Question

Assume you are offered a $20,000 annual payment, made quarterly (m =4). Payments begin in 10 years and last for 25 yrs. Payments grow at an annual rate of 4.0%. If you require 12% discounted quarterly (m=4) to make the investment, what is the maximum price you would be willing to pay today?

Answer 1

Annual payment = $20,000

Quarterly payment = Annual payment / 4

Quarterly payment = $20,000 / 4

Quarterly payment = $5000

Annual growth rate = 4%

Quarterly growth rate = Annual growth rate/ 4

Quarterly growth rate = 4% / 4

Quarterly growth rate = 1%

Annual required rate = 4%

Quarterly required rate = Annual growth rate/ 4

Quarterly required rate = 12% / 4

Quarterly required rate = 3%

For year 10.25

Dicount factor = 1 / (1 + (Required rate / Compounding frequency))^{periods * Compounding frequency}

Dicount factor = 1 / (1 + (12% / 4))^{(10.25 * 4)}

Dicount factor = 0.2976

Quarterly Dividend = Quarterly Dividend previous period * (1 + quarterly growth rate)

Quarterly Dividend = $5000 * (1 + (4% / 4))

Quarterly Dividend = $5050

Present value of Quarterly dividend = Quarterly Dividend * Discount factor

Present value of Quarterly dividend = $5050 * 02976

Present value of Quarterly dividend = $1503.02

Year	Required rate	Dicount factor	Dividend growth rate	Quarterly Dividend	Present value of Quarterly dividend
10	12%	0.3066	4%	$5,000.00	$1,532.78
10.25	12%	0.2976	4%	$5,050.00	$1,503.02
10.5	12%	0.2890	4%	$5,100.50	$1,473.84
10.75	12%	0.2805	4%	$5,151.51	$1,445.22
11	12%	0.2724	4%	$5,203.02	$1,417.16
11.25	12%	0.2644	4%	$5,255.05	$1,389.64
11.5	12%	0.2567	4%	$5,307.60	$1,362.65
11.75	12%	0.2493	4%	$5,360.68	$1,336.20
12	12%	0.2420	4%	$5,414.28	$1,310.25
12.25	12%	0.2350	4%	$5,468.43	$1,284.81
12.5	12%	0.2281	4%	$5,523.11	$1,259.86
12.75	12%	0.2215	4%	$5,578.34	$1,235.40
13	12%	0.2150	4%	$5,634.13	$1,211.41
13.25	12%	0.2088	4%	$5,690.47	$1,187.89
13.5	12%	0.2027	4%	$5,747.37	$1,164.82
13.75	12%	0.1968	4%	$5,804.84	$1,142.20
14	12%	0.1910	4%	$5,862.89	$1,120.02
14.25	12%	0.1855	4%	$5,921.52	$1,098.28
14.5	12%	0.1801	4%	$5,980.74	$1,076.95
14.75	12%	0.1748	4%	$6,040.54	$1,056.04
15	12%	0.1697	4%	$6,100.95	$1,035.53
15.25	12%	0.1648	4%	$6,161.96	$1,015.43
15.5	12%	0.1600	4%	$6,223.58	$995.71
15.75	12%	0.1553	4%	$6,285.82	$976.37
16	12%	0.1508	4%	$6,348.67	$957.42
16.25	12%	0.1464	4%	$6,412.16	$938.83
16.5	12%	0.1421	4%	$6,476.28	$920.60
16.75	12%	0.1380	4%	$6,541.04	$902.72
17	12%	0.1340	4%	$6,606.45	$885.19
17.25	12%	0.1301	4%	$6,672.52	$868.00
17.5	12%	0.1263	4%	$6,739.24	$851.15
17.75	12%	0.1226	4%	$6,806.64	$834.62
18	12%	0.1190	4%	$6,874.70	$818.42
18.25	12%	0.1156	4%	$6,943.45	$802.52
18.5	12%	0.1122	4%	$7,012.88	$786.94
18.75	12%	0.1089	4%	$7,083.01	$771.66
19	12%	0.1058	4%	$7,153.84	$756.68
19.25	12%	0.1027	4%	$7,225.38	$741.98
19.5	12%	0.0997	4%	$7,297.64	$727.58
19.75	12%	0.0968	4%	$7,370.61	$713.45
20	12%	0.0940	4%	$7,444.32	$699.60
20.25	12%	0.0912	4%	$7,518.76	$686.01
20.5	12%	0.0886	4%	$7,593.95	$672.69
20.75	12%	0.0860	4%	$7,669.89	$659.63
21	12%	0.0835	4%	$7,746.59	$646.82
21.25	12%	0.0811	4%	$7,824.05	$634.26
21.5	12%	0.0787	4%	$7,902.29	$621.94
21.75	12%	0.0764	4%	$7,981.32	$609.87
22	12%	0.0742	4%	$8,061.13	$598.03
22.25	12%	0.0720	4%	$8,141.74	$586.41
22.5	12%	0.0699	4%	$8,223.16	$575.03
22.75	12%	0.0679	4%	$8,305.39	$563.86
23	12%	0.0659	4%	$8,388.44	$552.91
23.25	12%	0.0640	4%	$8,472.33	$542.18
23.5	12%	0.0621	4%	$8,557.05	$531.65
23.75	12%	0.0603	4%	$8,642.62	$521.33
24	12%	0.0586	4%	$8,729.05	$511.20
24.25	12%	0.0569	4%	$8,816.34	$501.28
24.5	12%	0.0552	4%	$8,904.50	$491.54
24.75	12%	0.0536	4%	$8,993.55	$482.00
25	12%	0.0520	4%	$9,083.48	$472.64
25.25	12%	0.0505	4%	$9,174.32	$463.46
25.5	12%	0.0490	4%	$9,266.06	$454.46
25.75	12%	0.0476	4%	$9,358.72	$445.64
26	12%	0.0462	4%	$9,452.31	$436.99
26.25	12%	0.0449	4%	$9,546.83	$428.50
26.5	12%	0.0436	4%	$9,642.30	$420.18
26.75	12%	0.0423	4%	$9,738.72	$412.02
27	12%	0.0411	4%	$9,836.11	$404.02
27.25	12%	0.0399	4%	$9,934.47	$396.18
27.5	12%	0.0387	4%	$10,033.82	$388.48
27.75	12%	0.0376	4%	$10,134.16	$380.94
28	12%	0.0365	4%	$10,235.50	$373.54
28.25	12%	0.0354	4%	$10,337.85	$366.29
28.5	12%	0.0344	4%	$10,441.23	$359.18
28.75	12%	0.0334	4%	$10,545.64	$352.20
29	12%	0.0324	4%	$10,651.10	$345.36
29.25	12%	0.0315	4%	$10,757.61	$338.66
29.5	12%	0.0306	4%	$10,865.19	$332.08
29.75	12%	0.0297	4%	$10,973.84	$325.63
30	12%	0.0288	4%	$11,083.58	$319.31
30.25	12%	0.0280	4%	$11,194.41	$313.11
30.5	12%	0.0272	4%	$11,306.36	$307.03
30.75	12%	0.0264	4%	$11,419.42	$301.07
31	12%	0.0256	4%	$11,533.61	$295.22
31.25	12%	0.0249	4%	$11,648.95	$289.49
31.5	12%	0.0241	4%	$11,765.44	$283.87
31.75	12%	0.0234	4%	$11,883.09	$278.36
32	12%	0.0227	4%	$12,001.92	$272.95
32.25	12%	0.0221	4%	$12,121.94	$267.65
32.5	12%	0.0214	4%	$12,243.16	$262.45
32.75	12%	0.0208	4%	$12,365.60	$257.36
33	12%	0.0202	4%	$12,489.25	$252.36
33.25	12%	0.0196	4%	$12,614.14	$247.46
33.5	12%	0.0190	4%	$12,740.28	$242.66
33.75	12%	0.0185	4%	$12,867.69	$237.94
34	12%	0.0180	4%	$12,996.36	$233.32
34.25	12%	0.0174	4%	$13,126.33	$228.79
34.5	12%	0.0169	4%	$13,257.59	$224.35
34.75	12%	0.0164	4%	$13,390.17	$219.99
35	12%	0.0160	4%	$13,524.07	$215.72
				Total	$68,044.39

Value of Stock = $68,044.39