	74	$18,000.00	$234,000.00
79	$24,000.00	$336,000.00	75	$18,000.00	$252,000.00
80	$24,000.00	$360,000.00	76	$18,000.00	$270,000.00
81	$24,000.00	$384,000.00	77	$18,000.00	$288,000.00
82	$24,000.00	$408,000.00	78	$18,000.00	$306,000.00
83	$24,000.00	$432,000.00	79	$18,000.00	$324,000.00
84	$24,000.00	$456,000.00	80	$18,000.00	$342,000.00
85	$24,000.00	$480,000.00	81	$18,000.00	$360,000.00
			82	$18,000.00	$378,000.00
			83	$18,000.00	$396,000.00
			84	$18,000.00	$414,000.00
			85	$18,000.00	$432,000.00

From the above table, it can be seen that the cumulative collection in Year 23 is $432,000 in case of Option 2 and in case of Option 1 the cumulative collection in Year 18 is $432,000.

Conclusion:

Hence the year in which higher payments catch up in total dollars received with the lower payment that begins earlier is determined.

To determine

(b)

Which alternative has the higher Present value.

Answer to Problem 101P

The alternative with the higher Present value is Option 1 i.e. Collect payments of $2,000 per month from age 66 − 85.

Explanation of Solution

Given information:

Option A: Receive $2,000 per month from age 66 − 85

Option B: Receive $1,500 per month from age 62 − 85.

Based on the above information, the following tables express the total cumulative dollars received.

Annual Receipts (Option 1) = $2,000 × 12 = $24,000

Annual Receipts (Option 2) = $1,500 × 12 = $18,000

Option 1: $2,000 from Age 66 - 85				Option 2: $1,500 from Age 62 - 85
Age	Annual Receipt	P.V.Factor @ 6%	Present Value of Amount	Age	Annual Receipt	P.V.Factor @ 6%	Present Value of Amount
1	$24,000.00	0.9434	$22,641.60	1	$18,000.00	0.9434	$16,981.20
2	$24,000.00	0.8900	$21,360.00	2	$18,000.00	0.8900	$16,020.00
3	$24,000.00	0.8396	$20,150.40	3	$18,000.00	0.8396	$15,112.80
4	$24,000.00	0.7921	$19,010.40	4	$18,000.00	0.7921	$14,257.80
5	$24,000.00	0.7473	$17,935.20	5	$18,000.00	0.7473	$13,451.40
6	$24,000.00	0.7050	$16,920.00	6	$18,000.00	0.7050	$12,690.00
7	$24,000.00	0.6651	$15,962.40	7	$18,000.00	0.6651	$11,971.80
8	$24,000.00	0.6274	$15,057.60	8	$18,000.00	0.6274	$11,293.20
9	$24,000.00	0.5919	$14,205.60	9	$18,000.00	0.5919	$10,654.20
10	$24,000.00	0.5584	$13,401.60	10	$18,000.00	0.5584	$10,051.20
11	$24,000.00	0.5268	$12,643.20	11	$18,000.00	0.5268	$9,482.40
12	$24,000.00	0.4970	$11,928.00	12	$18,000.00	0.4970	$8,946.00
13	$24,000.00	0.4688	$11,251.20	13	$18,000.00	0.4688	$8,438.40
14	$24,000.00	0.4423	$10,615.20	14	$18,000.00	0.4423	$7,961.40
15	$24,000.00	0.4173	$10,015.20	15	$18,000.00	0.4173	$7,511.40
16	$24,000.00	0.3936	$9,446.40	16	$18,000.00	0.3936	$7,084.80
17	$24,000.00	0.3714	$8,913.60	17	$18,000.00	0.3714	$6,685.20
18	$24,000.00	0.3503	$8,407.20	18	$18,000.00	0.3503	$6,305.40
19	$24,000.00	0.3305	$7,932.00	19	$18,000.00	0.3305	$5,949.00
20	$24,000.00	0.3118	$7,483.20	20	$18,000.00	0.3118	$5,612.40
				21	$18,000.00	0.2942	$5,295.60
				22	$18,000.00	0.2775	$4,995.00
				23	$18,000.00	0.2618	$4,712.40
				24	$18,000.00	0.2470	$4,446.00
	Net Present Value		$275,280.00				$225,909.00

Net present value is the difference of Sum of Present values of cash inflows and Sum of Present values of cash outflows. If the value is positive then the project may be accepted. While evaluation of two or more alternatives takes place, then the proposal with the higher net present value may be selected since it results in a greater cash inflow over the duration of the project.

In the given scenario, Present values are calculated by calculating the present values of cash inflows in the form of annual receipts.

Present value factor is calculated as 1/1.06 ^ N where N is the year.

From the above table, it can be seen that the net present value of Option 1 far exceeds the net present value of option 2.

Conclusion:

Hence the option with the higher net present value is determined.